TITRIMETRIC METHODS OF ANALYSIS

Titrimetric Methods of Analysis

Titrimetry, in which we measure the volume of a reagent reacting stoichiometrically with the analyte, first appeared as an analytical method in the early eighteenth century. Unlike gravimetry, titrimetry initially did not receive wide acceptance as an analytical technique. Many prominent late-nineteenth century analytical chemists preferred gravimetry over titrimetry and few of the standard texts from that era include titrimetric methods. By the early twentieth century, however, titrimetry began to replace gravimetry as the most commonly used analytical method. Interestingly, precipitation gravimetry developed in the absence of a theory of precipitation. The relationship between the precipitates mass and the mass of analyte, called a gravimetric factor, was determined experimentally by taking known masses of analyte (an external standardization). Gravimetric factors could not be calculated using the precipitation reactionÕs stoichiometry because chemical

formulas and atomic weights were not yet available! Unlike gravimetry, the growth and acceptance of titrimetry required a deeper understanding of stoichiometry, thermodynamics, and chemical

equilibria. By the early twentieth century the accuracy and precision of titrimetric methods were comparable to that of gravimetry, establishing titrimetry as an accepted analytical technique.

Titrimetric methods are classified into four groups based on the type of reaction involved. These groups are acid–base titrations, in which an acidic or basic titrant reacts with an analyte that is a base or an acid; complexometric titrations involving a metal–ligand complexation reaction; redox titrations, where the titrant is an oxidizing or reducing agent; and precipitation titrations, in which the analyte and titrant react to form a precipitate. Despite the difference in chemistry, all titrations share several common features, providing the focus for this section.

Based on the measurement of the amount of reagent that combined with an analyte. Titrimetic methods are widely used for routine analysis because they are rapid, convenient, accurate, and readily automated. There are such variants of titrimetry:

1.  Volumetric. Volume of reagent solution required for a complete reaction.

2.  Gravimetric. Weight of reagent required for a complete reaction.

3.  Coulometric. Time/current required for complete oxidation or reducing of an analyte.

Requirements to chemical reaction used in titrimetric methods of analysis:

1. Reaction between reagent and analyte must be specific. Titrant caot react with impurities or additions of analyte solution.

2. Reaction must be stoichiometric.

3. Titrant must react rapidly with the analyte so that the time required between additions of reagent is minimised.

4. Titrant must react more or less completely with the analyte so that satisfactory end points are realised.

5. Undergo a selective reaction with the analyte that can be described by simple balanced equation. Equilibrium constant must have high value.

Titration is a process in which a standard reagent (titrant) is added to a solution of an analyte until the reaction between the analyte and reagent is judged to be complete. Titration can be:

1) direct titration – titrant add to an analyte solution and react with determined substrance;

2) back-titration – is a process in which the excess of a standard solution used to react with an analyte is determined by titration with a second standard solution. Back-titrations are required when the reagent is slow or when the standard solution lacks stability. For example:

CaCO₃ + HCl = CaCl₂ + H₂O + CO₂

surplus (titrant 1)

HCl + NaOH = NaCl + H₂O

residue                titrant 2

 

3) substitute-titration – is a process in which a standard solution used to react with an additional (substitute) substance, amount of which is equivalent an analyte amount. Substitute-titrations are required when the analytes are unstable substance or when is impossible to indicate the equivalent (end) point in direct reaction. For example:

 

CrCl₂ + FeCl₃ = CrCl₃ + FeCl₂

     analyte                    substitute

5FeCl₂ + KMnO₄ + HCl = 5FeCl₃ + KCl + MnCl₂ + 4H₂O

 

Equivalence point is the point where sufficient titrant has been added to be stoichiometrically equivalent to the amount of analyte. The equivalence point of a titration is a theoretical point that caot be determined experimentally, but can be determined experimentally the end point.

End point is the point in a titration when a physical change that is associated with the condition of chemical equivalence occurs. We can estimate its position by observing some physical changes with various indicating techniques:

a)  without any special means. The visible changes occur in titrated solution – change of titrant or analyte colour, turbidity arise, precipitation formation;

b)               with internal indicator using. The special chemical substances called indicators are added to the analyte solution. Typical indicator changes include the appearance or disappearance of a colour, a change in colour, or the appearance or disappearance of turbidity;

c)  with instruments. This instruments respond to certain properties of the solution that change in a characteristic way during the titration.

The difference in volume between the equivalence point and the end point is the titration error.

A standard solution (or titrant) is a reagent of exactly known concentration that is used in a titrimetric analysis. Standard solutions are the main participants in all titrimetric methods of analysis. The titrant solutions must be of known composition and concentration. Ideally, we would like to start with a primary standard material.

Primary standard is an highly purified compound that serves as the reference materials for a titrimetric method of analysis. Important requirements for a primary standard are:

1. High purity.

2. Stability toward air.

3. Absence of hydrate water so that the composition of the solid does not change with variations in relative humidity.

4. Ready availability at modest cost.

5. Reasonable solubility in the titration medium.

6. Reasonable large molar mass so that the relative error associated with weighing the standard is minimised.

A secondary standard is compound whose purity has been established by chemical analysis and serves as the reference material to a titrimetric method of analysis.

