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Методическое указание

June 20, 2024

Fifth group of cations. Precipitation equilibrium.

1. The common and characteristic reactions of cations of V analytical group.

2. The systematic analysis of a cations mix of V analytical group.

3. The systematic analysis of a cations mix of I-V analytical groups.

5. Calculations of a constant of solubility product and solubility for electrolits of different types.

6. Fractional sedimentation.

Equilibrium constant of reaction of sedimentation – dissolution: thermodynamic, real, conditional.

Precipitation is the formation of a solid in a solution or inside another solid during a chemical reaction or by diffusion in a solid. When the reaction occurs in a liquid, the solid formed is called the precipitate. The chemical that causes the solid to form is called the precipitant. Without sufficient force of gravity (settling) to bring the solid particles together, the precipitate remains in suspension. After sedimentation, especially when using a centrifuge to press it into a compact mass, the precipitate may be referred to as a pellet. The precipitate-free liquid remaining above the solid is called the supernate or supernatant. Powders derived from precipitation have also historically been known as flowers.

Precipitation may occur if the concentration of a compound exceeds its solubility (such as when mixing solvents or changing their temperature). Precipitation may occur rapidly from a supersaturated solution.

In solids, precipitation occurs if the concentration of one solid is above the solubility limit in the host solid, due to e.g. rapid quenching or ion implantation, and the temperature is high enough that diffusion can lead to segregation into precipitates. Precipitation in solids is routinely used to synthesize nanoclusters.^[1]

An important stage of the precipitation process is the onset of nucleation. The creation of a hypothetical solid particle includes the formation of an interface, which requires some energy based on the relative surface energy of the solid and the solution. If this energy is not available, and no suitable nucleation surface is available, supersaturation occurs.

Chemical Precipitation

Using law of mass action to equations in heterogeneous system precipitate–saturated solution.

Heterogeneous equilibrium is equilibrium involving reactants and products in more than one phase. Example of the heterogeneous equilibrium is system consisting from saturated solution of ionic compound and its sediment (precipitate).

A precipitate is a solid formed by a reaction in solution. Precipitation reactions depend on one product’s not dissolving readily in water.

A saturated solution is a solution that is in equilibrium with respect to a given dissolved substance.

Solubility equilibrium. The solid crystalline phase is in dynamic equilibrium with ions in a saturated solution. The rate at which ions leave the crystals equals the rate at which ions return to the crystal.

Solubility of a substance in a solvent is the maximum amount that can be dissolved at equilibrium at a given temperature. The solubility of one substance in another is determined by two factors. One of these is the natural inclination toward disorder, reflected in the tendency of substances to mix. The other factor is the strength of the forces of attraction between species (molecules and ions). These forces, for example, may favour the unmixed solute and solvent, whereas the natural tendency to mix favours the solution. In such a case, the balance between these two factors determines the solubility of the solute.

Definition the solubility of common ionic substances:

– soluble – a compound dissolves to the extent at 1 gram or more per 100 ml;

– slightly soluble – a compound is less than 1 gram, but more than 0,1 gram per 100 ml;

– insoluble – a compound is less than 0,1 gram per 100 ml.

There are three types of solutions:

1. Real solutions:

– molecular solutions (depends on London forces);

– ionic solutions (depends on ion-dipole forces).

2. Colloid systems.

Molecular solutions

If the process of dissolving one molecular substance in another were nothing more than the simple mixing of molecules, we would not expect a limit of solubility. Substance may be miscible even when the intermolecular forces are not negligible. The different intermolecular attractions are about the same strength, so there are no favoured attractions. Therefore the tendency of molecules to mix results in miscibility of the substances.

Ionic solutions

Ionic substances differ markedly in their solubility in water. In most cases, their differences in solubility can be explained in terms of the different energies of attraction between ions in the crystal and between ions and water.

The energy of attraction between an ion and a water molecule is due to an ion-dipole force. The attraction of ions for water molecules is called hydrolysis. Hydration of ions favours the dissolving of an ionic solid in water. If the hydration of ions were the only factor in the solution process, we would expect all ionic solids to be soluble in water.

The ions in a crystal, however, are very strongly attracted to one another. Therefore, the solubility of an ionic solid depends not only on the energy of hydration of ions but also on lattice energy, the energy holding ions together in the crystal lattice. Lattice energy works against the solution process, so an ionic solid with relatively large lattice energy is usually insoluble.

Colloids

Colloids are a dispersion of particles of one substance (the dispersed phase) throughout another substance of solution (the continuous phase).

The solubility product constant

When an ionic compound is dissolved in water, it usually goes into solution as the ions. When an express of the ionic compound is mixed with water, equilibrium occurs between the solid compound and the ions in the saturated solution:

Kt_xAn_y « xKt⁺ + yAn^–. The equilibrium constant for this solubility process can be written:

K_c = .

However, because the concentration of the solid remain constant (in heterogeneous systems), we normally combine its concentration with K_c to give the equilibrium constant K_s, which is called the solubility product constant:

K_s = K_c×[Kt_xAn_y] = [Kt⁺]^x×[An^–]^y

In general, the solubility product constant, K_s, is the equilibrium constant for the solubility equilibrium of slightly soluble (or nearly insoluble) ionic compounds. It equals the product of the equilibrium concentrations of the ions in the compound, each concentration raised to a power equal to the number of such ions in the formula of the compound.

At equilibrium in saturated solution of slightly soluble compound at given temperature and pressure the value of Ks is constant and not depend on ions concentration. The solubility product constant is thermodynamic constant and depends on temperature and ions activity (ionic strength).

The reaction quotient, Q, is an expression that has the same form as the equilibrium constant expression K_s, but whole concentration values are not necessarily those at equilibrium. Though the concentrations of the products are starting values:

Q = [Kt⁺]×[An^–]

Here Q for a solubility reaction is often called the ion product, because it is product of ion concentrations in a solution, each concentration raised to a power equal to the number of ions in the formula of the ionic compound.

– Precipitation is expressed to occur if the ion product Q for a solubility reaction is greater than K_s: Q > K_s.

– If the ion product Q is less than K_s, precipitation will not occur (the solution is unsaturated with respect to the ionic compound): Q < K_s.

– If the ion product Q equal K_s, the reaction is at equilibrium (the solution is saturated with the ionic compound): Q = K_s.

Calculation of solubility

Solubility, S, is the molar concentration of compound in saturated solution.

I. Saturated solution of slightly soluble ionic compound: S = .

II. Saturated solution of good soluble ionic compound.

This type of solutions not used in analytical practice. Such solutions are very concentrated and have large ionic strength. Components of these solutions (ion, molecules) can associate and form various polymers and colloids.

III. Saturated solution of slightly soluble compound with very small solubility:

– the substance have limited solubility but create ion pairs and various molecular forms. The ionic strength of this solution is high and solubility depends on common concentration of all molecular and ionic forms;

– slightly soluble compound takes part in protolytic reaction with water with the pH change. The solubility is affected by pH. If the anion is the conjugate base of a weak acid, it reacts with H⁺ ion. Therefore, the solubility slightly soluble compound to be more in acid solution (low pH) than it is in pure water.

In sour environment solubility of slightly soluble compounds is more than more is its K_s and more is the hydrogen ion concentration:

S_KtAn = [Kt⁺] = ;

when [H⁺] = K_a, S_KtAn =.

Factors which influence to solubility

1. Temperature. Solubility for most of substances is endothermic process. Increase temperature occurs decrease solubility. But crystal compounds at various temperature form hydrates another structure (composition). Hydrates formation may be exothermic reaction.

2. Ionic strength of solution.

Increasing of ionic strength causes decreasing of ions activity and, accordingly, K_s will increase. Because, solubility will increase. An example of it is salting effect.

Salting effect is increase the solubility of slightly soluble compounds in presence of strong electrolytes, which not have common ions with precipitate and not react with precipitate ions.

3. Common-ion electrolytes. Completeness of precipitation.

The importance of the solubility product constant becomes apparent when we consider the solubility of one salt in the solution of another having the same cation or anion. The effect of the common ion is to make slightly soluble salt less soluble than it would be in pure water. This decrease in solubility can be explained in terms of LeChatelier’s principle. It is example of the common-ion effect.

Decrease of solubility of slightly soluble compounds in presence of electrolyte with common ions called common-ion effect.

But solubility of slightly soluble compounds decrease to moment when ionic strength of solution will begin to influence to solubility.

The ion is completely precipitated when its residual concentration (C_min) is less than 1×10^-6 M (C_min < 1×10^-6 M). Amount of precipitant must be more at 20-50 % it is necessary to stoichiometry equation.

If in solution are ions, which form slightly soluble compounds with precipitant, the sequence of its precipitation determines (depends on) K_s value.

Fractional precipitation is the technique of separating two or more ions from a solution by adding a reactant that precipitates first one ion, than another, and so forth.

4. The pH value (see above).

5. Complex compound formation.

Solubility increases with increasing concentration of ligand, complex compound stability and K_s value.

6. Redox process.

Redox reaction shift on equilibrium in heterogeneous system and change solubility of slightly soluble compounds.

Using precipitation and solubility processes in analysis

1. Reaction of ions detection.

2. Fractional precipitation.

3. Dividing ions on analytical groups in systematic analysis with group reagents.

4. Precipitation with controlled pH value.

5. Selective dissolving:

SrC₂O₄¯ + CH₃COOH ® Sr(CH₃COO)₂ + H₂C₂O₄

CaC₂O₄¯ + CH₃COOH ® not dissolve

6. Conversion (transformation) one slightly soluble compounds to another:

CaSO₄¯ + Na₂CO₃ « CaCO₃¯ + Na₂SO₄

Colloid systems, their importance for chemical analysis

Signs of colloids formation on chemical reaction

For analytical purposes often carry out reactions of sulphides and hydroxides precipitation. In these reactions may form colloids and may be observed next phenomenon:

1) precipitates pass through the filters;

2) slightly soluble compounds are soluble in water more than determined by K_s;

3) substance not forms precipitate even with great surplus of precipitant.

Colloids are a dispersion of particles of one substance (the dispersed phase) throughout another substance of solution (the continuous phase). Colloids differ from true solutions in that the dispersed particles are larger thaormal molecules, thought they are too small to be seen with a microscope. The particles are from about 1×10^-9 m to about 2×10^-7 m in size.

Colloids are characterised accordingly to the state (solid, liquid, or gas) of the dispersed phase and the state continuous phase: aerosol, foam, emulsion, sol, gel:

– fog and smoke are aerosols, which are liquid droplets or solid particles dispersed throughout a gas;

– an emulsion consist of liquid droplets dispersed throughout another liquid;

– a sol consist of solid particles dispersed in liquid.

Colloids in which the continuous phase is water also divided into two major classes:

I. Hydrophilic colloid is a colloid in which there is a strong attraction between the dispersed phase and the continuous phase (water) – for example, H₂SiO₃, Fe(OH)₃. Many such colloids consist of macromolecules (very large molecules) dispersed in water. Except for the large size of the dispersed molecules, these are like normal solution.

II. Hydrophobic colloid is a colloid in which there is a lack of attraction between the dispersed phase and the continuous phase (water) – for example, AgI, As₂S₃. Hydrophobic colloids are basically unstable. Given different time, the dispersed phase comes out of solution by aggregation into larger particles. In this behaviour, they are quite unlike true solutions and hydrophilic colloids.

Hydrophobic sol (solid phase dispersed in water) are often formed when a solid crystallises rapidly from a chemical reaction or a supersaturated solution. When crystallisation occurs rapidly, many centres of crystallisation (called nuclei) are formed at once. Ions are attracted to these nuclei and very small crystals are formed. These small crystals are prevented from setting out by random thermal motion of the solvent molecules, which continue to buffer them.

