Question

A student is asked to prepare a \(0.030 \mathrm{M}\) aqueous solu- $$ \text { tion of } \mathrm{PbCl}_{2} $$ (a) Is this possible at \(25^{\circ} \mathrm{C}\) ? (Hint: Is dissolving \(0.030 \mathrm{~mol}\) of \(\mathrm{PbCl}_{2}\) at \(25^{\circ} \mathrm{C}\) possible?) (b) If the student used water at \(100^{\circ} \mathrm{C},\) would this be possible?

Short answer

Short answer: It's not possible to prepare a 0.030 M solution of PbCl₂ at 25°C because the solubility of PbCl₂ at this temperature is only 0.0061 M. At 100°C, solubility might be higher, but without knowing the exact Ksp value, we cannot definitively determine if it's possible to prepare a 0.030 M solution at this temperature.

Step-by-step solution

Given information

We are given the following data: - A student needs to prepare 0.030 M aqueous solution of PbCl₂ - Temperature 1: 25°C - Temperature 2: 100°C Ksp of PbCl₂ at 25°C = \(1.7\times10^{-5}\)

Write the solubility product expression

The balanced equation for the dissolution of PbCl₂ in water is: \(\ce{PbCl2(s) <=> Pb^{2+}(aq) + 2Cl^-(aq)}\) The solubility product expression, Ksp, is given by: Ksp = [Pb²⁺][Cl⁻]²\

Calculate the solubility of PbCl₂ at 25°C

Let the solubility of PbCl₂ at 25°C be S. When PbCl₂ dissolves, the concentration of Pb²⁺ will be S, and the concentration of Cl⁻ will be 2S. Using the solubility product expression: Ksp = [Pb²⁺][Cl⁻]² → \(1.7\times10^{-5}\) = S(2S)² Solving the equation for S: S₃ = \(\frac{1.7\times10^{-5}}{4}\) S = \(0.0061 M\) The solubility of PbCl₂ at 25°C is 0.0061 M.

Determine if it's possible to prepare the solution at 25°C

The solubility of PbCl₂ at 25°C is 0.0061 M. Since the student needs to prepare a 0.030 M solution, it's not possible to dissolve enough PbCl₂ at 25°C. Answer (a): No, it's not possible to prepare a 0.030 M solution of PbCl₂ at 25°C.

Solubility at 100°C

We are not provided with the Ksp value for PbCl₂ at 100°C. However, in general, the solubility of salts increases with temperature as the dissolution process is often an endothermic reaction. Answer (b): Without knowing the exact Ksp value for PbCl₂ at 100°C, we cannot definitively determine if it's possible to prepare a 0.030 M solution. However, solubility may be higher at this temperature, so there is a possibility, but it's not guaranteed.