The concentration of the standard solutions can be established by two basic methods:

1. Direct method – a carefully weighed quantity of a primary standard is dissolved in a suitable solvent and diluted to an exactly known volume in a volumetric flask. A made solution is referred to as a primary standard solution (titrant).

2. Standardisation – concentration of a volumetric solution (titrant) is detrmined by using to titrate

1) a weighed quantity of a primary standard,

2) a weighed quantity of a secondary standard,

3) a measured volume of another standard solution.

A titrant that is standardised against a secondary standard or against another standard solution is referred to as a secondary standard solution (titrant).

Equivalence Points and End Points

For a titration to be accurate we must add a stoichiometrically equivalent amount of titrant to a solution containing the analyte. We call this stoichiometric mixture the equivalence point. Unlike precipitation gravimetry, where the precipitant is added in excess, determining the exact volume of titrant needed to reach the equivalence point is essential. The product of the equivalence point volume, V_eq, and the titrant’s concentration, C_T, gives the moles of titrant reacting with the analyte.

Knowing the stoichiometry of the titration reaction(s), we can calculate the moles of analyte.

Unfortunately, in most titrations we usually have no obvious indication that the equivalence point has been reached. Instead, we stop adding titrant when we reach an end point of our choosing. Often this end point is indicated by a change in the color of a substance added to the solution containing the analyte. Such substances are known as indicators. The difference between the end point volume and the equivalence point volume is a determinate method error, often called the titration error. If the end point and equivalence point volumes coincide closely, then the titration error is insignificant and can be safely ignored. Clearly, selecting an appropriate end point is critical if a titrimetric method is to give accurate results.

 

Units of concentration of standard solutions

The concentration of standard solutions (titrants) are generally expressed in units of either molarity (C_M, or M) or normality (C_N, or N).

Molarity (M) – is the number of moles of a material per liter of solution.

Normality (N) – is the number of species equivalents per liter of solution.

Sometime is used also one unite of concentration – titer (T). Titer established the relationship between volume of titrant and amount of analysed substance present. The most commonly titer is in units of mg analysed substance per ml of titrant. This system was developed to assist in doing routine calculations. It reduces the amount of time and training for technicians.

Equivalents law

Titrimetry is based on equivalents law:

N_a·V_a = N_s·V_s,

or number of analyte equivalent present = number of standard reagent added,

or one equivalent of one material will react exactly with one equivalent of another

The weight of one equivalent of a compound depends on reference to a chemical reaction in which that compound is a participant. Similarly, the normality of a solution caever be specified without knowledge about how the solution will be used. Equivalent value is based on the type of reaction and the reactants:

1. One equivalent weight of a substance participating in a neutralisation reaction is that amount of substance that either react with or supplied one mol of hydrogen ions in that reaction.

2. One equivalent weight of a participant in an oxidation-reduction reaction is that amount that directly or indirectly produces or consumer one mol of electrons.

3. The equivalent weight of a participant in a precipitation or a complex-formation reaction is that weight which or provides one mole of the univalent reacting cation.

 

Volume as a Signal

Almost any chemical reaction can serve as a titrimetric method provided that three conditions are met. The first condition is that all reactions involving the titrant and analyte must be of known stoichiometry. If this is not the case, then the moles of titrant used in reaching the end point cannot tell us how much analyte is in our sample. Second, the titration reaction must occur rapidly. If we add titrant at a rate that is faster than the reaction’s rate, then the end point will exceed the equivalence point by a significant amount. Finally, a suitable method must be available for determining the end point with an acceptable level of accuracy. These are significant limitations and, for this reason, several titration strategies are commonly used. A simple example of a titration is an analysis for Ag+ using thiocyanate, SCN–, as a titrant.

This reaction occurs quickly and is of known stoichiometry. A titrant of SCN– is easily prepared using KSCN. To indicate the titration’s end point we add a small amount of Fe³⁺ to the solution containing the analyte. The formation of the redcolored Fe(SCN)²⁺ complex signals the end point. This is an example of a direct titration since the titrant reacts with the analyte.

If the titration reaction is too slow, a suitable indicator is not available, or there is no useful direct titration reaction, then an indirect analysis may be possible. Suppose you wish to determine the concentration of formaldehyde, H₂CO, in an aqueous solution. The oxidation of H2CO by I₃^–

is a useful reaction, except that it is too slow for a direct titration. If we add a known amount of I₃^–, such that it is in excess, we can allow the reaction to go to completion.

The I₃^– remaining can then be titrated with thiosulfate, S₂O₃^2–.

This type of titration is called a back titration.

Calcium ion plays an important role in many aqueous environmental systems. A useful direct analysis takes advantage of its reaction with the ligand ethylenediaminetetraacetic acid (EDTA), which we will represent as Y^4–.

Unfortunately, it often happens that there is no suitable indicator for this direct titration. Reacting Ca²⁺ with an excess of the Mg²⁺–EDTA complex

releases an equivalent amount of Mg²⁺. Titrating the released Mg²⁺ with EDTA

gives a suitable end point. The amount of Mg2+ titrated provides an indirect measure of the amount of Ca2+ in the original sample. Since the analyte displaces a species that is then titrated, we call this a displacement titration.

