Precipitation Titrimetry

Precipitation titrimetry. Determination of weight of NaCl, KCl in solutions.

Precipitation titrimetry is based upon reactions that yield ionic compounds of limited solubility. The slow rate of precipitate formation limits the number of precipitating agents that can be used in titrimetry to a handful.

A reaction in which the analyte and titrant form an insoluble precipitate also can form the basis for a titration. We call this type of titration a precipitation titration.

One of the earliest precipitation titrations, developed at the end of the eighteenth century, was for the analysis of K₂CO₃ and K₂SO₄ in potash. Calcium nitrate, Ca(NO₃)₂, was used as a titrant, forming a precipitate of CaCO₃ and CaSO₄. The end point was signalled by noting when the addition of titrant ceased to generate additional precipitate. The importance of precipitation titrimetry as an analytical method reached its zenith in the nineteenth century when several methods were developed for determining Ag⁺ and halide ions.

http://www.youtube.com/watch?v=XMaClYp-djA

 

Requirements to reactions and defined substances:

§        The defined substance should be dissolved in water and give an ion which would be active in sedimentation reaction.

§        The received precipitate should be practically insoluble (Ksp<10^{-8 ¸ – 10}, S<10^-5 mol/L).

§        Results of titration should not be deformed by the adsorption phenomena (coprecipitation).

§        Precipitate should form enough quickly.

§        There should be a possibility of fixing of an equivalence point.

 

Classification of methods precipitation titration (on titrant):

1.     Argentometry

2.     Thiocyanatometry

3.     Mercurometry

4.     Sulphatometry

5.     Hexacianoferratometry

Titration Curves

Titration curves for a single anion are derived in a way completely analogous to another titration methods. The only difference is that the solubility product of the precipitate is substituted to for the ion-product constant for water.

The change in p-function value at the equivalence point becomes grater as the solubility products become smaller – that is, as the reaction between the analyte and precipitant becomes more complete. Ions forming precipitates with solubility products much larger than about 10^-10 do not yield satisfactory end point.

The titration curve for a precipitation titration follows the change in either the analyte’s or titrant’s concentration as a function of the volume of titrant. For example, in an analysis for I^– using Ag⁺ as a titrant

Ag⁺ + I^– ® AgI¯

the titration curve may be a plot of pAg or pI as a function of the titrant’s volume.

As we have done with previous titrations, we first show how to calculate the titration curve and then demonstrate how to quickly sketch the titration curve.

According to the general guidelines we will calculate concentration before the equivalence point assuming titrant was a limiting reagent – thus concentration of titrated substance is that of unreacted excess. Usually that’s already the answer, however, sometimes, instead of calculating concentration of titrated substance, we may want to calculate concentration of titrant. To do so it is enough to put concentration of excess titrated substance into solubility product and to solve for unknown concentration of titrant. After equivalence point situation reverses – if what we are looking for is a concentration of titrant, we simply calculate it from dilution of added titrant excess, if what we are looking for is a concentration of titrated substance – we put concentration of excess titrant into solubility product and we solve for unknown.

Calculating the Titration Curve. As an example, let’s calculate the titration curve for the titration of 50.0 mL of 0.0500 M Cl^– with 0.100 M Ag⁺. The reaction in this case is

Ag⁺ + Cl^– ® AgCl¯

The equilibrium constant for the reaction is

K = (K_sp)^–1 = (1.8 ´10^–10)^–1 = 5.6 ´10⁹

Since the equilibrium constant is large, we may assume that Ag⁺ and Cl^– react completely.

By now you are familiar with our approach to calculating titration curves. The first task is to calculate the volume of Ag⁺ needed to reach the equivalence point. The stoichiometry of the reaction requires that

Moles Ag⁺ = Moles Cl^–

or

M_AgV_Ag = M_ClV_Cl

Solving for the volume of Ag⁺

shows that we need 25.0 mL of Ag⁺ to reach the equivalence point.

Before the equivalence point Cl^– is in excess. The concentration of unreacted Cl^– after adding 10.0 mL of Ag⁺, for example, is

If the titration curve follows the change in concentration for Cl^–, then we calculate pCl as

pCl = –log[Cl^–] = –log(2.50 ´10^–2) = 1.60

However, if we wish to follow the change in concentration for Ag⁺ then we must first calculate its concentration. To do so we use the K_sp expression for AgCl

 

K_sp = [Ag⁺][Cl^–] = 1.8 ´10^–10

Solving for the concentration of Ag⁺

gives a pAg of 8.14.