These very small crystals aggregate into large crystals because the aggregation would bring ions of opposite charge into contact. However, sol formation appears to happen when, for some reason, each of the small crystals gets a preponderance of the kind of charge on its surface.

For example: iron (III) hydroxide forms a colloid because an excess of iron (III) ion (Fe⁺³) is present on the surface, giving each crystal an excess of positive charge. These positive charged crystals repel one another, so aggregation to larger particles is prevent. A positively charged colloidal particle of iron (III) hydroxide gathers a layer of anions around it. The thickness of this layer is determined by the charge of the anions – the greater magnitude of the negative charge; the more compact the layer of charge:

FeCl₃ + 3NaOH ® {Fe(OH)₃×Fe⁺³×Cl^–}¯ + 3NaCl.

When molecules that have both a hydrophobic and a hydrophilic end are dispersed in water, they associate or aggregate to form colloidal-size particles, or micelles.

A micelle is a colloidal-size particle formed in water by the association of molecules that each has a hydrophobic end and hydrophilic end. The hydrophobic ends point inward toward one another, while the hydrophilic ends are on the outside of the micelle facing the water. A colloid in which the dispersed phase consists of micelle is called an association colloid.

Scheme of micelle structure:

KI + AgNO₃ ® {m[AgI]×nAg⁺× (n-x)NO₃^–}^x-×xNO₃^– + KNO₃ (surplus of AgNO₃)

Structure of Al(OH)₃ micelle in:

– acidic solution {m[Al(OH)₃] ×nH₂O× (n-x)Al⁺³}^x-×3xCl^–

– basic solution {m[Al(OH)₃] ×nH₂O× (n-x)AlO₂^–}^x-×xNa⁺

Coagulation is the process by which a colloid is made to come out solution by aggregation. Coagulation causes when

– heat the colloid or

– add to colloid solution strong electrolyte with great charge of ions (Schulze-Ghardi rule).

Example of hydrophilic colloid coagulation:

1. Heating accelerates the random thermal moving of the colloid particles. The micelles get in touch one to another frequently and can stick together. These cause the colloid coagulation.

2. An iron (III) hydroxide sol can be made to aggregate by the addition of an ionic solution, particularly if the solution contains anions with multiple charge (such as phosphate PO₄^3–). Phosphate ion gathers more closely to the positively charged colloidal particles than chloride ions. If the ion layer is gathered close to the colloidal particle, the overall charge is effectively neutralised. In that case, two colloidal particles can approach close enough to aggregate.

Washing the precipitate by water removes the electrolyte-coagulant and restores precipitate in colloid. Transition the precipitate into colloid solution called peptisation. Washing of precipitates occurs removing of ions layer around colloid particles. For peptisation prevention precipitates must be washed by suitable electrolyte solution.

Using colloids in analysis

1. All colloids (sols) are inclined to adsorption of another substance from solutions. On this phenomenon based techniques of:

– detection reactions. Some colloids (hydroxides, in particular) are colourless and not visible. To reaction mixture add the coloured substance, which would be adsorbed on colloids particles:

2NaOH + I₂ ® NaOI + NaI + H₂O (iodine solution becomes colourless)

MgCl₂ + 2NaOH ® Mg(OH)₂ + 2NaCl (colourless colloid)

Mg(OH)₂ + NaOI + NaI + H₂O ® Mg(OH)₂×I₂ + 2NaOH

(adsorption of iodine on brown colloid particles)

– and common precipitation with concentration of small amounts of detected substances:

ZnCl₂ + H₂S ® ZnS¯ + 2HCl ZnS is collector (adsorbent)

MnCl₂ + H₂S ® MnS¯ + 2HCl concentration of Mn⁺² ions on collector surface

2. Identification of ions:

H₃PO₄ + 12(NH₄)₃MoO₄ + 21HNO₃ ®

® (NH₄)₃PO₄×12MoO₃×2H₂O¯ + 21NH₄NO₃ + 10 H₂O

colloid with navy colour

2Na₃AsO₄ + 5Na₂S + 16H₂O ® As₂S₅¯ + 16NaCl + 8H₂O

colloid with yellow colour

Prevention of colloids formation

For prevention of colloids formation on analytical reactions is necessary:

1) to add a small surplus of precipitant. It promotes the little solubility of precipitant and prevents to colloid formation;

2) to carry out precipitation process at heating;

3) for precipitation and washing of precipitates add electrolytes;

4) do not dilute with water solutions over precipitate (sediment).

Applications

Precipitation reactions can be used for making pigments, removing salts from water in water treatment, and in classical qualitative inorganic analysis.

Precipitation is also useful to isolate the products of a reaction during workup. Ideally, the product of the reaction is insoluble in the reaction solvent. Thus, it precipitates as it is formed, preferably forming pure crystals. An example of this would be the synthesis of porphyrins in refluxing propionic acid. By cooling the reaction mixture to room temperature, crystals of the porphyrin precipitate, and are collected by filtration:

Precipitation may also occur when an antisolvent (a solvent in which the product is insoluble) is added, drastically reducing the solubility of the desired product. Thereafter, the precipitate may easily be separated by filtration, decanting, or centrifugation). An example would be the synthesis of chromic tetraphenylporphyrin chloride: water is added to the DMF reaction solution, and the product precipitates. Precipitation is also useful in purifying products: crude bmim-Cl is taken up in acetonitrile, and dropped into ethyl acetate, where it precipitates. Another important application of an antisolvent is in ethanol precipitation of DNA.

Solubility equilibrium is a type of dynamic equilibrium. It exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation or with chemical reaction with another constituent of the solvent, such as acid or alkali. Each type of equilibrium is characterized by a temperature-dependent equilibrium constant. Solubility equilibria are important in pharmaceutical, environmental and many other scenarios.

A solubility equilibrium exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The equilibrium is an example of dynamic equilibrium in that some individual molecules migrate between the solid and solution phases such that the rates of dissolution and precipitation are equal to one another. When equilibrium is established, the solution is said to be saturated. The concentration of the solute in a saturated solution is known as the solubility. Units of solubility may be molar (mol dm⁻³) or expressed as mass per unit volume, such as μg ml⁻¹. Solubility is temperature dependent. A solution containing a higher concentration of solute than the solubility is said to be supersaturated. A supersaturated solution may be induced to come to equilibrium by the addition of a “seed” which may be a tiny crystal of the solute, or a tiny solid particle, which initiates precipitation.

There are three main types of solubility equilibria.

1. Simple dissolution.

2. Dissolution with dissociation. This is characteristic of salts. The equilibrium constant is known in this case as a solubility product.

3. Dissolution with reaction. This is characteristic of the dissolution of weak acids or weak bases in aqueous media of varying pH.

In each case an equilibrium constant can be specified as a quotient of activities. This equilibrium constant is dimensionless as activity is a dimensionless quantity. However, use of activities is very inconvenient, so the equilibrium constant is usually divided by the quotient of activity coefficients, to become a quotient of concentrations. See equilibrium chemistry#Equilibrium constant for details. Moreover, the concentration of solvent is usually taken to be constant and so is also subsumed into the equilibrium constant. For these reasons, the constant for a solubility equilibrium has dimensions related to the scale on which concentrations are measured. Solubility constants defined in terms of concentrations are not only temperature dependent, but also may depend on solvent composition when the solvent contains also species other than those derived from the solute.

Phase effect

Equilibria are defined for specific crystal phases. Therefore, the solubility product is expected to be different depending on the phase of the solid. For example, aragonite and calcite will have different solubility products even though they have both the same chemical identity (calcium carbonate). Nevertheless, under given conditions, most likely only one phase is thermodynamically stable and therefore this phase enters a true equilibrium.

Particle size effect

The thermodynamic solubility constant is defined for large monocrystals. Solubility will increase with decreasing size of solute particle (or droplet) because of the additional surface energy. This effect is generally small unless particles become very small, typically smaller than 1 μm. The effect of the particle size on solubility constant can be quantified as follows:

$\log(^*K_{A}) = \log(^*K_{A \to 0}) + \frac{\gamma A_m} {3.454RT}$

where $^*K_{A}$ is the solubility constant for the solute particles with the molar surface area A, $^*K_{A \to 0}$ is the solubility constant for substance with molar surface area tending to zero (i.e., when the particles are large), γ is the surface tension of the solute particle in the solvent, A_m is the molar surface area of the solute (in m²/mol), R is the universal gas constant, and T is the absolute temperature.

Salt effect

The salt effect refers to the fact that the presence of a salt which has no ion in common with the solute, has an effect on the ionic strength of the solution and hence on activity coefficients, so that the equilibrium constant, expressed as a concentration quotient, changes.

Temperature effect

Solubility is sensitive to changes in temperature. For example, sugar is more soluble in hot water than cool water. It occurs because solubility constants, like other types of equilibrium constants, are functions of temperature. In accordance with Le Chatelier’s Principle, when the dissolution process is endothermic (heat is absorbed), solubility increases with rising temperature, but when the process is exothermic (heat is released) solubility decreases with rising temperature. The temperature effect is the basis for the process of recrystallization, which can be used to purify a chemical compound.

Sodium sulfate shows increasing solubility with temperature below about 32.4 °C, but a decreasing solubility at higher temperature. This is because the solid phase is the decahydrate, Na₂SO₄.10H₂O, below the transition temperature but a different hydrate above that temperature.

Pressure effect

For condensed phases (solids and liquids), the pressure dependence of solubility is typically weak and usually neglected in practice. Assuming an ideal solution, the dependence can be quantified as:

where the index i iterates the components, N_i is the mole fraction of the i^th component in the solution, P is the pressure, the index T refers to constant temperature, V_i,aq is the partial molar volume of the i^th component in the solution, V_i,cr is the partial molar volume of the i^th component in the dissolving solid, and R is the universal gas constant.

The pressure dependence of solubility does occasionally have practical significance. For example, precipitation fouling of oil fields and wells by calcium sulfate (which decreases its solubility with decreasing pressure) can result in decreased productivity with time.

Simple dissolution

Dissolution of an organic solid can be described as an equilibrium between the substance in its solid and dissolved forms. For example, when sucrose (table sugar) forms a saturated solution

$\mathrm{{C}_{12}{H}_{22}{O}_{11}(s)} \rightleftharpoons \mathrm{{C}_{12}{H}_{22}{O}_{11}(aq)}$ .

An equilibrium expression for this reaction can be written, as for any chemical reaction (products over reactants):

$K^\ominus = \frac{\left\{\mathrm{{C}_{12}{H}_{22}{O}_{11}}(aq)\right\}}{ \left \{\mathrm{{C}_{12}{H}_{22}{O}_{11}}(s)\right\}}$

where K is called the thermodynamic solubility constant. The braces indicate activity. The activity of a pure solid is, by definition, unity. Therefore

$K^\ominus = \left\{\mathrm{{C}_{12}{H}_{22}{O}_{11}}(aq)\right\}$

The activity of a substance, A, in solution can be expressed as the product of the concentration, [A], and an activity coefficient, γ. When K is divided by γ the solubility constant, K_s,

$K_s = \left[\mathrm{{C}_{12}{H}_{22}{O}_{11}}(aq)\right]\,$

is obtained. This is equivalent to defining the standard state as the saturated solution so that the activity coefficient is equal to one. The solubility constant is a true constant only if the activity coefficient is not affected by the presence of any other solutes that may be present. The unit of the solubility constant is the same as the unit of the concentration of the solute. For sucrose K = 1.971 mol dm⁻³ at 25 °C. This shows that the solubility of sucrose at 25 °C is nearly 2 mol dm⁻³ (540 g/l). Sucrose is unusual in that it does not easily form a supersaturated solution at higher concentrations, as do most other carbohydrates.

