Problem 13 - Chemistry The Central Science

Question

Which of these statements about the common-ion effect is most correct? (a) The solubility of a salt MA is decreased in a solution that already contains either M \(^{+}\) or \(A^{-} .(\mathbf{b})\) Common ions alter the equilibrium constant for the reaction of an ionic solid with water. (c) The common-ion effect does not apply to unusual ions like \(\mathrm{SO}_{3}^{2-}\) . (d) The solubility of a salt MA is affected equally by the addition of either \(\mathrm{A}^{-}\) or a noncommon ion.

Step-by-Step Solution

Answer

The most correct statement about the common-ion effect is (a): The solubility of a salt MA is decreased in a solution that already contains either M^+ or A^-. This is because the presence of a common ion shifts the equilibrium, causing a decrease in solubility as described by Le Châtelier's principle.

Step 1: Understand the Common-Ion Effect

The common-ion effect occurs when an ionic compound MA is dissolved in a solution that already contains either M^+ or A^-. This will result in a shift in the equilibrium of the reaction, which in turn decreases the solubility of the compound MA. This effect is an application of Le Châtelier's principle, which states that if a stress is applied to a system at equilibrium, the system will adjust to oppose the applied stress. In this case, the "stress" is the presence of the common ion, either M^+ or A^-. To answer the question, we'll analyze each statement to see which one best describes the common-ion effect.

Step 2: Analyze statement (a)

This statement states that the solubility of a salt MA is decreased in a solution that already contains either M^+ or A^-. This is a correct explanation of the common-ion effect, as the solubility will decrease due to the shift in equilibrium caused by the additional ions. We can consider this statement as a possible answer.

Step 3: Analyze statement (b)

The statement (b) says that common ions alter the equilibrium constant for the reaction of an ionic solid with water. This statement is incorrect because although the presence of the common ion affects the equilibrium position, the equilibrium constant remains unchanged. Le Châtelier's principle affects the position of the equilibrium but not the equilibrium constant.

Step 4: Analyze statement (c)

Statement (c) claims that the common-ion effect does not apply to unusual ions like SO_3^{2-}. This statement is incorrect as the common-ion effect can still apply to unusual ions if they share a common ion with another compound in the solution. The identity of the ions is not directly relevant to the common-ion effect; the important factor is the presence of common ions between the compounds involved.

Step 5: Analyze statement (d)

Statement (d) states that the solubility of a salt MA is affected equally by the addition of either A^- or a noncommon ion. This statement is also incorrect, as the addition of a noncommon ion will not have the same effect on solubility as the addition of a common ion (A^- in this case). The common-ion effect specifically involves a decrease in solubility due to the presence of a common ion in the solution.

Step 6: Determine the correct statement

Based on our analysis of the given statements, we can conclude that statement (a) is the most correct description of the common-ion effect. The solubility of a salt MA is decreased in a solution that already contains either M^+ or A^-, which is a direct consequence of the common-ion effect and Le Châtelier's principle.

Key Concepts

Solubility Equilibrium

When we talk about solubility equilibrium, we are referring to a particular type of chemical equilibrium that is established when an ionic compound dissolves in water. At this point, the rate at which the solid dissolves to form ions is equal to the rate at which the ions come together to form the solid.

Imagine a beaker with water and solid salt MA at the bottom. As some salt dissolves and MA breaks into M⁺ and A^- ions, an equilibrium state can be reached where the number of solid particles dissolving matches the number forming from ions.

This equilibrium can be represented by the equation: \[ MA_{(s)} \rightleftharpoons M^{+}_{(aq)} + A^{-}_{(aq)} \] The solubility product constant (Ksp) is the constant for this equilibrium representing the product of the ion concentrations raised to the power of their stoichiometric coefficients when the solution is saturated. Understanding this concept helps explain the behavior of salts in various conditions, like in the presence of a common ion.

Le Châtelier's Principle

When considering any equilibrium, Le Châtelier's principle is crucial. It tells us that if a system at equilibrium experiences a change in concentration, temperature, or pressure, the system will respond to counteract the imposed change and restore a new state of equilibrium.

Consider our example with the salt MA; if we add more M⁺ ions to the solution, Le Châtelier's principle predicts that the equilibrium will shift to oppose this increase. This means that more MA will form, hence reducing the concentration of A^- ions, because the system is attempting to minimize the effect of the added M⁺ ions by forming more of the solid MA.

This principle is beautifully intelligent—it tells us that a system at equilibrium is poised to maintain its status quo, shifting only as much as needed to counterbalance external stresses.

Ionic Compounds

Delving into what makes up these equilibriums, we come across ionic compounds, which are substances composed of positively charged ions (cations) and negatively charged ions (anions). These ions are held together by the strong electrostatic forces of attraction known as ionic bonds.

In the context of solubility, ionic compounds may dissolve in water, separating into their constituent ions which are then surrounded by water molecules—a process called hydration. The extent to which an ionic compound dissolves varies from one compound to another and can be influenced by the presence of other ions in the solution. This is particularly relevant when it comes to understanding the common-ion effect.

Chemical Equilibrium

Beyond just solubility, the idea of chemical equilibrium applies widely in chemistry to situations where the forward and reverse reactions occur at the same rate, resulting in no net change in the amounts of reactants and products. \[ aA + bB \rightleftharpoons cC + dD \] At the equilibrium point in this general reaction, the concentrations of A, B, C, and D remain constant. They are not necessarily equal, but they are steady, which can be expressed by an equilibrium constant (K_eq). It's important to note that equilibrium tells us about the ratios of products to reactants but does not give any information about the reaction rates.

Understanding chemical equilibrium helps us forecast the outcome of chemical reactions and tailor conditions to favor desired products in industrial chemical processes.