At the equivalence point, we know that the concentrations of Ag⁺ and Cl^– are equal. Using the solubility product expression

K_sp = [Ag⁺][Cl^–] = [Ag⁺]² = 1.8 ´10^–10

gives

[Ag⁺] = [Cl^–] = 1.3 ´10^–5 M.

At the equivalence point, therefore, pAg and pCl are both 4.89.

After the equivalence point, the titration mixture contains excess Ag⁺. The concentration of Ag⁺ after adding 35.0 mL of titrant is

or a pAg of 1.93. The concentration of Cl^– is

or a pCl of 7.82.

Additional results for the titration curve are shown in Table and Figure.

 

Data for Titration of 50.0 mL of 0.0500 M Cl– with 0.100 M Ag

Volume AgNO3(mL)	pCl	pAg
0.00	1.30	—
5.00	1.44	8.31
10.00	1.60	8.14
15.00	1.81	7.93
20.00	2.15	7.60
25.00	4.89	4.89
30.00	7.54	2.20
35.00	7.82	1.93
40.00	7.97	1.78
45.00	8.07	1.68
50.00	8.14	1.60

 

Precipitation titration curve for 50.0 mL of 0.0500 M Cl^– with 0.100 M Ag⁺. (a) pCl versus volume of titrant; (b) pAg versus volume of titrant.

 

The factors which define value of inflection points of titration on curves of precipitation titration

§        Concentration of titrant solutions and a defined ion (than more concentration, the titration inflection point is more)

§        Solubility of a precipitate (than solubility less, the titration inflection point is more)

§        Temperature (than more temperature, the solubility of a precipitate will be more and the inflection point is  less)

§        Ionic strength of a solution (than more ionic strength of a solution, the solubility of a precipitate will be more and the inflection point is  less)

http://www.youtube.com/watch?v=kMrCANM1VVk

 

End point detection

Compared to other types of titration – complexometric, potentiometric and acid base – precipitation titrations don’t have a set of universal indicators, that you can select from when designing a new method. Each precipitation titration method has its own, specific way of end point detection. The closest to being universal are Fajans adsorption indicators, but even these are very limited in their applications.

Probably most popular precipitation titration – determination of chlorides by Mohr method – uses red silver chromate for the end point detection. At the beginning of the titration we add some small amount of CrO42- to the solution. As long as there are still chlorides present, Ag+ concentration is too low for the silver chromate to precipitate. After equivalence point Ag+ concentration goes up and chromate precipitates, making solution red.

This is an interesting case to discuss, as it is relatively easy to estimate necessary concentrations. We have two weakly soluble salts, silver chloride:

 (1)

and silver chromate

 (2)

 

Reaction taking place during titration is

Ag+ + Cl- → AgCl

At the equivalence point

 (3)

At this Ag+ concentration we should start to see precipitating silver chromate. That means we need

 (4)

 

This is a nice, easily calculated number, which has an unfortunate practical flaw. 0.02 M chromate solution is so strongly colored, that the red precipitate is not easily visible and the end point is hard to spot. Thus it is necessary to use lower concentration of chromate, and experiments show that concentration of about 0.004 M is acceptable – titrated solution is still yellowish, but the red color is hard to miss. However, as the chromate concentration is lower than optimal, question is, how much excess silver we have to add to the solution before we will be able to see the color change. This excess will mean a positive error in the determination.

If concentration of chromate is 0.004 M, concentration of Ag+ when the preipitation starts must be

 (5)

 

That is 1.2 × 10-5 M more than the equivalence concentration. Assuming final volume of the titrated solution is about 100 mL and titrant concentration is about 0.1M, that means we need to add

 (6)

 

excess of the Ag+ solution. This is well below errors from all other sources – please remember, that 50 mL class A burette has accuracy of 0.05 mL. In practice even smaller concentrations of chromate will still not change error much, besides, it is easy to check error with a blind test.

 

Note, that in the discussion above we have assumed no protonation of CrO42-. That’s not necessarily correct – pKa2 for chromic acid is 6.5, so even ieutral solution substantial part of the acid is in the form of HCrO4-. Luckily, even at these lower concentrations of CrO42- errors are so small we can safely ignore them, as long as pH doesn’t differ much from neutral.