Dissolution with dissociation

Ionic compounds normally dissociate into their constituent ions when they dissolve in water. For example, for calcium sulfate:

$\mathrm{CaSO}_4(s) \rightleftharpoons \mbox{Ca}^{2+}(aq) + \mbox{SO}_4^{2-}(aq)\,$

As for the previous example, the equilibrium expression is:

$K^\ominus = \frac{\left\{\mbox{Ca} ^{2+}(aq)\right\}\left\{\mbox{SO}_4^{2-}(aq)\right\}}{ \left\{\mbox{CaSO}_4(s)\right\}} =\left\{\mbox{Ca} ^{2+}(aq)\right\}\left\{\mbox{SO}_4^{2-}(aq)\right\}$

where K is the thermodynamic equilibrium constant and braces indicate activity. The activity of a pure solid is, by definition, equal to one.

When the solubility of the salt is very low the activity coefficients of the ions in solution are nearly equal to one. By setting them to be actually equal to one this expression reduces to the solubility product expression:

$K_{\mathrm{sp}} = \left[\mbox{Ca}^{2+}(aq)\right]\left[\mbox{SO}_4^{2-}(aq)\right].\,$

The solubility product for a general binary compound A_pB_q is given by

A_pB_q pA^q+ + qB^p-

K_sp = [A]^p[B]^q (electrical charges omitted for simplicity of notation).

When the product dissociates the concentration of B is equal to q/p times the concentration of A.

[B] = q/p [A]

Therefore

K_sp = [A]^p (q/p)^q [A]^q= (q/p)^q × [A]^p+q

$[A] = \sqrt[p+q]{K_{\mathrm{sp}} \over {(q/p)^q}}$

The solubility, S is 1/p [A]. One may incorporate 1/p and insert it under the root to obtain

$S = {[A] \over p} = {[B] \over q} = \sqrt[p+q]{K_{\mathrm{sp}} \over {(q/p)^q} p^{p+q}} = \sqrt[p+q]{K_{\mathrm{sp}} \over {q^q} p^p}$

Examples

CaSO₄: p=1, q=1, $S=\sqrt{K_{sp}}$

Na₂SO₄: p=2, q=1, $S=\sqrt[3]{K_{sp}\over4}$

Al₂(SO₄)₃: p=2, q=3, $S=\sqrt[5]{K_{sp}\over 108}$

Solubility products are often expressed in logarithmic form. Thus, for calcium sulfate, K_sp = 4.93×10⁻⁵, log K_sp = -4.32. The smaller the value, or the more negative the log value, the lower the solubility.

Some salts are not fully dissociated in solution. Examples include MgSO₄, famously discovered by Manfred Eigen to be present in seawater as both an inner sphere complex and an outer sphere complex.^[6] The solubility of such salts is calculated by the method outlined in dissolution with reaction.

Hydroxides

For hydroxides solubility products are often given in a modified form, K*_sp, using hydrogen ion concentration in place of hydroxide ion concentration.^[7] The two concentrations are related by the self-ionization constant for water, K_w.

K_w=[H⁺][OH^–]

For example,

Ca(OH)₂ Ca²⁺ + 2 OH^–

K_sp = [Ca²⁺][OH^–]² = [Ca²⁺]K_w²[H⁺]^-2

K*_sp = K_sp/K_w² = [Ca²⁺][H⁺]^-2

log K_sp for Ca(OH)₂ is about -5 at ambient temperatures;

log K*_sp = -5 + 2 × 14 = 23, approximately.

Common ion effect

The common-ion effect is the effect of decreasing the solubility of one salt, when another salt, which has an ion in common with it, is also present. For example, the solubility of silver chloride, AgCl, is lowered when sodium chloride, a source of the common ion chloride, is added to a suspension of AgCl in water.

AgCl(s) Ag⁺(aq) + Cl^–(aq); K_sp = [Ag⁺][Cl^–]

The solubility, S, in the absence of a common ion can be calculated as follows. The concentrations [Ag⁺] and [Cl^–] are equal because one mole of AgCl dissociates into one mole of Ag⁺ and one mole of Cl^–. Let the concentration of [Ag⁺](aq) be denoted by x.

K_sp = x²; S = x = $\sqrt{K_{sp}}$

K_sp for AgCl is equal to 1.77×10⁻¹⁰ mol²dm⁻⁶ at 25 °C, so the solubility is 1.33×10⁻⁵ mol dm⁻³.

Now suppose that sodium chloride is also present, at a concentration of 0.01 mol dm⁻³. The solubility, ignoring any possible effect of the sodium ions, is now calculated by

K_sp = x(0.01 + x)

This is a quadratic equation in x, which is also equal to the solubility.

x² + 0.01 x – K_sp = 0

In the case of silver chloride x² is very much smaller than 0.01 x, so this term can be ignored. Therefore

S = x = K_sp / 0.01 = 1.77×10⁻⁸ mol dm^-3,

a considerable reduction. In gravimetric analysis for silver, the reduction in solubility due to the common ion effect is used to ensure “complete” precipitation of AgCl.

Solubility

The ability of one compound to dissolve in another compound is called solubility. When a liquid can completely dissolve in another liquid the two liquids are miscible. Two substances that caever mix to form a solution are called immiscible.

All solutions have a positive entropy of mixing. The interactions between different molecules or ions may be energetically favored or not. If interactions are unfavorable, then the free energy decreases with increasing solute concentration. At some point the energy loss outweighs the entropy gain, and no more solute particles can be dissolved; the solution is said to be saturated. However, the point at which a solution can become saturated can change significantly with different environmental factors, such as temperature, pressure, and contamination. For some solute-solvent combinations a supersaturated solution can be prepared by raising the solubility (for example by increasing the temperature) to dissolve more solute, and then lowering it (for example by cooling).

Usually, the greater the temperature of the solvent, the more of a given solid solute it can dissolve. However, most gases and some compounds exhibit solubilities that decrease with increased temperature. Such behavior is a result of an exothermic enthalpy of solution. Some surfactants exhibit this behaviour. The solubility of liquids in liquids is generally less temperature-sensitive than that of solids or gases.

Dissolution with reaction

When a concentrated solution of ammonia is added to a suspension of silver chloride dissolution occurs because a complex of Ag⁺ is formed

A typical reaction with dissolution involves a weak base, B, dissolving in an acidic aqueous solution.

B(s) + H⁺ (aq) BH⁺ (aq)

This reaction is very important for pharmaceutical products. Dissolution of weak acids in alkaline media is similarly important.

H_nA(s) + OH^–(aq) H_n-1A^–(aq) + H₂O

The uncharged molecule usually has lower solubility than the ionic form, so solubility depends on pH and the acid dissociation constant of the solute. The term “intrinsic solubility” is used to describe the solubility of the un-ionized form in the absence of acid or alkali.

Leaching of aluminium salts from rocks and soil by acid rain is another example of dissolution with reaction: alumino-silicates are bases which react with the acid to form soluble species, such as Al³⁺(aq).

Formation of a chemical complex may also change solubility. A well-known example, is the addition of a concentrated solution of ammonia to a suspension of silver chloride, in which dissolution is favoured by the formation of an ammine complex.

AgCl(s) +2 NH₃(aq) [Ag(NH₃)₂]⁺ (aq) + Cl^– (aq)

When a concentrated solution of ammonia is added to a suspension of silver chloride dissolution occurs because a complex of Ag⁺ is formed

Another example involves the addition of water softeners to washing powders to inhibit the precipitation of salts of magnesium and calcium ions, which are present in hard water, by forming complexes with them.

The calculation of solubility in these cases requires two or more simultaneous equilibria to be considered. For example,

Intrinsic solubility equilibrium	B(s) B(aq): K_s = [B(aq)]
Acid-base equilibrium	B(aq) + H⁺(aq) BH⁺(aq) K_a = [B(aq)][H⁺(aq)]/[BH⁺(aq)]

Dimensionless quantity

In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a “pure” number, and as such always has a dimension of 1.^[1] Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and in everyday life (such as in counting). Numerous well-known quantities, such as π, e, and φ, are dimensionless. By contrast, non-dimensionless quantities are measured in units of length, area, time, etc.

Dimensionless quantities are often defined as products or ratios of quantities that are not dimensionless, but whose dimensions cancel out when their powers are multiplied. This is the case, for instance, with the engineering strain, a measure of deformation. It is defined as change in length over initial length but, since these quantities both have dimensions L (length), the result is a dimensionless quantity.

Properties

Even though a dimensionless quantity has no physical dimension associated with it, it can still have dimensionless units. To show the quantity being measured (for example mass fraction or mole fraction), it is sometimes helpful to use the same units in both the numerator and denominator (kg/kg or mol/mol). The quantity may also be given as a ratio of two different units that have the same dimension (for instance, light years over meters). This may be the case when calculating slopes in graphs, or when making unit conversions. Such notation does not indicate the presence of physical dimensions, and is purely a notational convention. Other common dimensionless units are % (= 0.01), ‰ (= 0.001), ppm (= 10⁻⁶), ppb (= 10⁻⁹), ppt (= 10⁻¹²) and angle units (degrees, radians, grad). Units of number such as the dozen and the gross are also dimensionless.

The ratio of two quantities with the same dimensions is dimensionless, and has the same value regardless of the units used to calculate them. For instance, if body A exerts a force of magnitude F on body B, and B exerts a force of magnitude f on A, then the ratio F/f is always equal to 1, regardless of the actual units used to measure F and f. This is a fundamental property of dimensionless proportions and follows from the assumption that the laws of physics are independent of the system of units used in their expression. In this case, if the ratio F/f was not always equal to 1, but changed if we switched from SI to CGS, that would mean that Newton’s Third Law‘s truth or falsity would depend on the system of units used, which would contradict this fundamental hypothesis. This assumption that the laws of physics are not contingent upon a specific unit system is the basis for the Buckingham π theorem. A statement of this theorem is that any physical law can be expressed as an identity involving only dimensionless combinations (ratios or products) of the variables linked by the law (e. g., pressure and volume are linked by Boyle’s Law – they are inversely proportional). If the dimensionless combinations’ values changed with the systems of units, then the equation would not be an identity, and Buckingham’s theorem would not hold.

Buckingham π theorem

Another consequence of the Buckingham π theorem of dimensional analysis is that the functional dependence between a certain number (say, n) of variables can be reduced by the number (say, k) of independent dimensions occurring in those variables to give a set of p = n − k independent, dimensionless quantities. For the purposes of the experimenter, different systems that share the same description by dimensionless quantity are equivalent.

Example:

The power consumption of a stirrer with a given shape is a function of the density and the viscosity of the fluid to be stirred, the size of the stirrer given by its diameter, and the speed of the stirrer. Therefore, we have n = 5 variables representing our example.

Those n = 5 variables are built up from k = 3 dimensions:

Length: L (m)

Time: T (s)

Mass: M (kg)

According to the π-theorem, the n = 5 variables can be reduced by the k = 3 dimensions to form p = n − k = 5 − 3 = 2 independent dimensionless numbers, which are, in case of the stirrer:

Reynolds number (a dimensionless number describing the fluid flow regime).

Power number (describing the stirrer and also involves the density of the fluid).

Equilibrium chemistry is a concerned with systems in chemical equilibrium. The unifying principle is that the free energy of a system at equilibrium is the minimum possible, so that the slope of the free energy with respect to the reaction coordinate is zero. This principle, applied to mixtures at equilibrium provides a definition of an equilibrium constant. Applications include acid-base, host-guest, metal-complex, solubility, partition, chromatography and redox equilibria.