When a suitable reaction involving the analyte does not exist it may be possible to generate a species that is easily titrated. For example, the sulfur content of coal can be determined by using a combustion reaction to convert sulfur to sulfur dioxide.

Passing the SO₂ through an aqueous solution of hydrogen peroxide, H2O2,

produces sulfuric acid, which we can titrate with NaOH,

providing an indirect determination of sulfur.

 

Titrimetric Methods of Analysis are based on the measurement of the amount of reagent that combined with an analyte. Titrimetic methods are widely used for routine analysis because they are rapid, convenient, accurate, and readily automated. There are such variants of titrimetry:

4.  Volumetric. Volume of reagent solution required for a complete reaction.

5.  Gravimetric. Weight of reagent required for a complete reaction.

6.  Coulometric. Time/current required for complete oxidation or reducing of an analyte.

Titrimetric methods are classified into four groups based on the type of reaction involved. These groups are

– acid–base titrations, in which an acidic or basic titrant reacts with an analyte that is a base or an acid;

– complexometric titrations involving a metal–ligand complexation reaction;

– redox titrations, where the titrant is an oxidizing or reducing agent;

– precipitation titrations, in which the analyte and titrant react to form a precipitate.

 

Classification of titrimetric analysis methods

 

Requirements to chemical reaction used in titrimetric methods of analysis:

6. Reaction between reagent and analyte must be specific. Titrant caot react with impurities or additions of analyte solution.

7. Reaction must be stoichiometric.

8. Titrant must react rapidly with the analyte so that the time required between additions of reagent is minimised.

9. Titrant must react more or less completely with the analyte so that satisfactory end points are realised.

10. Undergo a selective reaction with the analyte that can be described by simple balanced equation. Equilibrium constant must have high value.

 

Titration is a process in which a standard reagent (titrant) is added to a solution of an analyte until the reaction between the analyte and reagent is judged to be complete. Titration can be:

4) direct titration – titrant add to an analyte solution and react with determined substrance;

A simple example of a titration is an analysis for Ag⁺ using thiocyanate, SCN^–, as a titrant.

AgNO₃ + KSCN = AgSCN¯ + KNO₃

 

This reaction occurs quickly and is of known stoichiometry. A titrant of SCN^– is easily prepared using KSCN. To indicate the titration’s end point we add a small amount of Fe³⁺ to the solution containing the analyte. The formation of the redcolored Fe(SCN)²⁺ complex signals the end point.

5) back-titration – is a process in which the excess of a standard solution used to react with an analyte is determined by titration with a second standard solution. Back-titrations are required when the reagent is slow or when the standard solution lacks stability. For example: determination the concentration of formaldehyde, H2CO, in an aqueous solution. The oxidation of H₂CO by I^–

H₂CO + 3NaOH + I₂ = HCOONa + 2NaI + 2H₂O

is a useful reaction, except that it is too slow for a direct titration. If we add a known amount of I₂, such that it is in excess, we can allow the reaction to go to completion. The I₂ remaining can then be titrated with thiosulfate, S₂O₃^2–.

I₂ + 2Na₂S₂O₃ = Na₂S₄O₆ + 2NaI

6) substitute-titration (displacement titration) – is a process in which a standard solution used to react with an additional (substitute) substance, amount of which is equivalent an analyte amount. Substitute-titrations (displacement titration) are required when the analytes are unstable substance or when is impossible to indicate the equivalent (end) point in direct reaction. For example: calcium ion plays an important role in many aqueous environmental systems. A useful direct analysis takes advantage of its reaction with the ligand ethylenediaminetetraacetic acid (EDTA), which we will represent as Y^4–.

Ca²⁺ + Y^4– « CaY^2–

Unfortunately, it often happens that there is no suitable indicator for this direct titration. Reacting Ca²⁺ with an excess of the Mg²⁺–EDTA complex

Ca²⁺ + MgY^2– « CaY^2– + Mg²⁺

releases an equivalent amount of Mg²⁺. Titrating the released Mg²⁺ with EDTA

Mg²⁺ + Y^4– « MgY^2–

gives a suitable end point. The amount of Mg²⁺ titrated provides an indirect measure of the amount of Ca²⁺ in the original sample.

 

When a suitable reaction involving the analyte does not exist it may be possible to generate a species that is easily titrated. For example, the sulfur content of coal can be determined by using a combustion reaction to convert sulfur to sulfur dioxide.

S(s) + O₂(g) ® SO₂(g)

Passing the SO₂ through an aqueous solution of hydrogen peroxide, H₂O₂,

SO₂(g) + H₂O₂ ® H₂SO₄

produces sulfuric acid, which we can titrate with NaOH,

H₂SO₄ + 2NaOH ® Na₂SO₄ + 2H₂O

providing an indirect determination of sulfur.

Equivalence point is the point where sufficient titrant has been added to be stoichiometrically equivalent to the amount of analyte. The equivalence point of a titration is a theoretical point that caot be determined experimentally, but can be determined experimentally the end point. The product of the equivalence point volume, Veq, and the titrant’s concentration, C_T, gives the moles of titrant reacting with the analyte.

Moles titrant =

Veq ´ C_T

Knowing the stoichiometry of the titration reaction(s), we can calculate the moles of analyte.

