Question

Which of the following statements are true? (a) For an insoluble metallic salt, \(K_{\mathrm{sp}}\) is always less than 1 . (b) More \(\mathrm{PbCl}_{2}\) can be dissolved at \(100^{\circ} \mathrm{C}\) than at \(25^{\circ} \mathrm{C}\). One can conclude that dissolving \(\mathrm{PbCl}_{2}\) is an exothermic process. (c) When strips of copper metal are added to a saturated solution of \(\mathrm{Cu}(\mathrm{OH})_{2},\) a precipitate of \(\mathrm{Cu}(\mathrm{OH})_{2}\) can be expected to form because of the common ion effect.

Short answer

(a) The lower the solubility product constant (\(K_{\mathrm{sp}}\)) of an insoluble metallic salt, the lower its solubility in water. (b) As the temperature of a \(\mathrm{PbCl}_{2}\) solution increases, more of it can be dissolved, which means that the dissolution process is exothermic. (c) Adding copper strips to a saturated solution of \(\mathrm{Cu}(\mathrm{OH})_{2}\) will result in the formation of a precipitate due to the common ion effect. Answer: (a) True, (b) False, (c) False

Step-by-step solution

(Statement (a): Relationship between \(K_{\mathrm{sp}}\) and Solubility)

For an insoluble metallic salt, the solubility product constant, \(K_{\mathrm{sp}}\) represents the maximum concentration of ions in the solution at equilibrium. The smaller the \(K_{\mathrm{sp}}\), the lower the solubility of the salt in water. In general, for salts that are considered insoluble, \(K_{\mathrm{sp}}\) is less than 1. Thus, statement (a) is true.

(Statement (b): Effect of Temperature on Solubility and Exothermic Processes)

The solubility of many salts increases with an increase in temperature. The given statement explains that more \(\mathrm{PbCl}_{2}\) can be dissolved at \(100^{\circ} \mathrm{C}\) than at \(25^{\circ} \mathrm{C}\). This indicates that the solubility of \(\mathrm{PbCl}_{2}\) increases with temperature, which is consistent with an endothermic process. If dissolving \(\mathrm{PbCl}_{2}\) were an exothermic process, its solubility would decrease with increasing temperature. Thus, statement (b) is false.

(Statement (c): Common Ion Effect and Precipitate Formation)

When strips of copper metal are added to a saturated solution of \(\mathrm{Cu}(\mathrm{OH})_{2}\), the copper metal would not introduce any new ions into the solution, since it is a solid. Therefore, the common ion effect does not apply in this case. The common ion effect occurs when an ion is added to the solution, which would potentially shift the equilibrium and lead to the formation of a precipitate. In this particular case, no precipitate of \(\mathrm{Cu}(\mathrm{OH})_{2}\) can be expected to form due to the common ion effect. Thus, statement (c) is false.