Mercurimetric Titration of Chloride in Presence of Sodium Nitroprusside as Indicator

A titration procedure aims to determine the concentration of a solute in a solution tested, in presence of an indicator used for registration of the end point (e) of the titration. For example, Cl-1 ions are determined in Mohr’s method by titration with AgNO3 standard solution, in presence of K2CrO4 in the titrand [1-3]; the end point is indicated here by the Ag2CrO4 precipitate. In the Liebig method of cyanide determination, KCN solution is titrated with AgNO3 solution; the end point is indicated here by AgCN precipitate [4,5], as auto-indicating species. In the Denigès’ modification of the Liebig titration, the solution of KCN + KI + NH3 is titrated with AgNO3 solution; the end point is indicated here by the AgI precipitate [4,6]. Systematic error of the analyses was evaluated from calculations made on the basis of charge and concentration balances, and all thermodynamic knowledge expressed by equilibrium constants for the species related to the systems in question.


Introduction
A titration procedure aims to determine the concentration of a solute in a solution tested, in presence of an indicator used for registration of the end point (e) of the titration. For example, Cl -1 ions are determined in Mohr's method by titration with AgNO 3 standard solution, in presence of K 2 CrO 4 in the titrand [1][2][3]; the end point is indicated here by the Ag 2 CrO 4 precipitate. In the Liebig method of cyanide determination, KCN solution is titrated with AgNO 3 solution; the end point is indicated here by AgCN precipitate [4,5], as auto-indicating species. In the Denigès' modification of the Liebig titration, the solution of KCN + KI + NH 3 is titrated with AgNO 3 solution; the end point is indicated here by the AgI precipitate [4,6].
Systematic error of the analyses was evaluated from calculations made on the basis of charge and concentration balances, and all thermodynamic knowledge expressed by equilibrium constants for the species related to the systems in question.
Here and in further parts of this paper, the charges z i of the corresponding species i z i X (i=1,2…) are omitted, when written in terms of molar concentrations, i.e., the notation [X i ] is applied here, for simplicity.

Some preliminary remarks
The system considered is an example of electrolytic non-redox system. The electrolytic non-redox (and redox too) systems can be considered according to GATES principles [14], if all (i) qualitative (specification of components forming a system, and species in the system thus formed), presented also in this Journal [16].
Static and dynamic electrolytic systems are distinguished.
A dynamic system is realized in titration, where V mL of titrant T is added into V 0 mL of titrand D, and V 0 +V mL of D+T mixture is obtained at defined point of the titration [17]. Concentrations of solutes (a) in D are denoted by C 0 (for analyte), C 01 , C 02 , …, and (b) in T by C (for reagent), C 1 , C 2 , …. In the reference system considered here, Hg(NO 3 ) 2 (C) is the reagent, NaCl (C 0 ) is the analyte, Na 2 Fe(CN) 5 NO⋅2H 2 O (C 01 ) is the indicator. Moreover, HNO 3 (C 1 ) is the component in T that prevents precipitation of HgO when Within GATES there are considered, among others, the systems in which a solid phase is formed. Examples of this kind are provided e.g. in [6]. There may also be a change in the solid phase composition, see e.g. [18].
The results of calculations preformed according to GATES principles with use of iterative computer programs [14], can be presented graphically on the related 2D diagrams, where the fraction titrated is marked on the abscissa, as an independent variable, where C and C 0 are expressed in mol/L, V and V 0 in mL. This is the simple way to normalize the respective graphs, i.e., the independence of their shape from the V 0 value.
The Φ plays also the key role in formulation of Generalized Equivalence Mass (GEM) concept [19], compatible with GATES principles. Within GEM formulation, the end (e) and equivalence (eq) points are related to the titration curve. At the end point, the visual titration is terminated, when indicated by a desired/ pre-assumed color change of the D+T mixture, or by the first appearance of a solid phase, e.g. AgI in the Liebig-Denigès method [6], or HgFe(CN) 5 NO in the titration considered here. Turbidity in D+T provides the appropriate indicator (indicating component), e.g., KI in the Liebig-Denigès method, or Na 2 Fe(CN) 5 NO⋅2H 2 O in the method discussed here.
Equation (1) can be rewritten as follows As we see, the fraction V/Φ value is constant during the titration in D+T system; it depends only on the pre-assumed/ imposed values for C, C 0 (intensive quantities) and V 0 From Eq. (2) it follows that V/Φ takes the same value at the end (e) and equivalent (eq) points, i.e., eq e e eq e eq We have From (3) and (5) However, Eq. (5a) cannot be applied for the evaluation of m A (V e known, Φ e unknown). Also, Eq. (5b) is useless (the "rounded" Φ eq value is known exactly, but V eq is unknown), as V e (not V eq ) in visual titrations is determined experimentally.
Because the Equations (5a) and (5b) are inapplicable, the third, approximate formula for m A has to be applied, namely: where Φ eq is put for Φ e in Eq. (5a), and is named as the equivalent mass of the analyte A. The relative error in accuracy resulting from this substitution equals to For Φ e = Φ eq one gets ϑ = 0 and ' A m = m A ; thus Φ e ≅ Φ eq , i.e. V e ≅ V eq corresponds to ' The numerical values for Φ e are usually close to Φ eq values expressed by a ratio of small natural numbers [19]. For example, in the system considered here we have Φ eq = 1/2. The difference Φ e -Φ eq , when compared with the uncertainty of Φ value, is acceptable from the one-drop error viewpoint when |Φ e -Φ eq | < 0.003 [19].

Calculation procedure
The calculation specified below differs significantly from the one usually practiced in GATES, where a complete set of independent balances and equilibrium constants is applied. In particular, the GATES procedure can be applied to the model D+T system with NaCl (C 0 ) + Na 2 Fe(CN) 5 NO⋅2H 2 O (C 01 ) as titrand D (V 0 ), and Hg(NO 3 ) 2 (C) + HNO 3 (C 1 ) as titrant T (V). However, the mercurimetric titration is applied also for the chloride samples from more complex media, where composition of a sample matrix is undefined [20]. Some kinds of the samples were also tested in clinical laboratories, e.g. [21]. Other indicators were also applied for this purpose, see [22].
i.e., the fraction titrated (Eq. 1) has the form  (12) and (13), is considered as titration curve, and presented in Figure 1. It should be noted that the jump on this curve occurs in close vicinity of the fraction titrated value Φ = Φ eq = 1/2. A detailed discussion on the balances (9), (10) From Equations (15) and (16) where Setting (17) into (15) gives the equation The V e value can be found from Equation (18)  formulation [19,24], and illustrated in Figure 2.

Final Comments
The paper provides an example of application of physicochemical (thermodynamic) knowledge involved with gaining the information involved with expected systematic error of analyses made at different concentrations of NaCl (C 0 ), Na 2 Fe(CN) 5 NO⋅2H 2 O (C 01 ) and Hg(NO 3 ) 2 (C). Generally, at given C value, the error of chloride analysis grows with a decrease of C 0 and C 01 values, as indicated in Figure 2.