Mohr’s method challenge
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Mohr's method challenge
Juris Meija 0 1 2
Anna Maria Michałowska-Kaczmarczyk 0 1 2
Tadeusz Michałowski 0 1 2
0 Faculty of Engineering and Chemical Technology, Technical University of Cracow , 31-155 Cracow , Poland
1 Department of Oncology, The University Hospital in Cracow , 31-501 Cracow , Poland
2 National Research Council Canada , 1200 Montreal Road, Ottawa, ON , Canada K1A 0R6
3 Tadeusz Michałowski
We would like to invite you to participate in the Analytical Challenge, a series of puzzles to entertain and challenge our readers. This special feature of “Analytical and Bioanalytical Chemistry” has established itself as a truly unique quiz series, with a new scientific puzzle published every other month. Readers can access the complete collection of published problems with their solutions on the ABC homepage at http://www. springer.com/abc. Test your knowledge and tease your wits in diverse areas of analytical and bioanalytical chemistry by viewing this collection. In the present challenge, titration is the topic. And please note that there is a prize to be won (a Springer book of your choice up to a value of €100). Please read on… determines the amount of chloride ions by titration with AgNO3. The endpoint of the titration is observed using potassium chromate as an indicator, which gives brown-red silver chromate precipitate when all chloride ions have reacted with the silver ions. Mohr's method remains one of the oldest titration methods and is still used in many laboratories. During the titration, the precipitation of silver chloride occurs
Meet the Mohr’s method challenge
Among the various methods of volumetric analysis,
precipitation titrations are based on the formation of compounds of
limited solubility [
]. In particular, titrimetric methods based
on the use of silver nitrate as precipitating reagent are termed
as argentometric titrations. Named after German chemist and
pharmacist Karl Friedrich Mohr (1806–1879), Mohr’s method
Agþ þ Cl– ¼ AgCl
and the endpoint of this titration is observed by the appearance
of silver chromate
2Agþ þ CrO42– ¼ Ag2CrO4
as the new equilibrium solid phase, when all chloride ions
have reacted with the silver ions. Mohr’s method remains
one of the oldest titration methods and is still used in many
laboratories. This challenge examines the slight difference that
exists between the observed endpoint and the actual chemical
equivalence in titration along with the magnitude of errors that
this discrepancy may cause.
Consider a V0 = 100 mL sample of sodium chloride
solution, C0 = 0.01 M, which is titrated with AgNO3 solution,
C = 0.1 M, in the presence of K2CrO4 indicator at
concentration Cind = 0.002 M. The oversimplified “textbook” model
of this titration assumes that the titration of 100 mL 0.01 M
NaCl sample “ends” after the addition of 10 mL 0.1 M AgNO3
solution. This assumes that Ag2CrO4 will start forming only
when all chloride ions are consumed by the silver ions.
However, the solubility of AgCl and Ag2CrO4 and other chemical
[H+][HCrO4–] = K11[H2CrO4]
[H+][CrO42–] = K21[HCrO4–]
[H+][Cr2O72–] = K22[HCr2O7–]
[Cr2O72–] = K1[HCrO4–]2
[H+][OH–] = Kw
[AgCl] = K1Cl[Ag+][Cl–]
[AgCl2–] = K2Cl[Ag+][Cl–]2
[AgCl32–] = K3Cl[Ag+][Cl–]3
[AgOH] = K1OH[Ag+][OH–]
[Ag(OH)2–] = K2OH[Ag+][OH–]2
[Ag(OH)32–] = K3OH[Ag+][OH–]3
[Ag+][Cl–] = Ksp1
[Ag+]2[CrO42–] = Ksp2
[Ag+]2[Cr2O72–] = Ksp3
[Ag+][OH–] = Ksp4
pK11 = 0.8
pK21 = 6.5
logK22 = 0.07
logK1 = 1.52
pKw = 14.0
logK1Cl = 3.08
logK2Cl = 5.08
logK3Cl = 6.0
logK1OH = 2.3
logK2OH = 3.6
logK3OH = 4.8
processes makes this trivial problem considerably more
complex. Conceptually, the endpoint of titration corresponds to the
point where the solubility product of Ag2CrO4 is crossed.
At what point will the endpoint of titration actually occur in
All relevant data for detailed calculations are presented in
Table 1 [
]. For this system, the titrand (D) is NaCl solution,
V0 = 100 mL and C0 = 0.01 M, with K2CrO4 (with concentration
Cind = 0.002 M), and the titrant (T) is AgNO3 solution, C = 0.1 M.
Volume of the titrant added up to a given point of titration is
denoted as V. In order to calculate the precise endpoint of
titration, it is instructive to follow the following steps:
Formulate the proton balance for D (i.e., at V = 0) and
show that it is alkaline.
Formulate the relationship between [CrO42–] and pH
Calculate the pH = pH0 of D for C0 = 0.01 M and
Cind = 0.001, 0.002, 0.005, and 0.010 M.
Plot the logarithmic concentration of the various
chromium species as a function of pH at Cind = 0.002 M and
compare the value of [CrO42–] with Cind at pH = pH0.
For the titration stage (V > 0), formulate the
concentration balances for Ag and Cl. Denote the concentration
of AgCl (precipitate) in the system as [pr]. Compare
these two concentration balances in order to eliminate
the [pr] in the resulting equation and simplify this
equation on the basis of quantitative knowledge in Table 1.
Calculate the titration endpoint (Vend) where the
solubility product Ksp2 is crossed. Assume that pH does
not change during the titration.
(VII) Calculate the Cind value at which Vend = Veq (i.e., the
bias in chloride determination vanishes).
(VIII) Check whether the solubility products for Ag2Cr2O7
and AgOH are crossed at Cind = 0.002 M and V = Vend.
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3. Kotrly S , Sucha L. Handbook of Chemical Equilibria in Analytical Chemistry , Ellis Horwood Series in Analytical Chemistry. New York: John Wiley and Sons; 1985 .