Thermodynamic equilibrium

Main articles: dynamic equilibrium and thermodynamic equilibrium

A chemical system is said to be in equilibrium when the quantities of the chemical entities involved do not and cannot change in time without the application of an external influence. In this sense a system in chemical equilibrium is in a stable state. The system at chemical equilibrium will be at a constant temperature, pressure (or volume) and composition. It will be insulated from exchange of heat with the surroundings, that is, it is a closed system. A change of temperature, pressure (or volume) constitutes an external influence and the equilibrium quantities will change as a result of such a change. If there is a possibility that the composition might change, but the rate of change is negligibly slow, the system is said to be in a metastable state. The equation of chemical equilibrium can be expressed symbolically as

reactant(s) product(s)

The sign means “are in equilibrium with”. This definition refers to macroscopic properties. Changes do occur at the microscopic level of atoms and molecules, but to such a minute extent that they are not measurable and in a balanced way so that the macroscopic quantities do not change. Chemical equilibrium is a dynamic state in which forward and backward reactions proceed at such rates that the macroscopic composition of the mixture is constant. Thus, equilibrium sign symbolizes the fact that reactions occur in both forward $\rightharpoonup$ and backward $\leftharpoondown$ directions.

A steady state, on the other hand, is not necessarily an equilibrium state in the chemical sense. For example, in a radioactive decay chain the concentrations of intermediate isotopes are constant because the rate of production is equal to the rate of decay. It is not a chemical equilibrium because the decay process occurs in one direction only.

Thermodynamic equilibrium is characterized by the free energy for the whole (closed) system being a minimum. For systems at constant volume the Helmholtz free energy is minimum and for systems at constant pressure the Gibbs free energy is minimum. Thus a metastable state is one for which the free energy change between reactants and products is not minimal even though the composition does not change in time.

The existence of this minimum is due to the free energy of mixing of reactants and products being always negative. For ideal solutions the enthalpy of mixing is zero, so the minimum exists because the entropy of mixing is always positive. The slope of the reaction free energy, δG_r with respect to the reaction coordinate, ξ, is zero when the free energy is at its minimum value.

$\delta G_r=\left(\frac{\partial G}{\partial \xi }\right)_{T,P}; \delta G_r(Eq)=0$

Equilibrium constant

Main articles: Equilibrium constant, Acid dissociation constant, and Stability constants of complexes

Chemical potential is the partial molar free energy. The potential, μ_i, of the ith species in a chemical reaction is the partial derivative of the free energy with respect to the number of moles of that species, N_i

$\mu_i=\left(\frac{\partial G}{\partial N_i}\right)_{T,P}$

A general chemical equilibrium can be written as

$\sum_j n_j Reactant_j\rightleftharpoons \sum_k m_k Product_k$

n_j are the stoichiometric coefficients of the reactants in the equilibrium equation, and m_j are the coefficients of the products. The value of δG_r for these reactions is a function of the chemical potentials of all the species.

$\delta G_r = \sum_k m_k \mu_k \, - \sum_j n_j \mu_j$

The chemical potential, μ_i, of the ith species can be calculated in terms of its activity, a_i.

$\mu_i = \mu_i^\ominus + RT \ln a_i$

μ_i is the standard chemical potential of the species, R is the gas constant and T is the temperature. Setting the sum for the reactants j to be equal to the sum for the products, k, so that δG_r (Eq) = 0

$\sum_j n_j(\mu_j^\ominus +RT\ln a_j)=\sum_k m_k(\mu_k^\ominus +RT\ln a_k)$

Rearranging the terms,

$\sum_k m_k\mu_k^\ominus-\sum_j n_j\mu_j^\ominus =-RT \left(\sum_k \ln {a_k}^{m_k}-\sum_j \ln {a_j}^{n_j}\right)$

$\Delta G^\ominus = -RT ln K.$

This relates the standard Gibbs free energy change, ΔG to an equilibrium constant, K, the reaction quotient of activity values at equilibrium.

$\Delta G^\ominus = \sum_k m_k\mu_k^\ominus-\sum_j n_j\mu_j^\ominus$

$\ln K= \sum_k \ln {a_k}^{m_k}-\sum_j \ln {a_j}^{n_j}; K=\frac{\prod_k {a_k}^{m_k}}{\prod_j {a_j}^{n_j}}$

It follows that any equilibrium of this kind can be characterized either by the standard free energy change or by the equilibrium constant. In practice concentrations are more useful than activities. Activities can be calculated from concentrations if the activity coefficient are known, but this is rarely the case. Sometimes activity coefficients can be calculated using, for example, Pitzer equations or Specific ion interaction theory. Otherwise conditions must be adjusted so that activity coefficients do not vary much. For ionic solutions this is achieved by using a background ionic medium at a high concentration relative to the concentrations of the species in equilibrium.

If activity coefficients are unknown they may be subsumed into the equilibrium constant, which becomes a concentration quotient. Each activity a_i is assumed to be the product of a concentration, [A_i], and an activity coefficient, γ_i

$a_i=[A_i]\gamma_i$

This expression for activity is placed in the expression defining the equilibrium constant.

$K=\frac{\prod_k {a_k}^{m_k}}{\prod_j {a_j}^{n_j}} =\frac{\prod_k \left([A_k]\gamma_k\right)^{m_k}}{\prod_j \left([A_j]\gamma_j\right)^{n_j}} =\frac{\prod_k [A_k]^{m_k}}{\prod_j [A_j]^{n_j}}\times \frac{\prod_k {\gamma_k}^{m_k}}{\prod_j {\gamma_j}^{n_j}} =\frac{\prod_k [A_k]^{m_k}}{\prod_j [A_j]^{n_j}}\times \Gamma$

By setting the quotient of activity coefficients, Γ, equal to one the equilibrium constant is defined as a quotient of concentrations.

$K=\frac{\prod_k [A_k]^{m_k}}{\prod_j [A_j]^{n_j}}$

In more familiar notation, for a general equilibrium

$\alpha A +\beta B ... \rightleftharpoons \sigma S+\tau T ...$

$K=\frac{[S]^\sigma [T]^\tau ... } {[A]^\alpha [B]^\beta ...}$

This definition is much more practical, but an equilibrium constant defined in terms of concentrations is dependent on conditions. In particular, equilibrium constants for species in aqueous solution are dependent on ionic strength, as the quotient of activity coefficients varies with the ionic strength of the solution.

The values of the standard free energy change and of the equilibrium constant are temperature dependent. To a first approximation, the van ‘t Hoff equation may be used.

$\frac{d \ln K}{dT}\ = \frac{\Delta H^\ominus}{RT^2} \mbox{ or } \frac{d \ln K}{d(1/T)}\ = -\frac{\Delta H^\ominus}{R}$

This shows that when the reaction is exothermic (ΔH, the standard enthalpy change, is negative), then K decreases with increasing temperature, in accordance with Le Chatelier’s principle. The approximation involved is that the standard enthalpy change, ΔH, is independent of temperature, which is a good approximation only over a small temperature range. Thermodynamic arguments can be used to show that

$\left(\frac{\partial H}{\partial T} \right)_p=C_p$

where C_p is the heat capacity at constant pressure.

Multiple equilibria

Two or more equilibria can exist at the same time. When this is so, equilibrium constants can be ascribed to individual equilibria, but they are not always unique. For example, three equilibrium constants can be defined for a dibasic acid, H₂A.^{[15][note 3]}

$A^{2-} + H^+ \rightleftharpoons HA^-; K_1=\frac{[HA^-]}{[H^+][A^{2-}]}$

$HA^- + H^+ \rightleftharpoons H_2A; K_2=\frac{[H_2A]}{[H^+][HA^-]}$

$A^{2-} + 2H^+ \rightleftharpoons H_2A; \beta_2=\frac{[H_2A]}{[H^+]^2[A^{2-}]}$

The three constants are not independent of each other and it is easy to see that β₂= K₁K₂. The constants K₁ and K₂ are stepwise constants and β is an example of an overall constant.

Speciation

Speciation diagram for a solution of citric acid as a function of pH.

The concentrations of species in equilibrium are usually calculated under the assumption that activity coefficients are either known or can be ignored. In this case, each equilibrium constant for the formation of a complex in a set of multiple equilibria can be defined as follows

$\alpha A +\beta B \ldots \rightleftharpoons A_\alpha B_\beta\ldots; K_{\alpha \beta \ldots}=\frac{[A_\alpha B_\beta \ldots]} {[A]^\alpha [B]^\beta \ldots}$

The concentrations of species containing reagent A are constrained by a condition of mass-balance, that is, the total (or analytical) concentration, which is the sum of all species’ concentrations, must be constant. There is one mass-balance equation for each reagent of the type

$T_A = [A] +\sum [A_\alpha B_\beta \ldots]= [A] +\sum \left(\alpha K_{\alpha \beta}\ldots[A]^\alpha [B]^\beta \ldots\right)$

There are as many mass-balance equations as there are reagents, A, B .., so if the equilibrium constant values are known, there are n mass-balance equations in n unknowns, [A], [B].., the so-called free reagent concentrations. Solution of these equations gives all the informatioeeded to calculate the concentrations of all the species.^[16]

Thus, the importance of an equilibrium constants lies in the fact that, once their values have been determined by experiment, they can be used to calculate the concentrations, known as the speciation, of mixtures that contain the relevant species.

Determination

Main article: Determination of equilibrium constants

There are five main types of experimental data that are used for the determination of solution equilibrium constants. Potentiometric data obtained with a glass electrode are the most widely used with aqueous solutions. The others are Spectrophotometric, Fluorescence (luminescence) measurements and NMR chemical shift measurements;^[8][17] simultaneous measurement of K and $\Delta$ H for 1:1 adducts in biological systems is routinely carried out using Isothermal Titration Calorimetry.

The experimental data will comprise a set of data points. At the i’th data point, the analytical concentrations of the reactants, , etc. will be experimentally known quantities and there will be one or more measured quantities, y_i, that depend in some way on the analytical concentrations and equilibrium constants. A general computational procedure has three main components.

1. Definition of a chemical model of the equilibria. The model consists of a list of reagents, A, B, etc. and the complexes formed from them, with stoichiometries A_pB_q… Known or estimated values of the equilibrium constants for the formation of all complexes must be supplied.

2. Calculation of the concentrations of all the chemical species in each solution. The free concentrations are calculated by solving the equations of mass-balance, and the concentrations of the complexes are calculated using the equilibrium constant definitions. A quantity corresponding to the observed quantity can then be calculated using physical principles such as the Nernst potential or Beer-Lambert law which relate the calculated quantity to the concentrations of the species.

3. Refinement of the equilibrium constants. Usually a Non-linear least squares procedure is used. A weighted sum of squares, U, is minimized.

$U=\sum^{i=1}_{i=np} w_i\left(y_i^{observed} - y_i^{calculated}\right)^2$

The weights, w_i and quantities y may be vectors. Values of the equilibrium constants are refined in an iterative procedure.

Solubility

Main article: solubility equilibrium

When a solute forms a saturated solution in a solvent, the concentration of the solute, at a given temperature, is determined by the equilibrium constant at that temperature.^[33]

$ln K=-RT \ln \left(\frac{\sum_k {a_k}^{m_k} (solution)}{a (solid)}\right)$

The activity of a pure substance in the solid state is one, by definition, so the expression simplifies to

$ln K=-RT \ln \left(\sum_k {a_k}^{m_k} (solution)\right)$

If the solute does not dissociate the summation is replaced by a single term, but if dissociation occurs, as with ionic substances

$K_{SP}=\prod_k{{a_k}^{m_k}}$

For example, with Na₂SO₄ m₁=2 and m₂=1 so the solubility product is written as

$K_{SP}=[Na^+]^2[SO_4^{2-}]$

Concentrations, indicated by [..], are usually used in place of activities, but activity must be taken into account of the presence of another salt with no ions in common, the so-called salt effect. When another salt is present that has an ion in common, the common-ion effect comes into play, reducing the solubility of the primary solute.

