In the Mohr titration, \(\mathrm{Cl}^{-}(\mathrm{aq})\) is titrated with \(\mathrm{AgNO}_{3}(\text { aq })\) in solutions that are at about \(\mathrm{pH}=7\). Thus, it is suitable for determining the chloride ion content of drinking water. The indicator used in the titration is \(\mathrm{K}_{2} \mathrm{CrO}_{4}(\text { aq }) .\) A red-brown precipitate of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}(\mathrm{s})\) forms after all the \(\mathrm{Cl}^{-}\) has precipitated. The titration reaction is \(\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq}) \longrightarrow \mathrm{AgCl}(\mathrm{s}) .\) At the equivalence point of the titration, the titration mixture consists of \(\mathrm{AgCl}(\mathrm{s})\) and a solution having neither \(\mathrm{Ag}^{+}\) nor \(\mathrm{Cl}^{-}\) in excess. Also, no \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}(\mathrm{s})\) is present, but it forms immediately after the equivalence point. (a) How many milliliters of \(0.01000 \mathrm{M} \mathrm{AgNO}_{3}(\mathrm{aq})\) are required to titrate \(100.0 \mathrm{mL}\) of a municipal water sample having \(29.5 \mathrm{mg} \mathrm{Cl}^{-} / \mathrm{L} ?\) (b) What is \(\left[\mathrm{Ag}^{+}\right]\) at the equivalence point of the Mohr titration? (c) What is \(\left[\mathrm{CrO}_{4}^{2-}\right]\) in the titration mixture to meet the requirement of no precipitation of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}(\mathrm{s})\) until immediately after the equivalence point? (d) Describe the effect on the results of the titration if \(\left[\mathrm{CrO}_{4}^{2-}\right]\) were (1) greater than that calculated in part (c) or (2) less than that calculated? (e) Do you think the Mohr titration would work if the reactants were exchanged - that is, with \(\mathrm{Cl}^{-}(\text {aq })\) as the titrant and \(\mathrm{Ag}^{+}(\) aq) in the sample being analyzed? Explain.

Step by step solution

01

Calculate the volume of the titrant

Firstly, calculate the mass of chloride ions in the water sample, then turn it into moles using molar mass. Use the stoichiometric ratio from the titration reaction to find the amount in moles of AgNO3 needed, and then calculate the volume of the 0.01000 M AgNO3 solution required using the molarity formula. Initial mass of Cl- \(= 100.0 \, mL \times \frac{29.5 \, mg}{L} \times \frac{1L}{1000 \, mL}\). Moles of Cl- \(= \frac{Initial \, mass}{35.45 \, g/mol} \) where 35.45 g/mol is the molar mass of chloride ion. Volume of AgNO3 (V) \(= Moles \times \frac{1}{0.01 \, M}\)

02

Determine the concentration of silver ion at the equivalence point

At the equivalence point of the titration, all the silver has reacted with the chloride ions and formed AgCl precipitate. Thus, there are no silver ions left in the titration mixture. So, \([\mathrm{Ag}^+]\) at the equivalence point is 0.

03

Determine concentration of chromate ion in the titration mixture

When no more chloride ions are left, the silver ions start reacting with the chromate ions. The chromate ion concentration should be such that Ag2CrO4 precipitates out just past the equivalence point. Using the solubility product expression and Ksp value for Ag2CrO4, calculate \([\mathrm{CrO}_4^{2-}]\). Knowing that \([\mathrm{Ag}^{+}]\) = 0.01 M (excess AgNO3 solution after the equivalence point), from \(K_{sp} = [\mathrm{Ag}^{+}]^2[\mathrm{CrO}_4^{2-}]\) we find \([\mathrm{CrO}_4^{2-}]\).

04

Analyze varying the chromate ion concentration

If the concentration of CrO4^2- were greater, Ag2CrO4 would precipitate out before the equivalence point leading to an underestimation of Cl- concentration. If it were lower, the precipitate would form after more AgNO3 is added leading to an overestimation of Cl- concentration.

05

Discuss the possibility of exchanging reactants

Exchanging reactants in the Mohr titration would be impractical because it would require detecting the presence of unreacted Cl- ions in the solution, which is not as straightforward as detecting the formation of Ag2CrO4 precipitate using a visible colour change.

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