Unfortunately, in most titrations we usually have no obvious indication that the equivalence point has been reached. Instead, we stop adding titrant when we reach an end point of our choosing. End point is the point in a titration when a physical change that is associated with the condition of chemical equivalence occurs. We can estimate its position by observing some physical changes with various indicating techniques:

d)               without any special means. The visible changes occur in titrated solution – change of titrant or analyte colour, turbidity arise, precipitation formation;

e)  with internal indicator using. The special chemical substances called indicators are added to the analyte solution. Typical indicator changes include the appearance or disappearance of a colour, a change in colour, or the appearance or disappearance of turbidity;

f)   with instruments. This instruments respond to certain properties of the solution that change in a characteristic way during the titration.

The difference between the end point volume and the equivalence point volume is a determinate method error, often called the titration error. If the end point and equivalence point volumes coincide closely, then the titration error is insignificant and can be safely ignored. Clearly, selecting an appropriate end point is critical if a titrimetric method is to give accurate results.

Titration Curves

To find the end point we monitor some property of the titration reaction that has a well-defined value at the equivalence point. For example, the equivalence point for a titration of HCl with NaOH occurs at a pH of 7.0. We can find the end point, therefore, by monitoring the pH with a pH electrode or by adding an indicator that changes color at a pH of 7.0.

A titration curve provides us with a visual picture of how a property, such as pH, changes as we add titrant (Figure 9.1). We can measure this titration curve experimentally by suspending a pH electrode in the solution containing the analyte, monitoring the pH as titrant is added. As we will see later, we can also calculate the expected titration curve by considering the reactions responsible for the change in pH. However we arrive at the titration curve, we may use it to evaluate an indicator’s likely titration error. For example, the titration curve in Figure 9.1 shows us that an end point pH of 6.8 produces a small titration error. Stopping the titration at an end point pH of 11.6, on the other hand, gives an unacceptably large titration error.

Figure 9.1. Acid–base titration curve for 25.0 mL of 0.100 M HCl with 0.100 M NaOH.

The titration curve in Figure 9.1 is not unique to an acid–base titration. Any titration curve that follows the change in concentration of a species in the titration reaction (plotted logarithmically) as a function of the volume of titrant has the same general sigmoidal shape.

Concentration is not the only property that may be used to construct a titration curve. Other parameters, such as temperature or the absorbance of light, may be used if they show a significant change in value at the equivalence point. Many titration reactions, for example, are exothermic. As the titrant and analyte react, the temperature of the system steadily increases. Once the titration is complete, further additions of titrant do not produce as exothermic a response, and the change in temperature levels off. The titration curve contains two linear segments, the intersection of which marks the equivalence point.

A standard solution (or titrant) is a reagent of exactly known concentration that is used in a titrimetric analysis. Standard solutions are the main participants in all titrimetric methods of analysis. The titrant solutions must be of known composition and concentration. Ideally, we would like to start with a primary standard material.

Primary standard is an highly purified compound that serves as the reference materials for a titrimetric method of analysis. Important requirements for a primary standard are:

7. High purity.

8. Stability toward air.

9. Absence of hydrate water so that the composition of the solid does not change with variations in relative humidity.

10. Ready availability at modest cost.

11. Reasonable solubility in the titration medium.

12. Reasonable large molar mass so that the relative error associated with weighing the standard is minimised.

A secondary standard is compound whose purity has been established by chemical analysis and serves as the reference material to a titrimetric method of analysis.

The concentration of the standard solutions can be established by two basic methods:

3. Direct method – a carefully weighed quantity of a primary standard is dissolved in a suitable solvent and diluted to an exactly known volume in a volumetric flask. A made solution is referred to as a primary standard solution (titrant).

4. Standardisation – concentration of a volumetric solution (titrant) is detrmined by using to titrate

4) a weighed quantity of a primary standard,

5) a weighed quantity of a secondary standard,

6) a measured volume of another standard solution.

A titrant that is standardised against a secondary standard or against another standard solution is referred to as a secondary standard solution (titrant).

 

Units of concentration of standard solutions

The concentration of standard solutions (titrants) are generally expressed in units of either molarity (C_M, or M) or normality (C_N, or N).

Molarity (M) – is the number of moles of a material per liter of solution.

Normality (N) – is the number of species equivalents per liter of solution.

Sometime is used also one unite of concentration – titer (T). Titer established the relationship between volume of titrant and amount of analysed substance present. The most commonly titer is in units of mg analysed substance per ml of titrant. This system was developed to assist in doing routine calculations. It reduces the amount of time and training for technicians.

Equivalents law

Titrimetry is based on equivalents law:

N_a·V_a = N_s·V_s,

or number of analyte equivalent present = number of standard reagent added,

or one equivalent of one material will react exactly with one equivalent of another

The weight of one equivalent of a compound depends on reference to a chemical reaction in which that compound is a participant. Similarly, the normality of a solution caever be specified without knowledge about how the solution will be used. Equivalent value is based on the type of reaction and the reactants:

4. One equivalent weight of a substance participating in a neutralisation reaction is that amount of substance that either react with or supplied one mol of hydrogen ions in that reaction.

