Question

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.

Short answer

a) The volume of 0.01000 M AgNO3 needed to titrate 100.0 mL of the water sample can be calculated using stoichiometry and molarity. b) The concentration of Ag+ at the equivalence point is 0 M. c) The concentration of CrO4^2- should be such that Ag2CrO4 precipitation begins just after the equivalence point. d) Varying the chromate ion concentration can lead to overestimation or underestimation of the Cl- concentration. e) Exchanging reactants would be impractical due to difficulties detecting unreacted Cl- ions.

Step-by-step solution

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) \(= Moles \times \frac{1}{0.01 \, M}\)

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.

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 \([\mathrm{CrO}_4^{2-}]\).

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.

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.

Key concepts

Chloride Ion Determination

In the context of Mohr titration, determining chloride ion concentration is crucial for assessing water quality. Chloride ions (\(\mathrm{Cl}^- \)) are commonly found in drinking water, and their concentration needs to be monitored to ensure safety and compliance with water standards.

• The process involves titrating chloride ions with silver nitrate (\(\mathrm{AgNO}_3 \)) solution.
• When chloride ions react with silver ions (\(\mathrm{Ag}^+ \)), they form an insoluble white precipitate of silver chloride (\(\mathrm{AgCl} \) ).

This reaction can be used to calculate the amount of chloride present through stoichiometric calculations based on the volume of titrant used. Precision is key in ensuring accurate results, which is essential for reliable water analysis.

Precipitation Reaction

In Mohr titration, the precipitation reaction is central to detecting the endpoint of the titration. The reaction between chloride ions and silver ions is a classic precipitation reaction: \[ \mathrm{Ag}^+(\mathrm{aq}) + \mathrm{Cl}^-(\mathrm{aq}) \rightarrow \mathrm{AgCl}(\mathrm{s}) \]

• At the reaction's endpoint, all chloride ions should have precipitated as \(\mathrm{AgCl} \).
• The appearance of a red-brown precipitate of silver chromate (\(\mathrm{Ag}_2\mathrm{CrO}_4 \)) signifies that all chloride ions have reacted.

This visual cue indicates the completion of the reaction and helps determine the correct amount of titrant needed.

Equivalence Point

The equivalence point in a titration marks the stage at which the quantity of titrant added is stoichiometrically equivalent to the amount of analyte in the sample. In Mohr's method, this means all \(\mathrm{Cl}^-\) ions have reacted with \(\mathrm{Ag}^+\) ions to form \(\mathrm{AgCl}\).

• No excess \(\mathrm{Cl}^-\) or \(\mathrm{Ag}^+\) ions remain in the solution.
• This point occurs just before any other precipitate, such as \(\mathrm{Ag}_2\mathrm{CrO}_4\), forms.

Understanding and accurately identifying the equivalence point through the appearance of the silver chromate precipitate is fundamental for precise \(\mathrm{Cl}^-\) determination.

Solubility Product

The solubility product (\(K_{sp}\)) concept plays a vital role in the Mohr titration, particularly when dealing with the potential formation of additional precipitates. The \(K_{sp}\) of a compound is the product of the concentrations of the ions involved, each raised to the power of its coefficient in the dissolution equation.

• In Mohr titration, the \(K_{sp}\) for \(\mathrm{AgCl}\) ensures that \(\mathrm{AgCl}\) precipitates initially.
• This must be considered alongside the \(K_{sp}\) of \(\mathrm{Ag}_2\mathrm{CrO}_4\).

Calculating the correct concentrations of ions is crucial to prevent the precipitation of \(\mathrm{Ag}_2\mathrm{CrO}_4\) until precisely after the equivalence point, ensuring an accurate titration.

Chemical Analysis Methods

Mohr titration is a widely recognized chemical analysis method, especially for chloride ion analysis. It exemplifies how titrimetric methods can be adapted for specific contaminants in various solutions.

• The simplicity of measuring end reactions with color changes makes it accessible and accurate for practical applications.
• However, factors such as pH and competing reactions must be managed for reliability.

Understanding the application and limitations of Mohr titration is essential for accurate chemical analysis, making it a valuable method in both academic and practical contexts.