However, due to the chromate protonation Mohr method will not work in the acidified solutions. That’s where Volhard method comes handy. Again, this method uses a specific indicator. Volhard method is based on the back titration – we add known amount of the Ag+ to the sample containing chlorides, once the chlorides precipitate we titrate excess Ag+ with thiocyanate solution in the presence of Fe3+. Once all Ag+ is precipitated excess SCN- creates FeSCN2+ complex with a strong wine color.

Much more interesting is the case of Zn2+ titration with ferrocyanide:

Zn2+ + Fe(CN)64- → Zn2Fe(CN)6

 

To detetect end point we use rather unexpected indicator – diphenylamine. Diphenylamine is a redox indicator. Before titration, we add to the solution some small amount of ferricyanide. Zinc ferricyanide is not so weakly soluble, so it doesn’t interfere with the main precipitation reaction. However, its presence means we have a well known redox system – Fe(CN)64-/Fe(CN)63- – in the solution. As long as we are before equivalence point, concentration of ferrocyanide is very low and redox potential, given by the Nernst equation:

 (7)

 

is relatively high. Once we are past the equivalence point concentration of the ferrocyanide goes up, potential goes down, and this difference can be easily detected thanks to the diphenylamine color change.

Adsorption indicators, mentioned earlier, are rarely used, but worth a few words. These are organic molecules, either basic (like rhodamine) or acidic (like fluorescein or eosin). Depending on the titration stage (before or after equivalence point) surface of the precipitate is slightly charged. For example, in the Mohr titration we precipitate AgCl. AgCl has a very large surface due to its colloidal nature. Before the equivalence point there is an excess of chlorides in the solution, and they tend to adsorb on the precipitate surface, charging it negative. After equivalence point there is an excess of Ag+ in the solution and situation changes – surface becomes charged positive. This charge on the surface attracts the organic indicator molecules. Here comes the most important part – these indicators have different colors when they are free in the solution and when they are adsorbed on the precipitate, which helps detect the end point.

Equivalence point calculation

At equivalence point we have just a saturated solution of insoluble salt, so calculation of concentration of the determined ion is identical to the solubility calculations. Just for fun, we can derive seriously looking formula that will describe the concentration.

Let’s assume we precipitate salt of a general formula MekXl, with known Ksp:

 (1)

Looking at the formula we can see that

 (2)

so

 (3)

and

 (4)

 

However, in practice you will probably find it easier to solve the problem manually each time, than to look for formula or trying to remember it. That’s what we will do in the following example.

Note, that in the real world it is quite ofteecessary to account for numerous side reactions – especially for protonation and hydrolysis of both metal cation and ligand.

Example: calculate pZn at the equivalence point of zinc titration with ferrocyanide, assuming pKsp = 16.8.

We don’t need any other information about volumes and concentrations! Let’s start with dissolution reaction and Ksp:

Zn2Fe(CN)6 → Zn2+ + Fe(CN)64-

 (5)

obviously

 (6)

so

 (7)

 

and

 (8)

and finally

 (9)

Let’s check, if our general formula gives the same result. From the Zn2Fe(CN)6 formula k=2 and l=1, so

 (10)

That’s the same.

 

Selecting and Evaluating the End Point

Initial attempts at developing precipitation titration methods were limited by a poor end point signal. Finding the end point by looking for the first addition of titrant that does not yield additional precipitate is cumbersome at best. Two types of end points are encountered in titration with precipitants:

1) chemical,

2) instrumental: potentiometric and amperometric.

 

Chemical indicators for precipitation titration

The end point produced by a chemical indicator usually consists of a colour change or, occasionally, the appearance or disappearance of turbidity in the solution being titrated. The requirements for an indicator for a precipitation titration are analogous to those for an indicator for a neutralisation titration:

1) the colour change should occur over the reagent limited range in p-function of the reagent or the analyte and

2) the colour change should take place within the steep portion of the titration curve for the analyte.

Standard substances

Remember to use analytical reagents (AR grade) for standards.

1.     Silver nitrate – dry for 2 hours at 150°C. Equivalent weight is 169.8731 g.

2.     Sodium chloride NaCl – dry at 130-150°C. Equivalent weight is 58.4428 g.

3.     Metallic zinc Zn – equivalent weight is 65.4090 g.

4.     Metallic silver Ag – equivalent weight is 107.8682 g.

 

Argentometry

Argentometry used for halide-like anions (Hal^–, CN^–, SCN^–) determination, which forms slightly soluble compounds with Ag⁺ ion. Standard titration solution is AgNO₃. For back-titration uses standard solution of NaCl, that titrated AgNO₃ surplus. The silver nitrate solution can be standardised against primary-standard-grade sodium chloride.