5. One equivalent weight of a participant in an oxidation-reduction reaction is that amount that directly or indirectly produces or consumer one mol of electrons.

6. The equivalent weight of a participant in a precipitation or a complex-formation reaction is that weight which or provides one mole of the univalent reacting cation.

 

Calculations in titrimetric method of analysis

 

 

Indicators of Titrimetry Methods

Indicators are the chemical compounds, which give some external effect attached to concentrations of reactive species according to equivalence point. This external effect can be accompanied by change, appearance or disappearance of colouring, and formation of slightly soluble compounds (precipitate formation).

On appliance technique indicators are external and internal.

Internal indicators are introduced into titrated solution. An end point install on changes of colour of analysed mixture.

The external indicators are used when internal indicators using is impossible. Reaction with external indicators runs out of analysed mixture. Some drops of analysed solution put on peace of filter paper, impregnated with indicator, or mix with drop of indicator solution on porcelain plate.

For effect the reactions appearance indicators are reversible and unreversible.

Reversible indicators – changes the colour can be repeated many times as changes the system state.

         Unreversible indicators – colour changes ones with destruction of indicator molecule. The unreversible indicators are less comfortable and thinly use.

 

Acid-Basic Titration

The earliest acid–base titrations involved the determination of the acidity or alkalinity of solutions, and the purity of carbonates and alkaline earth oxides. Before 1800, acid–base titrations were conducted using H₂SO₄, HCl, and HNO₃ as acidic titrants, and K₂CO₃ and Na₂CO₃ as basic titrants. End points were determined using visual indicators such as litmus, which is red in acidic solutions and blue in basic solutions, or by observing the cessation of CO₂ effervescence wheeutralizing CO₃^2–. The accuracy of an acid–base titration was limited by the usefulness of the indicator and by the lack of a strong base titrant for the analysis of weak acids.

The utility of acid–base titrimetry improved when NaOH was first introduced as a strong base titrant in 1846. In addition, progress in synthesizing organic dyes led to the development of many new indicators. Phenolphthalein was first synthesized by Bayer in 1871 and used as a visual indicator for acid–base titrations in 1877. Other indicators, such as methyl orange, soon followed. Despite the increasing availability of indicators, the absence of a theory of acid–base reactivity made selecting a proper indicator difficult.

Developments in equilibrium theory in the late nineteenth century led to significant improvements in the theoretical understanding of acid–base chemistry and, in turn, of acid–base titrimetry. Sørenson’s establishment of the pH scale in 1909 provided a rigorous means for comparing visual indicators. The determination of acid–base dissociation constants made the calculation of theoretical titration curves possible, as outlined by Bjerrum in 1914. For the first time a rational method existed for selecting visual indicators, establishing acid–base titrimetry as a useful alternative to gravimetry.

This is a quick and accurate method for determining acidic or basic substances in many samples. This method enable to determine some inorganic and hundred of organic acids and bases of different types; frequently organic compounds are titrated in waterless environment. The used titrant is typically a strong acid or base. The sample species can be either a strong or weak acid or base. The neutralisation method based on acid-basic reactions (exchange reactions by protons), which one can be expressed by general scheme:

HA + BOH = B⁺ + A^– + H₂O

         Titrations according to the applied titrant are

1)  acidimetric (titrants are the acids solutions) – uses for determination of strong and weak bases, salts of strong bases and weak acids and organic compounds;

2)  alkalimetric (titrants are solutions of bases) – uses for titration of strong and weak acids, sour salts, salts of strong acids and weak bases, organic compounds having acidic disposition (acids, phenols).

 

Standard Titrants

I.    Bases.

NaOH is the most common although KOH can be serve the same purpose. There are not primary standards.

Primary standards for bases standardisation are weak acids:

oxalic acid H₂C₂O₄∙2H₂O, benzoic acid C₆H₅COOH, succinic acid HOOC(CH₂)₂COOH, potassium hydrogen phthalate KHC₈H₄O₄, potassium hydrogen iodate KH(IO₃)₂, potassium hydrogen tartrate KHC₄H₄O₆.

II. Acids.

More frequently are used HCl and H₂SO₄. There are not primary standards too. Primary standards for acids standardisation are weak bases:

borax Na₂B₄O₇´10H₂0, TRIS (hydroxymethyl-aminomethane) (HOCH₂)₂CNH₂, sodium carbonate Na₂CO₃, mercury oxide HgO, sodium oxalate Na₂C₂O₄, potassium iodate KIO₃.

Standardization of НСl solution on sodium tetraborate.

§  Weigh exact shot of Na₂B₄O₇×5H₂O or Na₂B₄O₇×10H₂O and place it in a measured flask, dissolve in hot water, after a solution is cooled and diluted of solution by water to necessary volume and it is mixed.

§  In a flask for titration place an aliquot of prepared primary standard solution Na₂B₄O₇×5H₂O or Na₂B₄O₇×10H₂O, add some drops of the methyl orange. The received solution is titrated by solution of НСl to change of colour with yellow to orange with a rose shade.

§  By 3-4 results of titration calculate average volume of used titrant and calculate concentration of hydrochloric acid.

