Question

For each statement, indicate whether it is true or false. (a) The solubility of a slightly soluble salt can be expressed in units of moles per liter. (b) The solubility product of a slightly soluble salt is simply the square of the solubility. (c) The solubility of a slightly soluble salt is independent of the presence of a common ion. (d) The solubility product of a slightly soluble salt is independent of the presence of a common ion.

Short answer

(a) True - The solubility of a slightly soluble salt can be expressed in units of moles per liter (M or mol/L). (b) False - The solubility product of a slightly soluble salt is not always simply the square of the solubility, as it depends on the stoichiometries of the constituent ions. (c) False - The solubility of a slightly soluble salt can be affected by the presence of a common ion, as explained by the common ion effect. (d) True - The solubility product of a slightly soluble salt is independent of the presence of a common ion, as it is a constant value that only depends on the temperature and the nature of the salt.

Step-by-step solution

Statement (a): The solubility of a slightly soluble salt can be expressed in units of moles per liter.

This statement is true. The solubility of a salt is a measure of the maximum amount of the salt that can dissolve in a given amount of solvent at a particular temperature. It is typically expressed in units of moles per liter (M or mol/L).

Statement (b): The solubility product of a slightly soluble salt is simply the square of the solubility.

This statement is false in general. The solubility product (K_sp) of a slightly soluble salt is the product of the concentrations of its constituent ions, each raised to the power of their stoichiometric coefficients in the balanced dissolution reaction. For a simple salt like \(AB\), which dissolves according to the reaction: \(AB \rightleftharpoons A^+ + B^-\), the solubility product is indeed the square of the solubility, because the stoichiometric coefficients are both 1 and the concentrations of the ions are equal: \(K_{sp} = [A^+][B^-]\). However, for salts with different stoichiometries, such as \(AB_2\), the solubility product is not simply the square of the solubility: \(K_{sp} = [A^+][B^-]^2\).

Statement (c): The solubility of a slightly soluble salt is independent of the presence of a common ion.

This statement is false. The solubility of a slightly soluble salt can be affected by the presence of a common ion, as explained by the common ion effect. The common ion effect is a consequence of Le Chatelier's principle: when a reaction is at equilibrium, adding a product will shift the equilibrium towards the reactants. Thus, if a common ion is introduced into the solution, the solubility of the slightly soluble salt can decrease, because the reaction will shift towards the undissolved salt to counteract the increase in product concentration.

Statement (d): The solubility product of a slightly soluble salt is independent of the presence of a common ion.

This statement is true. The solubility product (K_sp) of a slightly soluble salt is a constant value that only depends on the temperature and the nature of the salt. It is not affected by the presence of a common ion, although the solubility of the salt may be affected, as explained in Statement (c). The solubility product provides information about the relative solubilities of different salts and can be used to predict whether a precipitation reaction will occur or not, given the concentrations of the ions in the solution.

Key concepts

Common Ion Effect

The common ion effect refers to the phenomenon where the solubility of a slightly soluble salt decreases in the presence of a common ion. Understanding this concept is important because it has implications for reactions at equilibrium. When a salt dissolves in a solution, it dissociates into its constituent ions. If one of these ions is already present in the solution, it results in a shift in equilibrium following Le Chatelier’s principle.

Let's break it down:

• Consider a salt like calcium sulfate (CaSO₄) in solution. If you add calcium ions (Ca²⁺) from another source, it introduces a common ion 'Ca²⁺.'
• As a result, the equilibrium shifts to decrease the concentration of dissolved ions, causing more salt to remain undissolved.
• This decrease in solubility due to additional common ion presence indicates the common ion effect in action.

In practical terms, this means that adding a substance that contains a common ion can lead to less overall solubility for that salt.

Le Chatelier's Principle

Le Chatelier's Principle states that if an external change is applied to a system at equilibrium, the system adjusts to minimize that change. This principle is essential in understanding chemical equilibria, including the solubility of salts.

In solutions involving sparingly soluble salts, Le Chatelier's Principle plays out through:

• The shifting of equilibria: If ions of the dissolved salt are increased, the equilibrium will favor the formation of more undissolved salt, reducing solubility.
• Response to concentration changes: For a reaction at equilibrium, adding more reactant or product will cause a shift that counteracts this addition. For example, adding a common ion shifts the equilibrium towards the reactants, thus reducing the solubility of the salt.

This principle explains why the addition of a common ion can reduce the solubility of a salt by shifting the dissolution reaction to favor the undissolved state.

Solubility Product Constant (Ksp)

The Solubility Product Constant, or Ksp, is a critical value that quantifies the extent to which a sparingly soluble salt can dissolve in a solution. Ksp is a measure of the equilibrium between a solid compound and its dissolved ions.

Here are key points about Ksp:

• For any equilibrated dissolution reaction, such as the dissolution of a salt, the Ksp is the product of the ion concentrations, each raised to a power equal to its stoichiometric coefficient in the balanced equation. For example, for a simple salt like AgCl, this can be described as: \[ K_{sp} = [Ag^+][Cl^-] \]
• Ksp is constant at a given temperature and is unaffected by the presence of a common ion; it only depends on inherent properties of the salt and temperature.
• While Ksp is constant, the presence of a common ion affects the solubility of the salt, illustrating the difference between Ksp and actual solubility.

Understanding Ksp allows us to predict the conditions under which a salt will precipitate from solution and helps compare the solubility among different salts.