Methods based on precipitation of silver compounds are called collectively argentometric methods. They are most often used for determination of chloride ions, but they can be used also for other halides (bromide, iodide) and some pseudohalides (thiocyanate).

It is also possible to use indirect argentometric methods for determination of anions, that create insoluble salts with Ag+ (for example phosphate PO43-, arsenate AsO43- and chromate CrO42-). These methods are based on back titration of excess silver with standardized thiocyanate solution.

http://prezi.com/kvviaznvkoih/precipitation-titration/

 

Argentometry – solutions

1.     Silver nitrate solution

Silver nitrate solution of known concentration can be prepared using pure solid AgNO3, after drying it (see standard substances used in precipitation titrations section). Most popular solution is that of 0.1M concentration, although for determination of small amount if chlorides more diluted solutions can be used (0.02M). However, use of diluted solutions should be preceded by thorough analysis of possible titration errors. This is especially important in the case of Mohr titration, where some excess of silver must be added before red silver dichromate precipitates and signals end point.

Silver nitrate solutions slowly decompose when exposed to light, so they should be kept in dark bottles.

2.     Potassium thiocyanate solution

Potassium thiocyanate is not used as a standard substance. Its solutions are prepared by dissolving solid KSCN and standardized against solution of silver nitrate of known concentration. Usually used solution is 0.1M.

3.     Potassium chromate solution

5% w/w potassium chromate solution is used as an indictaor in titration with silver nitrate.

4.     Nitric acid 1+1

About 40% solution of nitric acid, used for acidification of the chlorides solution in Volhard method. 1+1 means simply 1 volume of the acid and 1 volume of water.

5.     Ammonium ferric sulfate solution

10% w/w ammonium ferric sulfate (FeNH4(SO4)2, iron alum) is a convenient source of Fe3+ cations, used for detection of excess thiocyanate. This solution is acidified with nitric acid to avoid iron (III) hydroxide precipitation.

Argentometry – standardization

1.     0.1M silver nitrate standardization against sodium chloride

Silver nitrate solutions of known concentration can be prepared from known mass of dried AgNO3. However, if we don’t have access to the high purity reagent, or if we have a solution of unknown concentration, we can easily standardize it against sodium chloride.

Reaction taking place during titration is

 

AgNO3 + NaCl → AgCl↓ + NaNO3

Procedure to follow:

–       Weight exactly about 0.15-0.20 g of dried sodium chloride into 250 mL erlenmayer flask.

–       Add about 100 mL of distilled water, dissolve.

–       Add 1 mL 5% w/w potassium chromate solution.

–       Titrate with AgNO3 solution till the first color change.

2.     0.1M potassium thiocyanate standardization against silver nitrate solution

Potassium thiocyanate solution has to be standardized, as it is not possible to prepare and dry KSCN pure enough so that it can be used as a standard substance for solution preparation. The easiest method if the standardization require standardized solution of silver nitrate. As KSCN solution is used for back titration of the excess of AgNO3, when we need to standardzie KSCN solution we usually have standardized silver nitrate solution ready.

Reaction taking place is

AgNO3 + KSCN → AgSCN↓ + KNO3

Procedure to follow:

–       Pipette 25 mL aliquot of about 0.1M AgNO3 solution into 250mL erlenmayer flask.

–       Add 50 mL of distilled water.

–       Add 1 mL of 10% FeNH4(SO4)2 solution.

–       Titrate with potassium thiocyanate till the first visible color change.

 

Argentometry:

§        without indicator:

                   – Gay-Lussac method (method of even      turbidity)

                   – method to point enlightenment

§        with inicator:     

                   – Mohr method

                   – Fajans – Fisher – Khodacov method

                   – Volhard method

 

Gay-Lussac method (method of even turbidity)

If solution NaBr titrate by solution AgNO3 (or on the contrary) there is a reaction:

Br- + Ag+ = AgBr↓

For fixation of equivalence point it is necessary to select two identical portions of a solution before the titration end. To one of them add a drop of AgNO3 solution, on another – a drop of NaBr solution at the same concentration. Titration is finished when will be identical intensity of turbidity in both portions of solution.