 

 

Standardization of HCl solution on sodium carbonate

§  In a flask for titration place exact shot of sodium carbonate, dissolve iecessary volume of water, add some drops methyl orange and titrate this solution by chloric acid.

§   Such titration repeat for 3-4 times. Each time calculate concentration of HCl:

§  By 3-4 results of titration calculate average concenration of chloric acid.

 

 

 

Standardization of NaOH solution on oxalic acid.

§  Weigh exact shot of H2C2O4×2H2O and place it in a measured flask, dissolve in hot water, after a solution is cooled and diluted of solution by water to necessary volume and it is mixed.

§  In a flask for titration place an aliquot of prepared primary standard solution H2C2O4×2H2O , add some drops of the  phenolphthalein. The received solution is titrated by solution of NaOH to change of colourless to rose (or red).

§  By 3-4 results of titration calculate average volume of used titrant and calculate concentration of NaOH.

 

 

 

 

 

Titration Curves

For an acid–base titration, the equivalence point is characterized by a pH level that is a function of the acid–base strengths and concentrations of the analyte and titrant. The pH at the end point, however, may or may not correspond to the pH at the equivalence point. To understand the relationship between end points and equivalence points we must know how the pH changes during a titration.

Acid-base property of titration system changes accordingly to proportion (ratio) of protolytes in mixture. Dependency on correlation of protolytes force the equivalence point can be ieutral, alkaline or acidic environment. Change the pH value during titration process, or dependence the pH value on concentration of titrated electrolytes, show the titration curves. A titration curve is a graph of the pH as a function of the amount of titrant (acid or base) added. This still results in four types of titration for simple acids or bases:

         Strong acid vs. strong base

Strong acid vs. weak base

Strong base acid vs. strong acid

Strong base vs. weak base

Strong Acid-Strong Base Titrations

Here is an example of a titration curve, produced when a strong base is added to a strong acid. This curve show how pH varies as 0,100 M NaOH is added to 50,0 ml of 0,100 M HCl.

For the reaction of a strong base with a strong acid the only equilibrium reaction of importance is

NaOH + HCl = NaCl + H₂O

or, in ionic form

H⁺ + OH^– = H₂O                                        (1)

The first task in constructing the titration curve is to calculate the volume of NaOH needed to reach the equivalence point. At the equivalence point we know from reaction that

Moles HCl = moles NaOH

or

M_aV_a = M_bV_b

where the subscript ‘a’ indicates the acid, HCl, and the subscript ‘b’ indicates the base, NaOH. The volume of NaOH needed to reach the equivalence point, therefore, is

 

 

The equivalence point of the titration is the point at which exactly enough titrant has been added to react with all of the substance being titrated with no titrant left over. In other words, at the equivalence point, the number of moles of titrant added so far corresponds exactly to the number of moles of substance being titrated according to the reaction stoichiometry. (In an acid-base titration, there is a 1:1 acid:base stoichiometry, so the equivalence point is the point where the moles of titrant added equals the moles of substance initially in the solution being titrated.)

Notice that the pH increases slowly at first, then rapidly as it nears the equivalence point. At the equivalence point, the pH = 7.00 for strong acid-strong base titrations. However, in other types of titrations, this is not the case.

Titrations Involving a Weak Acid

There are three major differences between this curve (in blue) and the one we saw before (in black):

1.     The weak-acid solution has a higher initial pH.

2.     The pH rises more rapidly at the start, but less rapidly near the equivalence point.

3.     The pH at the equivalence point does not equal 7.00. The equivalence point for a weak acid-strong base titration has a pH > 7.00.

         For a strong acid-weak base or weak acid-strong base titration, the pH will change rapidly at the very beginning and then have a gradual slope until near the equivalence point. The gradual slope results from a buffer solution being produced by the addition of the strong acid or base, which resists rapid change in pH until the added acid or base exceeds the buffer’s capacity and the rapid pH change occurs near the equivalence point.

Titration curve of a weak acid being titrated by a strong base:

 

Here, 0,100 M NaOH is being added to 50,0 ml of 0,100 M acetic acid.

Titrations Involving a Weak Base

Titration curve of a weak base being titrated by a strong acid:

 

Here, 0,100 M HCl is being added to 50,0 ml of 0,100 M ammonia solution.

As in the weak acid-strong base titration, there are three major differences between this curve (in blue) and a strong base-strong acid one (in black): (Note that the strong base-strong acid titration curve is identical to the strong acid-strong base titration, but flipped vertically.)

         The weak-acid solution has a lower initial pH.

1.     The pH drops more rapidly at the start, but less rapidly near the equivalence point.

2.     The pH at the equivalence point does not equal 7.00. The equivalence point for a weak base-strong acid titration has a pH < 7.00.

Titrations of Polyprotic Acids

An example of a polyprotic acid is H₂CO₃ which neutralises in two steps:

H₂CO₃  + OH^–  « H₂O + HCO₃^–

HCO₃^–  + OH^–  « H₂O + CO₃^2–

The titration curve for these reactions will look like this, with two equivalence points.

 

Uses of Titrations

Use titration data or a titration curve to calculate reaction quantities such as the concentration of the substance being titrated.

