Problem 89 - A Complete Resource Book in Chemistry for JEE Main

Question

The solubility of \(\mathrm{AgCl}\) in \(0.2 \mathrm{M} \mathrm{NaCl}\) is \([\mathrm{Ksp} \mathrm{AgCl}=\) \(\left.1.8 \times 10^{-10}\right]\) (a) \(1.8 \times 10^{-11} \mathrm{M}\) (b) \(9 \times 10^{-10} \mathrm{M}\) (c) \(6.5 \times 10^{-12} \mathrm{M}\) (d) \(5.6 \times 10^{-11} \mathrm{M}\)

Step-by-Step Solution

Answer

The solubility of AgCl in 0.2 M NaCl is \(9 \times 10^{-10} \mathrm{M}\).

Step 1: Understand the problem

We need to find the solubility of AgCl in a 0.2 M NaCl solution. Given the Ksp of AgCl, which is \(1.8 \times 10^{-10}\), the presence of a common ion (Cl-) will affect this solubility.

Step 2: Write the solubility product expression

The solubility product constant (Ksp) for AgCl is given by \(K_{sp} = [Ag^+][Cl^-]\). In pure water, both ions would have the same concentration as the solubility, \(s\). However, in 0.2 M NaCl, \([Cl^-]\) is initially 0.2 M.

Step 3: Substitute known values into Ksp equation

Let the solubility of AgCl in the NaCl solution be \(s\). Then, \([Ag^+]=s\) and \([Cl^-]=0.2 + s\). Approximating that \(s\) is very small compared to 0.2, we rewrite as \([Cl^-] \approx 0.2\).

Step 4: Calculate Ag+ concentration

Substitute \([Cl^-]\approx 0.2\) into the Ksp equation: \(1.8 \times 10^{-10} = s \cdot 0.2\). Solve for \(s\): \(s = \frac{1.8 \times 10^{-10}}{0.2}\).

Step 5: Solve for solubility s

Calculate \(s = \frac{1.8 \times 10^{-10}}{0.2} = 9 \times 10^{-10}\). This gives the solubility of AgCl in a 0.2 M NaCl solution.

Key Concepts

Common Ion Effect and Its Impact on Solubility

In a solution where a common ion is present, the solubility of a compound is reduced. This phenomenon is known as the common ion effect. It plays a significant role in determining the solubility of salts in solutions where ions are shared between the dissolved species and the solvent additives. For example, when silver chloride (AgCl) is dissolved in a sodium chloride (NaCl) solution, both solutions share chloride ions (Cl-). This shared ion presence limits the solubility of AgCl, causing it to dissolve less in comparison to a scenario with pure water.

• Cl- is the common ion in this case when both NaCl and AgCl are in the solution.
• The higher the concentration of the common ion, the lower the solubility of the salt in question.

Understanding this effect is crucial in predicting the behavior of ionic compounds in various chemical environments, especially in industrial and laboratory settings.

Solubility of Salts in Ionic Solutions

Solubility refers to the ability of a salt to dissolve in a solvent, such as water, forming a stable solution. Ionic salts, like AgCl, dissociate into their constituent ions when dissolved. The solubility product constant (Ksp) helps in quantifying this dissolution process. A salt's solubility can be affected by temperature, pressure, and the presence of other ions.
In the presence of a strong electrolyte like NaCl, the solubility process is influenced by the concentration of ions contributed by NaCl. For AgCl in 0.2 M NaCl, the substantial presence of chloride ions shifts the equilibrium, reducing the amount of AgCl that can successfully dissolve. This adjustment in solubility due to ion presence is a profound concept in solution chemistry, especially when dealing with ionic compounds.

Chemistry Problem Solving with Ionic Equilibria

Solving chemistry problems involving ionic equilibria requires a systematic approach. The process often revolves around building and solving equilibrium expressions or equations for the system in question.
Approaching a typical problem involves:

• Identifying the salts and ions present in the solution.
• Recognizing significant constants such as the Ksp, or solubility product.
• Using known concentrations to approximate unknowns reasonably, such as applying the common ion effect knowledge.
• Substituting values into equilibrium expressions to calculate desired concentrations or solubilities.

Chemistry problem-solving in this context relies on not only a firm grasp of the underlying principles but also on the ability to apply these principles practically to retrieve meaningful answers.

Equilibrium Expressions for Solubility Calculations

Equilibrium expressions are mathematical expressions that describe the balance between product and reactant concentrations in chemical equilibria. In the context of solubility, these expressions guide us in determining the amount of salt that can dissolve in the presence of other ions.
For the dissolution of AgCl, the equilibrium expression is written based on its solubility product: \[ K_{sp} = [Ag^+][Cl^-] \] Given the known concentration of one ion, one can solve for the other utilizing the Ksp value. In the presence of a common ion, such as Cl- from NaCl in this example, the equation adjusts by incorporating the initial concentration, allowing for the calculation of the remaining ion's equilibrium concentration. Solving these expressions aids in understanding how ionic equilibria operate within different chemical contexts and provides insights into the ways solubility can be modulated by ion presence.