 

Method to enlightenment point

The method of titration to an enlightenment point can be applicable when insoluble compounds is in colloidal state. For example, definition of І- ions by silver nitrate, AgІ forms, it is adsorbing І- and receive negative charges (colloidal solution of AgІ forms).

As more and more І- ions react with Ag+ ions, particles AgІ gradually lose adsorbed by them І- ions, and their charge decreases. In the end of titration occur coagulation of particles and their sedimentation. The solution thus is absolutely clarified.

 

Four indicators have found extensive use for argentometric titration:

1. Chromate ion. The Mohr method.

§        Titrant: AgNO3 – secondary standard solution

§        Stanardization  on primary standard solution of sodium chloride NaCl (by a measured volume of primary standard solution):

AgNO₃ + NaCl = AgCl¯ + NaNO₃

§        Indicator – 5 % potassium chromate K₂CrO₄ (to formation precipitate of reddish-brown Ag₂CrO₄):

2AgNO₃ + K₂CrO₄  = Ag₂CrO₄¯+ 2KNO₃

§        Determinate substance: chloride Cl-, bromide Br-.

§        Medium: рН~ 6,5-10,3.

§        Usage: quantitative definition of sodium chloride, potassium chloride, sodium bromide, potassium bromide, etc.

 

The first important visual indicator to be developed was the Mohr method for Cl^– using Ag⁺ as a titrant. By adding a small amount of K₂CrO₄ to the solution containing the analyte, the formation of a precipitate of reddish-brown Ag₂CrO₄ signals the end point. Because K₂CrO₄ imparts a yellow colour to the solution, obscuring the end point, the amount of CrO₄^2– added is small enough that the end point is always later than the equivalence point. To compensate for this positive determinate error an analyte-free reagent blank is analyzed to determine the volume of titrant needed to effect a change in the indicator’s colour. The volume for the reagent blank is subsequently subtracted from the experimental end point to give the true end point. Because CrO₄^2– is a weak base, the solution usually is maintained at a slightly alkaline pH. If the pH is too acidic, chromate is present as HCrO₄^–, and the Ag₂CrO₄ end point will be in significant error. The pH also must be kept below a level of 10 to avoid precipitating silver hydroxide.

         Sodium chromate serves as indicator for the argentometric detrmination of chloride, bromide, and cyanide ions by reacting with silver cation to form a brick-red silver chromate (Ag₂CrO₄) precipitate in the equivalence point region:

AgNO₃ + NaCl = AgCl¯ + NaNO₃

white

AgNO₃ + Na₂CrO₄ = Ag₂CrO₄¯ + NaNO₃

red

The Mohr titration must be carried out at a pH between 7 and 10, because chromate ion is the conjugate base of the weak chromic acid. In more acidic solutions the chromate ion concentration is too low to produce the precipitate at the equivalence point. A suitable pH is achieved with sodium hydrogen carbonate.

The Mohr titration caot be used for iodide and thiocyanate determination, because these ions form colloid solutions with silver ion.

 

Restrictions of usage of Mohr method:

§        It is impossible to use titration in acidic solutions:

2CrO₄^2- + 2H⁺ = Cr₂O₇^2- +  H₂O

§        It is impossible to use titration in the presence of ammonia, etc. ions, molecules which can be ligands on relation to Silver ions

§        It is impossible to use titration in the presence of many cations (Ba2+, Pb2+, etc.) which form the painted precipitates with chromate ions CrO42-

§        It is impossible to use titration in the presence of reducers which reduce chromate ions CrO₄^2- to Cr³⁺ ions

§        It is impossible to use titration in the presence of many anions (PO43-, AsO43-, AsO33-, S2- etc.) which with Silver ions give the painted precipitates

 

procedure

–       Pipette aliquot of chlorides solution into 250mL Erlenmeyer flask.

–       Dilute with distilled water to about 100 mL.

–       Add 1 mL of 5% potassium chromate solution.

–       Titrate with silver nitrate solution till the first color change.

 

result calculation

According to the reaction equation

Ag+ + Cl- → AgCl

silver nitrate reacts with chloride anion on the 1:1 basis. That makes calculation especially easy – when we calculate number of moles of AgNO3 used it will be already number of moles of Cl- titrated.