The most common use of titrations is for measuring unknown concentrations. This is done by titrating a known volume of the unknown solution with a solution of known concentration (where the two react in a predictable manner) and finding the volume of titrant needed to reach the equivalence point using some method appropriate to the particular reaction. Then, the volume and concentration of titrant can be used to calculate the moles of titrant added, which, when used with the reaction stoichiometry, gives the number of moles of substance being titrated. Finally, this quantity, along with the volume of substance being titrated, gives the unknown concentration.

         For acid-base titrations, the equivalence point can be found very easily. A pH meter is simply placed in the solution being titrated and the pH is measured after various volumes of titrant have been added to produce a titration curve. The equivalence point can then be read off the curve.

In the same way, knowing the equivalence point can also be used to calculate other unknown quantities of interest in acid base reactions, such as concentration of titrant or volume of solution being titrated, provided that enough other information is known to perform the calculations.

 

Nonaqueous Titrations

Nonaqueous titration is the special technique of the acid-base titration. Acids with dissociation constant value less than 1×10^–7 (pK_a > 7) and bases with dissociation constant value less than 1×10^–7 (pK_b > 7) caot be titrated in water solutions. The ionisation degree of such weak acid and weak bases is comparable with indicator ionisation degree. During titration of aqueous solutions of these compounds caot be indicated equivalent point.

For titration of weak acid and weak bases are used waterless (nonaqueous) solvents, which intensify its acidic/basic properties. Indeed, water is the most common solvent in acid–base titrimetry. When considering the utility of a titration, however, the solvent’s influence cannot be ignored.

 

Autoprotolysis of solvents

Many solvents autoprotolysise like as water:

2C₂H₅OH « C₂H₅OH₂⁺ + C₂H₅O^–

2H₂N–(CH₂)₂–NH₂ « R–NH₃⁺ + R–NH^–

2(CH₃)₂SO « (CH₃)₂SOH⁺ + CH₃–SO–CH₂^–

The dissociation, or autoprotolysis constant for a solvent, SH, relates the concentration of the protonated solvent, SH₂⁺, to that of the deprotonated solvent, S^–. For amphoteric solvents, which can act as both proton donors and proton acceptors, the autoprotolysis reaction is

2SH « SH₂⁺ + S^–

with an equilibrium constant of

K_s = [SH₂⁺][S^–]

Remember, that water autoprolysis constant K_S = K_W = 1×10^–14.

 

You should recognize that K_w is just the specific form of K_s for water. The pH of a solution is now seen to be a general statement about the relative abundance of protonated solvent

pH = –log[SH₂⁺]

where the pH of a neutral solvent is given as

Perhaps the most obvious limitation imposed by K_s is the change in pH during a titration. To see why this is so, let’s consider the titration of a 50 mL solution of 10^–4 M strong acid with equimolar strong base. Before the equivalence point, the pH is determined by the untitrated strong acid, whereas after the equivalence point the concentration of excess strong base determines the pH. In an aqueous solution the concentration of H⁺ when the titration is 90% complete is

 = 5.3´10^–6 M

corresponding to a pH of 5.3. When the titration is 110% complete, the concentration of OH^– is

or a pOH of 5.3. The pH, therefore, is

pH = pK_w – pOH = 14.0 – 5.3 = 8.7

The change in pH when the titration passes from 90% to 110% completion is

DpH = 8.7 – 5.3 = 3.4

If the same titration is carried out in a nonaqueous solvent with a K_s of 1.0´10^–20, the pH when the titration is 90% complete is still 5.3. However, the pH when the titration is 110% complete is now

pH = pK_s – pOH = 20.0 – 5.3 = 14.7

In this case the change in pH of

DpH = 14.7 – 5.3 = 9.4

is significantly greater than that obtained when the titration is carried out in water. Figure 1 shows the titration curves in both the aqueous and nonaqueous solvents. Nonaqueous solvents also may be used to increase the change in pH when titrating weak acids or bases (Figure 2).

 

	Figure 1. Titration curves for 50.00 mL of 10–4 M HCl with 10–4 M NaOH in (a) water, Kw = l´10–14, and (b) nonaqueous solvent, Ks = 1´10–20.
	Figure 2. Titration curves for 50.00 mL of 0.100 M weak acid (pKa = 11) with 0.100 M NaOH in (a) water, Kw = 1´10–14; and (b) nonaqueous solvent, Ks = 1´10–20. The titration curve in (b) assumes that the change in solvent has no effect on the acid dissociation constant of the weak acid.

 

If autoprolysis constant (K_S) of solvent is low, we have great titration jump. Solvent with K_SH less than water (CH₃COOH, C₂H₅OH) used for the charged acid titration – for example, NH₄⁺.

 

Classification of solvents for nonaqueous titration

Accordance to donator-acceptor interaction (or acid-base properties) with protons and accordance to chemical nature of participants all solvents are divided on protonic (protolytic) and aprotonic (nonprotolytic). There are three groups of protolytic solvents:

1)    acidic, or protogenic,

2)    basic, or protophylic,

3)    amphiprotic, or amphoteric.