Solvent

A solvent (from the Latin solvō, “I loosen, untie, I solve”) is a substance that dissolves a solute (a chemically different liquid, solid or gas), resulting in a solution. A solvent is usually a liquid but can also be a solid or a gas. The maximum quantity of solute that can dissolve in a specific volume of solvent varies with temperature. Common uses for organic solvents are in dry cleaning (e.g., tetrachloroethylene), as paint thinners (e.g., toluene, turpentine), as nail polish removers and glue solvents (acetone, methyl acetate, ethyl acetate), in spot removers (e.g., hexane, petrol ether), in detergents (citrus terpenes), in perfumes (ethanol), nail polish and in chemical synthesis. The use of inorganic solvents (other than water) is typically limited to research chemistry and some technological processes.

The global solvent market is expected to earn revenues of about US$33 billion in 2019. The dynamic economic development in emerging markets like China, India, Brazil, or Russia will especially continue to boost demand for solvents. Specialists expect the worldwide solvent consumption to increase at an average annual rate of 2.5% over the next years. Accordingly, the growth rate seen during the past eight years will be surpassed.

Solution

Making a saline water solution by dissolving table salt (NaCl) in water. The salt is the solute and the water the solvent.

In chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. The solvent does the dissolving. The solution more or less takes on the characteristics of the solvent including its phase, and the solvent is commonly the major fraction of the mixture. The concentration of a solute in a solution is a measure of how much of that solute is dissolved in the solvent.

Activity coefficient

An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances.^[1] In an ideal mixture, the interactions between each pair of chemical species are the same (or more formally, the enthalpy change of solution is zero) and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult’s law. Deviations from ideality are accommodated by modifying the concentration by an activity coefficient. Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.

The concept of activity coefficient is closely linked to that of activity in chemistry.

Thermodynamics

The chemical potential, $\mu_B$ , of a substance B in an ideal mixture is given by

$\mu_B = \mu_{B}^{\ominus} + RT \ln x_B \,$

where $\mu_{B}^{\ominus}$ is the chemical potential in the standard state and x_B is the mole fraction of the substance in the mixture.

This is generalised to include non-ideal behavior by writing

$\mu_B = \mu_{B}^{\ominus} + RT \ln a_B \,$

when is the activity of the substance in the mixture with

$a_B = x_B \gamma_B$

where $\gamma_B$ is the activity coefficient. As $\gamma_B$ approaches 1, the substance behaves as if it were ideal. For instance, if $\gamma_B \approx 1$ , then Raoult’s Law is accurate. For $\gamma_B > 1$ and $\gamma_B < 1$ , substance B shows positive and negative deviation from Raoult’s law, respectively. A positive deviation implies that substance B is more volatile.

In many cases, as goes to zero, the activity coefficient of substance B approaches a constant; this relationship is Henry’s Law for the solvent. These relationships are related to each other through the Gibbs-Duhem equation. Note that in general activity coefficients are dimensionless.

Modifying mole fractions or concentrations by activity coefficients gives the effective activities of the components, and hence allows expressions such as Raoult’s law and equilibrium constants constants to be applied to both ideal and non-ideal mixtures.

Knowledge of activity coefficients is particularly important in the context of electrochemistry since the behaviour of electrolyte solutions is often far from ideal, due to the effects of the ionic atmosphere. Additionally, they are particularly important in the context of soil chemistry due to the low volumes of solvent and, consequently, the high concentration of electrolytes.

Application to chemical equilibrium

At equilibrium, the sum of the chemical potentials of the reactants is equal to the sum of the chemical potentials of the products. The Gibbs free energy change for the reactions, $\Delta_r G$ , is equal to the difference between these sums and therefore, at equilibrium, is equal to zero. Thus, for an equilibrium such as

$\alpha A + \beta B \rightleftharpoons \sigma S + \tau T$

$\Delta_r G = \sigma \mu_S + \tau \mu_T - (\alpha \mu_A + \beta \mu_B) = 0\,$

Substitute in the expressions for the chemical potential of each reactant:

$\Delta_r G = \sigma \mu_S^\ominus + \sigma RT \ln a_S + \tau \mu_T^\ominus + \tau RT \ln a_T -(\alpha \mu_A^\ominus + \alpha RT \ln a_A + \beta \mu_B^\ominus + \beta RT \ln a_B)=0$

Upon rearrangement this expression becomes

$\Delta_r G =\left(\sigma \mu_S^\ominus+\tau \mu_T^\ominus -\alpha \mu_A^\ominus- \beta \mu_B^\ominus \right) + RT \ln \frac{a_S^\sigma a_T^\tau} {a_A^\alpha a_B^\beta} =0$

The sum $\left(\sigma \mu_S^\ominus+\tau \mu_T^\ominus -\alpha \mu_A^\ominus- \beta \mu_B^\ominus \right)$ is the standard free energy change for the reaction, $\Delta_r G^\ominus$ . Therefore

$\Delta_r G^\ominus = -RT \ln K$

K is the equilibrium constant. Note that activities and equilibrium constants are dimensionless numbers.

This derivation serves two purposes. It shows the relationship between standard free energy change and equilibrium constant. It also shows that an equilibrium constant is defined as a quotient of activities. In practical terms this is inconvenient. When each activity is replaced by the product of a concentration and an activity coefficient, the equilibrium constant is defined as

$K= \frac{[S]^\sigma[T]^\tau}{[A]^\alpha[B]^\beta} \times \frac{\gamma_S^\sigma \gamma_T^\tau}{\gamma_A^\alpha \gamma_B^\beta}$

where [S] denotes the concentration of S, etc. In practice equilibrium constants are determined in a medium such that the quotient of activity coefficient is constant and can be ignored, leading to the usual expression

$K= \frac{[S]^\sigma[T]^\tau}{[A]^\alpha[B]^\beta}$

which applies under the conditions that the activity quotient has a particular (constant) value.

Measurement and prediction of activity coefficients

UNIQUAC Regression of Activity Coefficients (Chloroform/Methanol Mixture)

Activity coefficients may be measured experimentally or calculated theoretically, using the Debye-Hückel equation or extensions such as Davies equation, Pitzer equations or TCPC model. Specific ion interaction theory (SIT) may also be used. Alternatively correlative methods such as UNIQUAC, NRTL, MOSCED or UNIFAC may be employed, provided fitted component-specific or model parameters are available.

A new alternative for activity coefficients prediction, which is less dependent on model parameters, is the COSMO-RS method. In this methods the required information comes from quantum mechanics calculations specific to each molecule (sigma profiles) combined with a statistical thermodynamics treatment of surface segments.

For uncharged species, the activity coefficient γ₀ mostly follows a “salting-out” model:

$\log_{10}(\gamma_{0}) = b I$

This simple model predicts activities of many species (dissolved undissociated gases such as CO₂, H₂S, NH₃, undissociated acids and bases) to high ionic strengths (up to 5 mol/kg). The value of the constant b for CO₂ is 0.11 at 10 °C and 0.20 at 330 °C.

For water (solvent), the activity a_w can be calculated using:^[12]

$\ln(a_{w}) = \frac{- u m}{55.51}$ φ

where ν is the number of ions produced from the dissociation of one molecule of the dissolved salt, m is the molal concentration of the salt dissolved in water, φ is the osmotic coefficient of water, and the constant 55.51 represents the molal concentration of water. In the above equation, the activity of a solvent (here water) is represented as inversely proportional to the number of particles of salt versus that of the solvent.

Common-ion effect

The common ion effect is responsible for the reduction in solubility of an ionic precipitate when a soluble compound combining one of the ions of the precipitate is added to the solution in equilibrium with the precipitate. It states that if the concentration of any one of the ions is increased, then, according to Le Chatelier’s principle, the ions in excess should combine with the oppositely charged ions. Some of the salt will be precipitated until the ionic product is equal to the solubility of the product. In simple words, common ion effect is defined as the suppression of the degree of dissociation of a weak electrolyte containing a common ion.^[1]

The solubility of a sparingly soluble salt is reduced in a solution that contains an ion in common with that salt. For instance, the solubility of silver chloride in water is reduced if a solution of sodium chloride is added to a suspension of silver chloride in water.

A practical example used very widely in areas drawing drinking water from chalk or limestone aquifers is the addition of sodium carbonate to the raw water to reduce the hardness of the water. In the water treatment process, highly soluble sodium carbonate salt is added to precipitate out sparingly soluble calcium carbonate. The very pure and finely divided precipitate of calcium carbonate that is generated is a valuable by-product used in the manufacture of toothpaste.

The salting out process used in the manufacture of soaps benefits from the common ion effect. Soaps are sodium salts of fatty acids. Addition of sodium chloride reduces the solubility of the soap salts. The soaps precipitate due to a combination of common ion effect and increased ionic strength.

Sea, brackish and other waters that contain appreciable amount of Na⁺ interfere with the normal behavior of soap because of common ion effect. In the presence of excess Sodium ions the solubility of soap salts is reduced, making the soap less effective.

A buffer solution contains an acid and its conjugate base or a base and its conjugate acid. Addition of the conjugate ion will result in a change of pH of the buffer solution. For example, if both sodium acetate and acetic acid are dissolved in the same solution they both dissociate and ionize to produce acetate ions. Sodium acetate is a strong electrolyte so it dissociates completely in solution. Acetic acid is a weak acid so it only ionizes slightly. According to Le Chatelier’s principle, the addition of acetate ions from sodium acetate will suppress the ionization of acetic acid and shift its equilibrium to the left. Thus the percent dissociation of the acetic acid will decrease and the pH of the solution will increase. The ionization of an acid or a base is limited by the presence of its conjugate base or acid.

NaCH₃CO₂(s) → Na⁺(aq) + CH₃CO₂^–(aq)

CH₃CO₂H (aq) H⁺(aq) + CH₃CO₂^–(aq)

This will decrease the hydrogen ion concentration and thus the common-ion solution will be less acidic than a solution containing only acetic acid.

The fifth analytical group of cations includes ions

Mg²⁺, Mn²⁺, Fe²⁺, Fe³⁺, Bi³⁺, Sb³⁺, Sb^V.

Compounds of Iron, Bismuth, Magnesium are a part of drugs – De-nol, Gastro-norm, Panangin, etc. Therefore the future pharmacist should own knowledge of chemical-analytical properties of the given group of ions.

The fifth analytical group includes ions Mg²⁺, Mn²⁺, Fe²⁺, Fe³⁺, Bi³⁺, Sb³⁺, Sb^V. 2 mol/L a Sodium hydroxide solution are a group reagent on cations of the fifth analytical group, sometimes apply 25 % aqueous ammonia solution. After action of a group reagent on cations of the fifth analytical group are formed Fe(OН)₂, Fe(OH)₃, Bi(OН)₃, Mg(OH)₂, Mn(OH)₂, Sb(OH)₃, SbО(OH)₃.

On air hydroxides Mn(OH)₂ and Fe(OН)₂gradually are oxidised oxygen of air and change colouring from white and green accordingly to the brown:

2Mn(OH)₂ + О₂ ® 2MnО(OH)₂;

4Fe(OН)₂ + О₂ + 2Н₂О 4 Fe(OН)₃.

Precipitate Bi(OН)₃ by heating becomes yellow BiО(OН).

These hydroxides are not dissolved in excess of a group reagent.

Only hydroxides Sb(OH)₃ and SbО(OH)₃ are dissolved in alkalis with formation [Sb(OH)₄]^– and [Sb(OH)₆]^–. In ammonium salts we will very slightly soluble Fe(OН)₂. Mg(OH)₂ is dissolved in ammonium salts. All hydroxides of the fifth group cations are dissolved in strong acids and are formed corresponding salts.