 

2. Iron(III) ion. The Volhard method.

A second end point is the Volhard method in which Ag⁺ is titrated with SCN^– in the presence of Fe³⁺. Silver ions are titrated with a standard solution of potassium or ammonium thiocyanate:

AgNO₃ + NaCl = AgCl¯ + NaNO₃

white

AgNO₃ + KSCN = AgSCN¯ + KNO₃

white

Iron(III) ion serve as the indicator. The end point for the titration reaction

Ag⁺ + SCN^– ® AgSCN¯

is the formation of the reddish coloured Fe(SCN)₃ complex:

SCN^– + Fe³⁺ ® Fe(SCN)₃

The solution turns red with the first slight excess of thiocyanate ion:

2NH₄Fe(SO₄)₂ + 6KSCN = 2Fe(SCN)₃ + 3K₂SO₄ + (NH₄)₂SO₄

red

The titration must be carried out in distinct acidic solution

1) to prevent precipitation of iron(III) as the hydrated oxide,

2) and such ions as carbonate, oxalate, and arsenate not interfere with silver ion.

The most important application of the Volhard method is for the indirect determination of halide ions. Sometime the indirect Volhard method called thiocyanometry. A measurement excess of standard silver nitrate solution is added to the sample, and the excess silver ion is determined by back-titration with a standard thiocyanate solution. At chloride determination occurs titration error, because silver chloride is more soluble than silver thiocyanate.

3. Adsorption indicators. The Fajans method.

A third end point is evaluated with Fajans’ method, which uses an adsorption indicator whose colour when adsorbed to the precipitate is different from that when it is in solution. The adsorption indicator is an organic compound that tends to be adsorbed onto the surface of the solid in a precipitation titration. The adsorption occurs near the equivalence point and colour transfers from the solution to the solid.

For example, when titrating Cl^– with Ag⁺ the anionic dye dichlorofluoroscein is used as the indicator. Before the end point, the precipitate of AgCl has a negative surface charge due to the adsorption of excess Cl^–. The anionic indicator is repelled by the precipitate and remains in solution where it has a greenish yellow colour. After the end point, the precipitate has a positive surface charge due to the adsorption of excess Ag⁺. The anionic indicator now adsorbs to the precipitate’s surface where its colour is pink. This change in colour signals the end point.

 

Tetrabromofluorescein (eosine)	Fluoresceine

         Fluorescein is a typical adsorption indicator that is useful for the titration of chloride ion with silver nitrate. In aqueous solution, fluorescein partially dissociates into hydronium ions and negatively charged fluoresceinate ions that are yellow-green. The fluoresceinate ion forms an intensively red silver salt at equivalence point. For bromide, iodide, and thiocyanate titration as an indicator is used tetrabromfluorescein, named eosin.

         Titration involving adsorption indicators are rapid, accurate, and reliable, but their application is limited to the relatively few precipitation reactions in which a colloidal precipitate is formed rapidly.

There are also so called the Gay-Lussac argentometric titration method without indicators. At equivalence point the titrated halide solution clears up because occurs coagulation of precipitate.

Mercurometry

For mercurometric titration is using mercury(I) salts for halide ion determination.

Hg₂(NO₃)₂ + 2NaCl = Hg₂Cl₂¯+ 2NaNO₃

white

Indicator is iron(III) thiocyanate, which disappearance at equivalence point:

3Hg₂(NO₃)₂ + 2Fe(SCN)₃ = 3Hg₂(SCN)₂¯+ 2Fe(NO₃)₃

red solution    white

Also as an indicator can be used diphenylcarbazon, which is an adsorption indicator and at equivalence point change colour of precipitate from white to blue.

 

Superiority of mercurometry:

1. Not required expensive silver salts.

2. Mercury(I) precipitates are less soluble than analogous silver salts. Therefore, equivalence point is clearly marked.

3. Mercurometric determination are carried out with direct titration in acidic solution.

4. Chloride ion can be determined with reducers (S^2–, SO₃^2–) and oxidisers (MnO₄^–, Cr₂O₇^–) presence.

5. Titration can be carried out in turbid and coloured solutions.

Thiocyanatometry

§        This is a precipitation titration in which SCN- is the titrant.

§        Titrant: ammonium or potassium thiocyanide NH4SCN, KSCN – secondary standard solution

§        Stardadization: on primary standard solution of AgNO3:

AgNO3 + NH4SCN = AgSCN¯ + NH4NO3

§        Indicator by standardization of ammonium or potassium thiocyanide with iron (ІІІ) salts:

Fe3+ + SCN- =  [Fe(SCN)]2+

§        Medium: in presence of nitric acid

§        Indicator: iron (ІІІ) salts NH4Fe(SO4)2×12H2O in presence of nitric acid

Determinate substance: drugs, which contain Silver (Albumosesilber, colloid silver – Kollargol, silver nitrate).

