Problem 188 - A Complete Resource Book in Chemistry for JEE Main

Question

In the precipitation titration of \(\mathrm{KCl}\) against \(\mathrm{AgNO}_{3}\), \(\mathrm{K}_{2} \mathrm{CrO}_{4}\) is used as an indicator since, \(\mathrm{AgCl}\) is white coloured. End point is detected by appearance of deep yellow coloured precipitate of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\). The minimum concentration of chromate ion required for detectionof end point is \(\left[\mathrm{K}_{s p}\right.\) of \(\mathrm{AgCl}=2.5 \times 10^{-10}\) and \(\mathrm{K}_{\text {sp }}\) of \(\left.\mathrm{Ag}_{2} \mathrm{CrO}_{4}=1.8 \times 10^{-12}\right]\) (a) \(7.3 \times 10^{-2} \mathrm{M}\) (b) \(5.3 \times 10^{-4} \mathrm{M}\) (c) \(7.3 \times 10^{-3} \mathrm{M}\) (d) \(3.6 \times 10^{-5} \mathrm{M}\)

Step-by-Step Solution

Answer

(d) \(3.6 \times 10^{-5} \mathrm{M}\)

Step 1: Understanding the Reaction

In the precipitation titration of KCl with AgNO3, silver ions (Ag+) react with chloride ions (Cl-) to form a white precipitate of AgCl as it reaches its maximum concentration.

Step 2: Determining the End Point

The titration continues until an excess of Ag+ is added, which then reacts with K2CrO4 to form a deep yellow precipitate of Ag2CrO4, signaling the endpoint of the titration.

Step 3: Utilizing Ksp for AgCl

The solubility product (Ksp) of AgCl is given by \( K_{sp} = [Ag^+][Cl^-] = 2.5 \times 10^{-10} \). At the endpoint, we have the maximum concentration of Ag+ ions in equilibrium when AgCl starts forming, therefore we assume \([Ag^+] = s\) where \(s\) is the solubility of AgCl.

Step 4: Utilizing Ksp for Ag2CrO4

The solubility product for Ag2CrO4 is \( K_{sp} = [Ag^+]^2[CrO_4^{2-}] = 1.8 \times 10^{-12} \). Since we know from the previous step \([Ag^+] = s\), we solve for \([Ag^+]\) which we know at equilibrium with AgCl at its threshold.

Step 5: Calculating [Ag+] from AgCl Equilibrium

Using the expression for \([Ag^+] = \sqrt{Ksp} = \sqrt{2.5 \times 10^{-10}} \). Calculate this value to be the concentration of Ag+ at AgCl equilibrium.

Step 6: Finding [CrO4^2-] Needed for Endpoint

Re-arrange the solubility product for Ag2CrO4 to find the minimum concentration of chromate ions needed: \([CrO_4^{2-}] = \frac{K_{sp}}{[Ag^+]^2} = \frac{1.8 \times 10^{-12}}{(\sqrt{2.5 \times 10^{-10}})^2}\). Calculate this value.

Key Concepts

Solubility Product

The solubility product, denoted as \( K_{sp} \), is a useful concept in understanding how salt solubility affects chemical reactions. In precipitation titration, it is crucial to predict when a precipitate will form. The solubility product constant provides a mathematical way to describe this balance.
In simple terms, \( K_{sp} \) is the product of the concentrations of the ions of a sparingly soluble salt, raised to the power of their coefficients in the balanced equation. For example, in the case of silver chloride (AgCl"):

• \( K_{sp} = [Ag^+] [Cl^-] \)

This equation helps in understanding when AgCl") will start to appear as a solid precipitate in a solution. Once the product of the ion concentrations equals the \( K_{sp} \) value, the precipitate will form. Similarly, for Ag2CrO4"):

• \( K_{sp} = [Ag^+]^2 [CrO_4^{2-}] \)

By setting up equations with known \( K_{sp} \) values, students can calculate ion concentrations that signal the formation of various precipitates and help in identifying endpoints in titration.

Chemical Equilibrium

Chemical equilibrium is an important concept in precipitation titration because it tells us how reactions can reach a point where no further net change occurs. This state is achieved when the forward reaction rate, where reactants are turning into products, equals the reverse reaction rate, where products turn back into reactants.
In titrations involving precipitation, chemical equilibrium plays out when the rate of ion deposition as a precipitate matches the rate at which the precipitate dissolves back into ions in the solution. To detect this balance effectively, particularly at the endpoint of a titration, it is crucial to understand the equilibrium concentrations of the involved ions.
For example, in the titration involving AgCl", determining when Ag+ and Cl− have reached equilibrium under the conditions that correspond to their K_{sp}") is essential. At this point, we know the chemical system is at equilibrium and the reaction changes direction, signaling the endpoint.

Chromate Indicator

In precipitation titrations, indicators such as chromate ion ( CrO_4^{2−}") are instrumental in determining the endpoint. The chromate indicator is particularly useful because it forms a colored precipitate, Ag2CrO4", that is easy to see. This colorful change marks the completion of the reaction.
When using K2CrO4", its role as a chromate indicator is pivotal. At first, silver ions are added until they all pair with chloride ions to form silver chloride. Any excess Ag+") beyond this reacts with the chromate ions to produce Ag2CrO4", which is yellow in color.
In the context of the titration described, the appearance of the deep yellow-colored precipitate of Ag2CrO4" confirms the endpoint. Knowing the minimum concentration requirement for the chromate ion is essential to ensure that the color change occurs at the correct time, providing an accurate measurement.