The common reactions of V analytical group cations

Solutions of alkalis (or NaOH) or the concentrated solution of ammonia with cations of the fifth analytical group form hydroxides: green Fe(OН)₂, dark brown Fe(OН)₃, white Bi(OН)₃, Mg(OH)₂, Mn(OH)₂, Sb(OH)₃, SbО(OH)₃:

Fe²⁺ + 2OH^– = Fe(OН)₂¯;

Fe³⁺ + 3NH₃×Н₂О = Fe(OН)₃¯ + 3NH₄⁺.

Reaction performance. Into test tubes select on 2-3 drops of 0,5 mol/L solutions of the fifth analytical group cations, into everyone add some drops of 2 mol/L Potassium hydroxide solution and observe formation precipitates of hydroxides. Investigate solubility Sb(OH)₃ and SbО(OH)₃ in excess of alkalis. Investigate solubility Mg(OH)₂ in 0,5 mol/L ammonium chloride solution. Investigate solubility of all precipitates in 2 mol/L HCl solution, and for hydroxides Sb^ІІІ and Sb^V – in 6 mol/L HCl solution.

Alkaline metals and ammonium hydrogenphosphate Na₂HPO₄, K₂HPO₄, (NH₄)₂HPO₄ form precipitates of phosphates or ammoniumphosphate constant structure. Only Sb^ІІІ and Sb^V form precipitates of phosphates of variable structure.

Mg²⁺ + HPO₄^2-+ NH₃ = MgNH₄PO₄¯;

Mn²⁺ + HPO₄^2-+ NH₃ = MnNH₄PO₄¯;

3Fe²⁺ + 2HPO₄^2- + 2NH₃ = Fe₃(PO₄)₂¯ + 2NH₄⁺;

Fe³⁺ + HPO₄^2- + NH₃ = FePO₄¯ + NH₄⁺;

Ві³⁺ + HPO₄^2- + NH₃ = ВіPO₄¯ + NH₄⁺.

Reaction performance. Into test tubes select on 2-3 drops of salts solutions of the fifth analytical group cations, add 2-3 drops of 0,5 mol/L solutions of alkaline metals and ammonium hydrogenphosphate and 2-3 drops of 2 mol/L ammonia solution and observe formation of precipitates.

Magnesium is a chemical element with the symbol Mg and atomic number 12. Its common oxidatioumber is +2. It is an alkaline earth metal and the eighth most abundant element in the Earth’s crust and ninth in the known universe as a whole. Magnesium is the fourth most common element in the Earth as a whole (behind iron, oxygen and silicon), making up 13% of the planet’s mass and a large fraction of the planet’s mantle. The relative abundance of magnesium is related to the fact that it easily builds up in supernova stars from a sequential addition of three helium nuclei to carbon (which in turn is made from three helium nuclei). Due to magnesium ion’s high solubility in water, it is the third most abundant element dissolved in seawater.

The free element (metal) is not found naturally on Earth, as it is highly reactive (though once produced, it is coated in a thin layer of oxide (see passivation), which partly masks this reactivity). The free metal burns with a characteristic brilliant white light, making it a useful ingredient in flares. The metal is now mainly obtained by electrolysis of magnesium salts obtained from brine. Commercially, the chief use for the metal is as an alloying agent to make aluminium-magnesium alloys, sometimes called magnalium or magnelium. Since magnesium is less dense than aluminium, these alloys are prized for their relative lightness and strength.

In human biology, magnesium is the eleventh most abundant element by mass in the human body. Its ions are essential to all living cells, where they play a major role in manipulating important biological polyphosphate compounds like ATP, DNA, and RNA. Hundreds of enzymes thus require magnesium ions to function. Magnesium compounds are used medicinally as common laxatives, antacids (e.g., milk of magnesia), and in a number of situations where stabilization of abnormal nerve excitation and blood vessel spasm is required (e.g., to treat eclampsia). Magnesium ions are sour to the taste, and in low concentrations they help to impart a natural tartness to fresh mineral waters.

In vegetation, magnesium is the metallic ion at the center of chlorophyll, and is thus a common additive to fertilizers.

Physical and chemical properties

Elemental magnesium is a rather strong, silvery-white, light-weight metal (two thirds the density of aluminium). It tarnishes slightly when exposed to air, although unlike the alkali metals, an oxygen-free environment is unnecessary for storage because magnesium is protected by a thin layer of oxide that is fairly impermeable and difficult to remove. Like its lower periodic table group neighbor calcium, magnesium reacts with water at room temperature, though it reacts much more slowly than calcium. When submerged in water, hydrogen bubbles almost unnoticeably begin to form on the surface of the metal—though if powdered, it reacts much more rapidly. The reaction occurs faster with higher temperatures (see precautions). Magnesium’s ability to react with water can be harnessed to produce energy and run a magnesium-based engine. Magnesium also reacts exothermically with most acids, such as hydrochloric acid (HCl). As with aluminium, zinc and many other metals, the reaction with hydrochloric acid produces the chloride of the metal and releases hydrogen gas.

Magnesium is a highly flammable metal, but while it is easy to ignite when powdered or shaved into thin strips, it is difficult to ignite in mass or bulk. Once ignited, it is difficult to extinguish, being able to burn in nitrogen (forming magnesium nitride), carbon dioxide (forming magnesium oxide and carbon) and water (forming magnesium oxide and hydrogen). This property was used in incendiary weapons used in the firebombing of cities in World War II, the only practical civil defense being to smother a burning flare under dry sand to exclude the atmosphere. On burning in air, magnesium produces a brilliant white light that includes strong ultraviolet. Thus magnesium powder (flash powder) was used as a source of illumination in the early days of photography. Later, magnesium ribbon was used in electrically ignited flash bulbs. Magnesium powder is used in the manufacture of fireworks and marine flares where a brilliant white light is required. Flame temperatures of magnesium and magnesium alloys can reach 3,100 °C (3,370 K; 5,610 °F), although flame height above the burning metal is usually less than 300 mm (12 in). Magnesium may be used as an ignition source for thermite, an otherwise difficult to ignite mixture of aluminium and iron oxide powder.

Magnesium compounds are typically white crystals. Most are soluble in water, providing the sour-tasting magnesium ion Mg²⁺. Small amounts of dissolved magnesium ion contribute to the tartness and taste of natural waters. Magnesium ion in large amounts is an ionic laxative, and magnesium sulfate (commoame: Epsom salt) is sometimes used for this purpose. So-called “milk of magnesia” is a water suspension of one of the few insoluble magnesium compounds, magnesium hydroxide. The undissolved particles give rise to its appearance and name. Milk of magnesia is a mild base commonly used as an antacid, which has some laxative side effect.

Characteristic reactions of ions Mg^{2 +}

Magnezon I (p-nitrobenzol-azo-rezortsin) in the basic medium is painted in red-violet colour. At presence Magnesium hydroxide is formed the adsorbed compound which paints a solution in dark blue colour.

The ions of Mn²⁺, Ni²⁺, Co²⁺, Cd²⁺interfere with the exposure of ions of Mg²⁺.

Reaction performance. To 2-3 drops of an investigated solution add 1-2 drops of a basic solution of a reagent. Depending on quantity of Magnesium in an investigated solution the dark blue precipitate or dark bluesolution is formed.

Sodium or ammonium hydrogenphosphate (pharmacopeia’s reaction) with ions Mg²⁺ in presence of ammonia and NH₄Cl, form white crystal precipitate MgNH₄PO₄6H₂O:

Mg²⁺ + HPO₄^2- + NH₃ + 6H₂O = MgNH₄PO₄6H₂O¯.

The ions of Ba^{2 +}, Ca^{2 +}and other heavy metals interfere with the exposure of ions of Mg²⁺.

Reaction performance. To 1-2 drops of an investigated solution add 2-3 drops of 2 mol/L HCl and 1-2 drops Na₂HPO₄. After that add some drops of 2 mol/L aqueous ammonia solution, slowly mixing it after addition of each drop. After ammonia will neutralise acid and is formed NH₄Cl, characteristic crystal precipitate MgNH₄PO₄×6H₂O forms. Ammonia is necessary adding to pН 9-10. Necessary rub the wall-side of test tube a glass stick.

Manganese is a chemical element, designated by the symbol Mn. It has the atomic number 25. It is found as a free element iature (often in combination with iron), and in many minerals. Manganese is a metal with important industrial metal alloy uses, particularly in stainless steels.

Historically, manganese is named for various black minerals (such as pyrolusite) from the same region of Magnesia in Greece which gave names to similar-sounding magnesium, Mg, and magnetite, an ore of the element iron, Fe. By the mid-18th century, Swedish chemist Carl Wilhelm Scheele had used pyrolusite to produce chlorine. Scheele and others were aware that pyrolusite (now known to be manganese dioxide) contained a new element, but they were not able to isolate it. Johan Gottlieb Gahn was the first to isolate an impure sample of manganese metal in 1774, by reducing the dioxide with carbon.

Manganese phosphating is used as a treatment for rust and corrosion prevention on steel. Depending on their oxidation state, manganese ions have various colors and are used industrially as pigments. The permanganates of alkali and alkaline earth metals are powerful oxidizers. Manganese dioxide is used as the cathode (electron acceptor) material in zinc-carbon and alkaline batteries.

In biology, manganese(II) ions function as cofactors for a large variety of enzymes with many functions. Manganese enzymes are particularly essential in detoxification of superoxide free radicals in organisms that must deal with elemental oxygen. Manganese also functions in the oxygen-evolving complex of photosynthetic plants. The element is a required trace mineral for all known living organisms. In larger amounts, and apparently with far greater activity by inhalation, manganese can cause a poisoning syndrome in mammals, with neurological damage which is sometimes irreversible.

Chemical properties

The most common oxidation states of manganese are +2, +3, +4, +6 and +7, though oxidation states from −3 to +7 are observed. Mn²⁺ often competes with Mg²⁺ in biological systems. Manganese compounds where manganese is in oxidation state +7, which are restricted to the unstable oxide Mn₂O₇ and compounds of the intensely purple permanganate anion MnO₄⁻, are powerful oxidizing agents.^[1] Compounds with oxidation states +5 (blue) and +6 (green) are strong oxidizing agents and are vulnerable to disproportionation.

Manganese(II) chloride crystals – the pale pink color of Mn (II) salts is due to a spin-forbidden 3d transition, which is rare.

Aqueous solution of KMnO₄ illustrating the deep purple of Mn(VII) as it occurs in permanganate

The most stable oxidation state for manganese is +2, which has a pale pink color, and many manganese(II) compounds are known, such as manganese(II) sulfate (MnSO₄) and manganese(II) chloride (MnCl₂). This oxidation state is also seen in the mineral rhodochrosite (manganese(II) carbonate). The +2 oxidation state is the state used in living organisms for essential functions; other states are toxic for the human body. The +2 oxidation of Mn results from removal of the two 4s electrons, leaving a “high spin” ion in which all five of the 3d orbitals contain a single electron. Absorption of visible light by this ion is accomplished only by a spin-forbidden transition in which one of the d electrons must pair with another, to give the atom a change in spin of two units. The unlikeliness of such a transition is seen in the uniformly pale and almost colorless nature of Mn(II) compounds relative to other oxidation states of manganese.

Oxidation states of manganese^[6]
0	Mn₂(CO)₁₀
+1	MnC₅H₄CH₃(CO)₃
+2	MnCl₂
+3	MnF₃
+4	MnO₂
+5	K₃MnO₄
+6	K₂MnO₄
+7	KMnO₄
Common oxidation states are in bold.

The +3 oxidation state is known in compounds like manganese(III) acetate, but these are quite powerful oxidizing agents and also prone to disproportionation in solution to manganese(II) and manganese(IV). Solid compounds of manganese(III) are characterized by their preference for distorted octahedral coordination due to the Jahn-Teller effect and its strong purple-red color.

The oxidation state 5+ can be obtained if manganese dioxide is dissolved in molten sodium nitrite.^[7] Manganate (VI) salts can also be produced by dissolving Mn compounds, such as manganese dioxide, in molten alkali while exposed to air.