!!! At the analysis of drugs which contaionionic silver, preliminary it is heated with sulphatic and nitric acids (receive  ionic compound).

!!! At definition of iodides the indicator is added in the end of titration to avoid parallel:

2Fe³⁺ + 2I^– = 2Fe²⁺ + I₂

Procedure

–       Pipette aliquot of chlorides solution into 250mL Erlenmeyer flask.

–       Add 5 mL of 1+1 nitric acid.

–       Dilute with distilled water to about 100 mL.

–       Add 50 mL of 0.1M silver nitrate solution.

–       Add 3 mL of nitrobenzene.

–       Add 1 mL of iron alum solution.

–       Shake the content for about 1 minute to flocullate the precipitate.

–       Titrate with thiocyanate solution till the first color change.

 

result calculation

As in every back titration, to calculate amount of substance we have to subtract amount of titrated excess from the initial amount of reactant used. In the case of argentometry calculations are easy, as all substances used react on the 1:1 basis.

First we have to calculate number of moles of silver nitrate initially added to the chlorides sample. Assuming it was 50 mL of 0.1 M solution, it contained 5 millimole of silver. Then, excess was titrated according to the reaction equation:

Ag+ + SCN- → AgSCN(s)

Thus amount of excess silver is C×V, and amount of Cl is 0.005-C×V moles.

 

sources of errors

Apart from problems listed on the general sources of titration errors page, results of titration can be skewed by the already mentioned replacement of precipitated chlorides by silver thiocyanate. It shouldn’t matter if the procedure was followed carefully.

 

Another Precipitation Titration Methods

1. Barium determination with sulphate:

BaCl₂ + H₂SO₄ = BaSO₄¯ + 2HCl

Indicator is sodium rhodizonate, which disappearance red colour of solution.

2. Lead determination with chromate:

Pb(NO₃)₂ + K₂CrO₄ = PbCrO₄¯ + 2KNO₃

Indicator is AgNO₃ solution. At equivalence point forms red precipitate.

3. Zinc determination with K₄[Fe(CN)₆]:

3ZnCl₂ + K₄[Fe(CN)₆] = Zn₃K₂[Fe(CN)₆] ¯ + 2KCl

Indicator is UO₂(NO₃)₂, which forms brown precipitate with K₄[Fe(CN)₆].

Finding the End Point Potentiometrically

Another method for locating the end point of a precipitation titration is to monitor the change in concentration for the analyte or titrant using an ion-selective electrode. The end point can then be found from a visual inspection of the titration curve.

Determinate the end-point by potenthiometric way

     

Quantitative Applications

Precipitation titrimetry is rarely listed as a standard method of analysis, but may still be useful as a secondary analytical method for verifying results obtained by other methods. Most precipitation titrations involve Ag⁺ as either an analyte or titrant. Those titrations in which Ag⁺ is the titrant are called argentometric titrations. Table provides a list of several typical precipitation titrations.

 

Representative Examples of Precipitation Titrations

Analyte	Titranta	End Pointb
AsO43–	AgNO3, KSCN	Volhard
Br–	AgNO3	Mohr or Fajans
	AgNO3, KSCN	Volhard
Cl–	AgNO3	Mohr or Fajans
	AgNO3, KSCN	Volhard*
CO32–	AgNO3, KSCN	Volhard*
C2O42–	AgNO3, KSCN	Volhard*
CrO42–	AgNO3, KSCN	Volhard*
I–	AgNO3	Fajans
	AgNO3, KSCN	Volhard
PO43–	AgNO3, KSCN	Volhard*
S2–	AgNO3, KSCN	Volhard*
SCN–	AgNO3, KSCN	Volhard

 

^a) When two reagents are listed, the analysis is by a back titration. The first reagent is added in excess, and the second reagent is used to back titrate the excess.

^b) For Volhard methods identified by an asterisk (*) the precipitated silver salt must be removed before carrying out the back titration.

 

Quantitative Calculations

The stoichiometry of a precipitation reaction is given by the conservation of charge between the titrant and analyte thus

 

 

Definition of the sodium chloride in an isotonic solution by argentometry method (Mohr method)

Into a conic flask by spaciousness of 50 ml place 10,0 ml of an  isotonic solution, add 2-3 drops of 5 % potassium chromate solution and titrate by 0,1 mol/L  silver nitrate solution. Titration spends not less than three times.