Protogenic solvent (HF, H₂SO₄, HCOOH, CH₃COOH) is acidic substance that can give protons. Molecules of protogenic solvent can join protons only from strong acids. For example, acetic acid as week acid joins protons from H₂SO₄ (or HCl, HClO₄):

CH₃COOH + H₂SO₄ « CH₃COOH₂⁺ + HSO₄^–,

base        acid

but: (CH₃)₃N + CH₃COOH « (CH₃)₃NH⁺ + CH₃COO^–

base           acid

Protophylic solvent (NH₃, N₂H₄, (CH₃)₂NH₂, dioxane) is basic substances that have attraction to protons. Tears off the protons from molecule can only very strong bases. There are no strong bases, that can interrupt (divert) proton from ammonia molecule. For example, acetamide interaction in liquid ammonium:

CH₂CONH₂ + NH₃ « NH₄⁺ + CH₃CONH^–

         weak base      strong base

H₂N–(CH₂)₂–NH₂ +NH₂^– « H₂N–(CH₂)₂–NH^– + NH₃

Amphiprotic solvent (H₂O, CH₃OH, C₂H₅OH) is amphoteric species which can exhibit as acid that basic properties. These solvents can accept or donate protons accordance to dissolved substances nature: water gives protons to NH₃, N₂H₄, CH₃NH₂ and takes protons from HCl, H₂SO₄, CH₃COOH.

H₂SO₄ + H₂S₂O₇ « H₃SO₄⁺ + HS₂O₇^–

H₂SO₄ + HSO₃F « H₃SO₄⁺ + SO₃F^–

Aprotonic solvent (C₆H₆, C₆H₅Cl, CH₃Cl) is neutral substance that caot accept neither donate protons. Molecules of aprotonic solvent not ionised.

 

Interaction the solute with solvents

Another parameter affecting the feasibility of a titration is the dissociation constant of the acid or base being titrated. For titration of weak acids are using proton-accepting solvents (ethylenediamine, dimethylformamide). For titration of weak bases are using proton-donating solvents (glacial acetic acid, formic acid).

Again, the solvent plays an important role. Acidic (basic) solvents have differentiating action, because in its environment can be titrated consecutively few acids (bases) in mixture.

The tendency of the solvent to accept or donate protons determines the strength of a solute acid or base dissolved in it. In the Brønsted–Lowry view of acid–base behavior, the strength of an acid or base is a relative measure of the ease with which a proton is transferred from the acid to the solvent, or from the solvent to the base. For example, the strongest acid that can exist in water is H⁺. The acids HCl and HNO₃ are considered strong because they are better proton donors than H⁺. Or another example, perchloric acid and hydrochloric acid are strong acids in water.

When acetic acid, which is a weak acid, is placed in water, the dissociation reaction

CH₃COOH + H₂O « H₃O⁺ + CH₃COO^–

does not proceed to a significant extent because acetate is a stronger base than water and the hydronium ion is a stronger acid than acetic acid. If acetic acid is placed in a solvent that is a stronger base than water, such as ammonia, then the reaction

 

CH₃COOH + NH₃ « NH₄⁺ + CH₃COO^–

 

proceeds to a greater extent. In fact, HCl and CH₃COOH are both strong acids in ammonia.

If anhydrous acetic acid, a weaker proton acceptor than water, is substituted as the solvent, neither of this acid undergoes complete dissociation. Instead the equilibrium such as the following are established

CH₃COOH + HClO₄ « CH₃COOH₂⁺ + ClO₄^–

base         acid     conjugated base    conjugated acid

Perchloric acid is, considerably stronger than hydrochloric acid in this solvent, its dissociation being about 5000 times greater. Acetic acid thus acts as a differentiating solvent toward the two acids by revealing the inherent differences in their acidities. Strong acids essentially donate all their protons to H₂O, “leveling” their acid strength to that of H⁺. In a different solvent HCl and HNO₃ may not behave as strong acids. Water, on the other hand, is a levelling solvent for perchloric, hydrochloric, nitric, and sulphuric acids because all four are completely ionised in this solvent and thus exhibit no differences in strength. Differentiating and levelling solvents also exist for bases.

All other things being equal, the strength of a weak acid increases if it is placed in a solvent that is more basic than water, whereas the strength of a weak base increases if it is placed in a solvent that is more acidic than water. In some cases, however, the opposite effect is observed. For example, the pK_b for ammonia is 4.76 in water and 6.40 in the more acidic glacial acetic acid. In contradiction to our expectations, ammonia is a weaker base in the more acidic solvent.

The weak bases often are titrated in the acetic acid medium
(strengthening of force of the bases)

§  Titrant: perchlorate acid HClO₄

§  Standardization: on potassium hydrogenphthalate, or on sodium salicylate if have solution of HClO₄ in CH₃OH

           

§  Indicators: crystal violet (violet – blue or green), thymol dark blue (yellow – rose).

 

The weak acids often are titrated in the medium dimethyl formamide, ethylene diamine, butylamine, pyridine
(strengthening of force of the acids)

§  Titrant: sodium hydroxide NaOH in the solution of benzene with methanol sodium methylate CH3ONa in methanol or in the solution of benzene with methanol.

§  Standardization of NaOH and CH₃ONa on benzoic acid

§  Indicators: thymol blue (red-yellow and yellow-blue) or physico-chemical methods (potentiometry).

 

Indicators for nonaqueous titrations

Neutral red