Permanganate (+7 oxidation state) compounds are purple, and can give glass a violet color. Potassium permanganate, sodium permanganate and barium permanganate are all potent oxidizers. Potassium permanganate, also called Condy’s crystals, is a commonly used laboratory reagent because of its oxidizing properties and finds use as a topical medicine (for example, in the treatment of fish diseases). Solutions of potassium permanganate were among the first stains and fixatives to be used in the preparation of biological cells and tissues for electron microscopy.

Characteristic reactions of ions Mn²⁺

Reactions of oxidation Manganese (II) to the higher oxidation state are very importance for determination and seperation Manganese from other elements, and also for its quantitative determination. Ions Mn²⁺can be oxidised by action of different oxidizers in the acidic and basic medium.

Ammonium persulphate (NH₄)₂S₂O₈ in the presence of the catalyst (ions Ag⁺) oxidises ions Mn²⁺ to MnО₄^–. The solution has violet colour:

2Mn²⁺ + 5S₂O₈^2- + 8H₂O = 2MnO₄^– + 10SO₄^2- + 16H⁺.

Reaction performance. Into a test tube place 2-3 crystals of (NH₄)₂S₂O₈, add 0,5 mL of 2 mol/L HNO₃ solution and 2-3 drops of 0,1 mol/L AgNO₃ solution. A mix is heated (do not boil!), in a hot solution dip the glass stick moistened by the investigated solution, and continue to heat a test tube (to 50°) throughout 1-2 minutes. If there are Mangan ions, the solution is painted in violet colour. If there are a lot of Manganese ions, but persulphate it is not enough and heatings strong black precipitate MnО(OH)₂ will be can form.

Sodium bismuthate in presence of nitric acid solution oxidises ions Mn²⁺to MnО₄^–:

2Mn²⁺ + 5BiO₃^– + 14H⁺ = 2MnO₄– + 5Bi³⁺ + 7H₂O.

Reaction performance. To 1-2 drops of an investigated solution add 3-4 drops concentrated HNO₃ and a few crystals of NaBiО₃. Solution is mixed and centrifugated. If there are ions Mn²⁺, the solution over a precipitate is painted in violet colour.

Bromic or chloric water, Hydrogene hydroxide in the basic medium oxidise Mn²⁺ions to MnО(OH)₂(or MnО₂×2H₂O) – this is a precipitate of black-brown colour:

Mn²⁺ + Br₂ + 4OH^– = MnО(OH)₂¯ + 2Br^– + H₂O.

Reaction performance. To one drop of an investigated solution add 5-7 drops of a basic solution of bromic water. Solution is mixed and heated. If there are ions Mn²⁺, the black-brown precipitate forms.

Iron is a chemical element with the symbol Fe (from Latin: ferrum) and atomic number 26. It is a metal in the first transition series. It is the most common element (by mass) forming the planet Earth as a whole, forming much of Earth’s outer and inner core. It is the fourth most common element in the Earth’s crust. Iron’s very common presence in rocky planets like Earth is due to its abundant production as a result of fusion in high-mass stars, where the production of nickel-56 (which decays to the most common isotope of iron) is the last nuclear fusion reaction that is exothermic. This causes radioactive nickel to become the last element to be produced before collapse of a supernova leads to the explosive events that scatter this precursor radionuclide of iron abundantly into space.

Like other group 8 elements, iron exists in a wide range of oxidation states, −2 to +6, although +2 and +3 are the most common. Elemental iron occurs in meteoroids and other low oxygen environments, but is reactive to oxygen and water. Fresh iron surfaces appear lustrous silvery-gray, but oxidize iormal air to give hydrated iron oxides, commonly known as rust. Unlike many other metals which form passivating oxide layers, iron oxides occupy more volume than iron metal, and thus iron oxides flake off and expose fresh surfaces for corrosion.

Iron metal has been used since ancient times, though copper alloys, which have lower melting temperatures, were used first in history. Pure iron is soft (softer than aluminium), but is unobtainable by smelting. The material is significantly hardened and strengthened by impurities from the smelting process, such as carbon. A certain proportion of carbon (between 0.002% and 2.1%) produces steel, which may be up to 1000 times harder than pure iron. Crude iron metal is produced in blast furnaces, where ore is reduced by coke to pig iron, which has a high carbon content. Further refinement with oxygen reduces the carbon content to the correct proportion to make steel. Steels and low carbon iron alloys with other metals (alloy steels) are by far the most common metals in industrial use, due to their great range of desirable properties and the abundance of iron.

Iron chemical compounds, which include ferrous and ferric compounds, have many uses. Iron oxide mixed with aluminium powder can be ignited to create a thermite reaction, used in welding and purifying ores. It forms binary compounds with the halogens and the chalcogens. Among its organometallic compounds is ferrocene, the first sandwich compound discovered.

Iron plays an important role in biology, forming complexes with molecular oxygen in hemoglobin and myoglobin; these two compounds are common oxygen transport proteins in vertebrates. Iron is also the metal used at the active site of many important redox enzymes dealing with cellular respiration and oxidation and reduction in plants and animals.

General properties

Name, symbol, number

iron, Fe, 26

Pronunciation

/ˈ aɪ .ər n /

Element category

transition metal

Group, period, block

8, 4, d

Standard atomic weight

55.845(2)

Electron configuration

[Ar] 3d⁶ 4s²
2, 8, 14, 2

History

Discovery

before 5000 BC

Physical properties

Phase

solid

Density (near r.t.)

7.874 g·cm⁻³

Liquid density at m.p.

6.98 g·cm⁻³

Melting point

1811 K2800 °F 1538 °C, ,

Boiling point

5182 °F 2862 °C, 3134 K,

Heat of fusion

13.81 kJ·mol⁻¹

Heat of vaporization

340 kJ·mol⁻¹

Molar heat capacity

25.10 J·mol⁻¹·K⁻¹

Vapor pressure

P (Pa)

100

1 k

10 k

100 k

at T (K)

1728

1890

2091

2346

2679

3132

Atomic properties

Oxidation states

6, 5,^[1] 4, 3, 2, 1^[2], -1, -2
(amphoteric oxide)

Electronegativity

1.83 (Pauling scale)

Ionization energies
(more)

1st: 762.5 kJ·mol⁻¹

2nd: 1561.9 kJ·mol⁻¹

3rd: 2957 kJ·mol⁻¹

Atomic radius

126 pm

Covalent radius

132±3 (low spin), 152±6 (high spin) pm

Characteristic reactions of ions Fe²⁺

Potassium hexacyanoferrate (III) K₃[Fe(CN)₆] (pharmacopeia’s reaction) with ions Fe²⁺ forms dark blue precipitate Fe₃[Fe(CN)₆]₂, so-called Turnbull`s blue:

3Fe²⁺ + 2[Fe(CN)₆]^3- = Fe₃[Fe(CN)₆]₂¯.

Precipitate Fe₃[Fe(CN)₆]₂ is not dissolved in acids, but decays in alkalis therefore it is formed Fe(OH)₂.

Reaction performance. To 2-3 drops of an investigated solution add some drops of Potassium hexacyanoferrate (III). If there is Fe²⁺, the dark blue precipitate (pН~3) forms.

Characteristic reactions of ions Fe^{3 +}

Potassium hexacyanoferrate (II) K₄[Fe(CN)₆] (pharmacopeia’s reaction) with Fe³⁺ ions forms dark blue precipitateFe₄[Fe(CN)₆]₃, so-called Prussian blue:

4Fe³⁺ +3[Fe(CN)₆]^4- = Fe₄[Fe(CN)₆]₃¯.

Precipitate Fe₄[Fe(CN)₆]₃ is not dissolved in the diluted mineral acids; alkalis decay Fe₄[Fe(CN)₆]₃ therefore forming Fe(OH)₃:

Fe₄[Fe(CN)₆]₃ + 12KOH = 4Fe(OH)₃¯ + 3K₄[Fe(CN)₆].

The ions of phosphate, oksalat, fluoride interfere with the exposure of ions of Fe³⁺.

Reaction performance. To 2-3 drops of an investigated solution add 1-2 drops K₄[Fe(CN)₆]. In the presence of ions Fe³⁺ the precipitate of “the Prussian blue” dark blue colour is formed. If it is not enough ions Fe³⁺, the precipitate does not form, but the solution is painted in dark blue colour. This reaction is possible to determinate of Fe³⁺-ions in a mix with all cation of other analytical groups. It can be used by the drop way. On a filtering paper strip put on one drop of an investigated solution and 2 mol/L HCl solution and solution K₄[Fe(CN)₆]. If there are ions Fe³⁺, the dark blue stain is formed.

Potassium or ammonium thiocyanide KSCN or NH₄SCN (pharmacopeia’s reaction) – with ions Fe³⁺ forms soluble complex painted in red colour: [FeSCN]²⁺, [Fe(SCN)₂]⁺, [Fe(SCN)₃], [Fe(SCN)₄]^–and etc. Sensitivity of reaction of Fe³⁺ ions determination with the thiocyanide increases in process extraction of products reaction by organic solvent, for example, an aether, butanol or isobutanol (organic layer will be red).

After addition of HgCl₂ solution to red complex [Fe(SCN)₆]^3- are observed colourless of solution:

2[Fe(SCN)₆]^3- + 3HgCl₂ ® 3[Hg(SCN)₄]^2- + 2Fe³⁺ + 6Cl^–.

Reaction performance. To 2-3 drops of an investigated solution add 1-2 drops HNO₃ and 2-3 drops of Potassium or ammonium tiocyanate. If there is of ions Fe³⁺,solution will be red colouring. Reaction can be executed in the drop way. On a filtering paper strip put on one drop of an investigated solution, diluted HCl and 2-3 drops of tiocyanate solution. If there are ions Fe³⁺, on a paper the red stain is formed.

Bismuth is a chemical element with symbol Bi and atomic number 83. Bismuth, a pentavalent poor metal, chemically resembles arsenic and antimony. Elemental bismuth may occur naturally, although its sulfide and oxide form important commercial ores. The free element is 86% as dense as lead. It is a brittle metal with a silvery white color when freshly produced, but is often seen in air with a pink tinge owing to surface oxidation. Bismuth is the most naturally diamagnetic and has one of the lowest values of thermal conductivity among metals.

Bismuth metal has been known from ancient times, although until the 18th century it was often confused with lead and tin, which share some physical properties. The etymology is uncertain, but possibly comes from Arabic bi ismid, meaning having the properties of antimony^[2] or German words weisse masse or wismuth (“white mass”), translated in the mid sixteenth century to New Latin bisemutum.

Bismuth has long been considered as the element with the highest atomic mass that is stable. However, it was recently discovered to be slightly radioactive: its only primordial isotope bismuth-209 decays with a half life more than a billion times the estimated age of the universe.

Bismuth compounds account for about half the production of bismuth. They are used in cosmetics, pigments, and a few pharmaceuticals, notably Pepto-Bismol. Bismuth has unusually low toxicity for a heavy metal. As the toxicity of lead has become more apparent in recent years, there is an increasing use of bismuth alloys (presently about a third of bismuth production) as a replacement for lead.

Chemical characteristics

Bismuth is stable to both dry and moist air at ordinary temperatures. When red-hot, it reacts with water to make bismuth(III) oxide.

2 Bi + 3 H₂O → Bi₂O₃ + 3 H₂

It reacts with fluorine to make bismuth(V) fluoride at 500 °C or bismuth(III) fluoride at lower temperatures (typically from Bi melts); with other halogens it yields only bismuth(III) halides. The trihalides are corrosive and easily react with moisture, forming oxyhalides with the formula BiOX.

2 Bi + 3 X₂ → 2 BiX₃ (X = F, Cl, Br, I)

Bismuth dissolves in concentrated sulfuric acid to make bismuth(III) sulfate and sulfur dioxide.