A 5% w/v solution of potassium chromate produces a red precipitate with silver nitrate ieutral solutions.

At titration to end-point:

NaCl + AgNO₃ = AgCl¯ + NaNO₃

After end-point:

K₂CrO₄ + 2AgNO₃ = Ag₂CrO₄¯ + 2KNO₃

Calculate %w/V of sodium chloride in an investigated solution:

Content of sodium chloride, NaCl must be  0.85 to 0.95% w/v (British Pharmacopoeia).

Calculate mass of sodium chloride in 1 ml of an investigated solution:

Content of sodium chloride in grams in 1 ml of a preparation must be 0,0087-0,0093 (UkPh).

 

Definition of the potassium chloride in a substance by argentometry method (Mohr method)

Nearby 0,25 g of investigated substance (exact weight) dissolve in water in a measured flask spaciousness of 50 ml and  dilute by water to necessary volume and mix. 10,00 ml of the received solution dilute with water to 40 ml in a conic flask spaciousness of 100 ml, add 2-3 drops of 5 % potassium chromate solution and titrate by 0,1 mol/L solution silver nitrate. Titration spends not less than three times.

A 5% w/v solution of potassium chromate produces a red precipitate with silver nitrate ieutral solutions.

At titration to end-point:

KCl + AgNO₃ = AgCl¯ + KNO₃

After end-point:

K₂CrO₄ + 2AgNO₃ = Ag₂CrO₄¯ + 2KNO₃

Calculate %w/V of potassium chloride in an investigated solution:

Content of potassium chloride, KCl in a substance must be not less than 99,5 %.

Definition of potassium bromide by Folgard method

Nearby 2,0 g of investigated substance (exact weight) dissolve in water in a measured flask spaciousness of 100 ml and  dilute to 100.0 ml with the same solvent. To 10.0 ml of the solution add 50 ml of water, 5 ml of dilute nitric acid, 25.0 ml of 0.1 M silver nitrate, shake. Titrate with 0.1 M ammonium thiocyanate, using 2 ml of ferric ammonium sulphate solution as indicator. A 10% w/v solution of ammonium iron(III) sulphate produces a deep red colour with ammonium thiocyanate in acid solutions.

To start of titration:

KBr + AgNO₃ = AgBr¯ + KNO₃

At titration to end-point:

AgNO₃ + NH₄SCN = AgSCN + NH₄NO₃

         After end-point:

NH₄Fe(SO₄)₂ + 3NH₄SCN = Fe(SCN)₃ + 2(NH₄)₂SO₄

Titration spends not less than three times.

Calculate %w/V of potassium bromide in an investigated solution:

 

Content of potassium bromide of  98.0 per cent to 100.5 per cent (dried substance

 

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

http://www.youtube.com/watch?v=9DkB82xLvNE

 

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.

   

stopcock buret for standartization

                                          

Gay-Lussac burette                       Buret with bottle of standard solution

 

                       

Mohr burette                                     Buret with rubber shutter

 

Microburet:

а) Shilov air-powered Buret; б) stopcock buret

 

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).

             

Volumetric flask — for preparing liquids with volumes of high precision. It is a flask with an approximately pear-shaped body and a long neck with a circumferential fill line.

 

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

1) a weighed quantity of a primary standard,

where:

         C_N and V are concentration and volume of secondary standard solution

         m and E_m are mass and equivalent weight of primary standard

 

2) “standard titrimetric substance” (primary standard),

More often in an ampoule contains 0,1 mol (0,1 equivalents) of substances, it is necessary for preparation of 0,1 mol/L solution.

 

3) a measured volume of another standard solution.

where:

         C_N2 and V₂ are concentration and volume of secondary standard solution

         C_N1 and V₁ are concentration and volume of primary 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.

 

 

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.

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.

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:

         where is the solubility constant for the solute particles with the molar surface area A, 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

.

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

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

 

         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,

         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:

         As for the previous example, the equilibrium expression is:

 

         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:

         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

 

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

         Examples

                                   CaSO₄: p=1, q=1,

                                   Na₂SO₄: p=2, q=1,

                                   Al₂(SO₄)₃: p=2, q=3,

         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 =

 

         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): Ks = [B(aq)]
Acid-base equilibrium	B(aq) + H+(aq) BH+(aq) Ka = [B(aq)][H+(aq)]/[BH+(aq)]