6 H₂SO₄ + 2 Bi → 6 H₂O + Bi₂(SO₄)₃ + 3 SO₂

It reacts with nitric acid to make bismuth(III) nitrate.

Bi + 6 HNO₃ → 3 H₂O + 3 NO₂ + Bi(NO₃)₃

It also dissolves in hydrochloric acid, but only with oxygen present.^[24]

4 Bi + 3 O₂ + 12 HCl → 4 BiCl₃ + 6 H₂O

It is used as a transmetalating agent in the synthesis of alkaline-earth metal complexes:

3 Ba + 2 BiPh₃ → 3 BaPh₂ + 2 Bi

Characteristic reactions of ions Bi³⁺

Hydrolysis. Solution BiCl₃ very dilute by water. The white precipitate of basic salt BiOCl forms:

BiCl₃ + 2H₂O = Bi(OH)₂Cl¯ + 2HCl;

Bi(OH)₂Cl¯ = BiOCl¯ + H₂O,

or Bi³⁺ + Cl^–+ H₂O = BiOCl¯ + 2H⁺.

Aqueous species

In aqueous solution, the Bi³⁺ ion exists in various states of hydration, depending on the pH:

pH range

Species

Bi(H₂O)₆³⁺

0-4

Bi(H₂O)₅OH²⁺

1-5

Bi(H₂O)₄(OH)+
2

5-14

Bi(H₂O)₃(OH)₃

>11

Bi(H₂O)₂(OH)4⁻

Reaction performance. To 2-3 drops of an investigated solution add 5-7 drops of water and 3-4 drops of Sodium chloride. If there are ions Bi³⁺, the white precipitate forms. Reaction passes in the neutral medium.

Bismuth oxychloride (BiOCl) structure (mineral bismoclite).

Bismuth atoms shown as grey, oxygen red, chlorine green.

Sodium sulphide Na₂S (pharmacopeia’s reaction) with Ві³⁺ ions in the acidic medium forms brown-black precipitate Ві₂S₃:

2Ві³⁺ + 3S^2- ® Ві₂S₃¯.

Precipitate insoluble in the diluted acids, except nitric:

Bi₂S₃ + 8НNО₃ ® 2Bi(NО₃)₃ + 2NО + 3S¯ + 4Н₂О.

Precipitate Ві₂S₃ is dissolved in solution FeCl₃:

Bi₂S₃ + 6FeCl₃ ®2ВіCl₃+ 3S¯ + 6FeCl₂.

The ions of Ag⁺, Pb²⁺, Hg²⁺, Cu²⁺, Cd²⁺ ions interfere with the exposure of ions of Bi³⁺.

Reaction performance. To 3-4 drops of an investigated solution add 1-2 drops of 1 mol/L chloridic acid, 5-6 drops of water and boil throughout 1 minute. If there are Ві³⁺ ions, the white or light yellow precipitate forms. After that add 3-4 drops of Sodium sulphide solution and observe formation of brown-black precipitate.

Potassium or Sodium hexahydroxostannate K₄[Sn(OH)₆] and Na₄[Sn(OH)₆] with ions Bi³⁺ form metal Bismuth (black precipitate):

Sn²⁺ + 2OH^– = Sn(OH)₂¯;

Sn(OH)₂ + 4OH^– = [Sn(OH)₆]^4-;

Bi³⁺ + 3OH^– = Bi(OH)₃¯;

2Bi(OH)₃ + 3[Sn(OH)₆]^4- = 2Bi¯ + 3[Sn(OH)₆]^2- + 6OH^–.

Reaction performance. To 2-3 drops of SnCl₂ solution add 8-10 drops of 2 mol/LKOH or NaOH solutionto dissolution of a white precipitate. To the received solution add a drop of an investigated solution (Bi³⁺). If there are ions Bi³⁺, the black precipitate of metal Bismuth forms.

Potassium iodide KI with ions Bi³⁺ forms a black precipitate of Bismuth (III) iodide which is easily dissolved in excess of potassium iodide with formation of solution orange colour:

Bi³⁺ + 3I^– = BiІ₃¯;

BiІ₃¯ + I^– = [BiІ₄]^–.

After dilute this solution by water observe formation of black precipitate Bismuth (III) iodide again.

[BiІ₄]^– = BiІ₃¯ + I^–;

After very dilute received mix by water observe formation the orange precipitate of the basic salt:

BiІ₃ + H₂O = BiOI¯ + 2H ⁺ + 2I^–.

Reaction performance. To 2-3 drops of an investigated solution add 2-3 drops of KI solution. If there are ions Bi^{3 +}, the black precipitate forms. To the received precipitate add 5-6 drops of KI solution, the solution is painted in orange colour.

Antimony (Latin: stibium) is a chemical element with symbol Sb and atomic number 51. A lustrous gray metalloid, it is found iature mainly as the sulfide mineral stibnite (Sb₂S₃). Antimony compounds have been known since ancient times and were used for cosmetics; metallic antimony was also known, but it was erroneously identified as lead. It was established to be an element around the 17th century.

For some time, China has been the largest producer of antimony and its compounds, with most production coming from the Xikuangshan Mine in Hunan. The industrial methods to produce antimony are roasting and subsequent carbothermal reduction or direct reduction of stibnite with iron.

The largest applications for metallic antimony are as alloying material for lead and tin and for lead antimony plates in lead-acid batteries. Alloying lead and tin with antimony improves the properties of the alloys which are used in solders, bullets and plain bearings. Antimony compounds are prominent additives for chlorine- and bromine-containing fire retardants found in many commercial and domestic products. An emerging application is the use of antimony in microelectronics.

General properties

Name, symbol, number

antimony, Sb, 51

Pronunciation

UK /ˈ æ n t ɨ m ə n i / AN-ti-mə-nee;
US /ˈ æ n t ɨ m oʊ n i / AN-ti-moh-nee

Element category

metalloid

Group, period, block

15 (pnictogens), 5, p

Standard atomic weight

121.760(1)

Electron configuration

[Kr] 4d¹⁰ 5s² 5p³
2, 8, 18, 18, 5

History

Discovery

3000 BC

First isolation

Vannoccio Biringuccio (1540)

Physical properties

Phase

solid

Density (near r.t.)

6.697 g·cm⁻³

Liquid density at m.p.

6.53 g·cm⁻³

Melting point

903.78 K1167.13 °F 630.63 °C, ,

Boiling point

2889 °F 1587 °C, 1860 K,

Heat of fusion

19.79 kJ·mol⁻¹

Heat of vaporization

193.43 kJ·mol⁻¹

Molar heat capacity

25.23 J·mol⁻¹·K⁻¹

Vapor pressure

P (Pa)

100

1 k

10 k

100 k

at T (K)

807

876

1011

1219

1491

1858

Atomic properties

Oxidation states

5, 3, -3

Electronegativity

2.05 (Pauling scale)

Ionization energies
(more)

1st: 834 kJ·mol⁻¹

2nd: 1594.9 kJ·mol⁻¹

3rd: 2440 kJ·mol⁻¹

Atomic radius

140 pm

Reactions of ions Sb^III and Sb^V

Hydrolysis reaction. Solution of salts Sb^III and Sb^V very dilute by water. The white precipitates of basic salt form:

[SbCl₆]^3-+ H₂O SSbOCl¯ + 5Cl^– + 2H⁺;

[SbCl₆]^– + 2H₂O SSbО₂Cl¯ + 5Cl^– + 4H⁺.

The ions of Ві³⁺, Sn²⁺ ions interfere with the exposure of ions of Sb ions.

SbOCl is dissolved (better by heating) in solution of chloridic acid, tartratic acid and its salts:

SbOCl + 2НCl + Cl^– ® [SbCl₄]^– + H₂O;

SbOCl + Н₂С₄Н₄О₆ ® [SbО(С₄Н₄О₆)]^– + 2Н⁺ + Cl^–

Or SbOCl + Н₂С₄Н₄О₆ ® [SbОН(С₄Н₄О₆)] + Н⁺ + Cl^–.

SbО₂Cl is dissolved in excess of chloridic acid, tartratic acid and its salts.

Reaction performance. Some drops of an investigated solution dilute by water. If there are Sb^III or Sb^V ions the white amorphous precipitates form.

Sodium thiosulphate Na₂S₂O₃ with ions Sb (ІІІ) in acidic medium forms red precipitate Sb₂ОS₂ („antimonic cinnabar”):

SbCl₃ + 2Na₂S₂O₃ + 3H₂O S Sb₂ОS₂¯ + 2Na₂SO₄ + 6HCl.

The ions of Ві^{3 +}, Cu^{2 +}, Hg^{2 +} ions interfere with the exposure of ions of Sb ions.

Reaction performance. To 3-4 drops of the acidic investigated solution add 2-3 drops of a Sodium thiosulphate solution. If there are ions Sb (ІІІ) the red precipitate is formed.

Reaction with crystal violet (diamond green). The crystal violet with ions [SbCl₆]^– form ionic associates (ionic pairs) of violet colour; it is well dissolved in toluene, benzene and other solvents. Reaction has high specificity and gives us chance to determine Sb in the presence of the majority of ions, except ions Hg₂²⁺ and Hg²⁺.

Reaction performance. To 2-3 drops of an investigated solution add 3-4 drops of concentrated HCl and one drop of solution SnCl₂ for reduction Sb (V) to Sb^III. After that add a few crystal NaNO₂ (or one drop of the sated solution) for formation [SbCl₆]^–. Excess of Sodium nitrite resolve by addition 1-2 drops of solution urea. After the resolvetion of NaNO₂ (finish of gas isolation) add 2-3 drops of dye solution, 5-6 drops of toluene or benzene, and this solution is mixed. In the presence of Sb ions the organic layer is painted in violet colour.

Crystal violet it is possible to replace on the methyl violet or diamond green. With methyl violet colouring of an organic layer violet, with diamond green it is blue-green.

Sodium sulphide Na₂S (pharmacopeia’s reaction) forms with connections Sb^III and Sb^V orange-red precipitates of sulphides:

2 [SbCl₆]^3- + 3Na₂S S Sb₂S₃¯ + 6Na⁺ + 12Cl^–;

2 [SbCl₆]^– + 5Na₂S S Sb₂S₅¯ + 10Na⁺ + 12Cl^–.

Precipitates of these sulphides are dissolved in alkalis.

Reaction performance. To 4-5 drops of an investigated solution add a few crystal of Sodium-Potassium tartratic and dissolve it by heating, and then cool. To the received solution add some drops of Sodium sulphide solution. If there are ions of Sb^III, Sb^V the orange-red precipitates forms.

Tetrathreemolybdatophosphatic acid monohydrate H₃[P(Mo₃O₁₀)₄]×H₂O. Molybdenum (VI) is reduced by different reducers (including compounds Sb^III) with formation of products of dark blue colour.

The ions of Sn²⁺, other ions (reducers) interfere with the exposure of ions of Sb ions.

Reaction performance. On a strip of the filtering paper put some drops of 5 % solution of H₃[P(Mo₃O₁₀)₄]×H₂O and it is dried. After that on it put a drop of an investigated solution. After that a paper is maintained some minutes in water steams. In the presence of compounds Sb^III the paper is painted in dark blue colour.

Zinc, iron, aluminium, magnesium, tin reduce cations Sb (ІІІ) and Sb (V) in the acidic medium to metal Sb (black precipitate):

Sb³⁺ + 3Zn 2Sb¯ + 3Zn²⁺.

Reaction performance. In a test tube place 3-5 drops of an investigated solution, add 3-4 drops of 2 mol/L chloric acid solution and a peace of metal aluminium or zinc, or iron. If there are Sb ions the metal surface blackens.

The scheme of V analytical group cations analysis