Problem 14 - Chemistry: The Central Science in SI Units, Global Edition

Question

Consider the equilibrium $$ \mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HB}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ Suppose that a salt of \(\mathrm{HB}^{+}(a q)\) is added to a solution of \(\mathrm{B}(a q)\) at equilibrium. (a) Will the equilibrium constant for the reaction increase, decrease, or stay the same? (b) Will the concentration of \(\mathrm{B}(a q)\) increase, decrease, or stay the same? (c) Will the pH of the solution increase, decrease, or stay the same?

Step-by-Step Solution

Answer

(a) The equilibrium constant, K, will stay the same. (b) The concentration of B(aq) will increase. (c) The pH of the solution will decrease.

Step 1: (a) Determining the change in the equilibrium constant

When analyzing a reaction in equilibrium and determining the effect of adding a reactant or a product, it is crucial to consider the Le Châtelier's principle. According to this principle, if a system at equilibrium is subjected to a change in concentration, temperature, or volume, the equilibrium will shift in a direction that counteracts the applied change to regain equilibrium. Let's consider the addition of HB+(aq) salt in our reaction. Remember that the equilibrium constant, K, only changes if there is a change in temperature. Since there is no mention of a change in temperature, we can conclude that the equilibrium constant will remain the same. Answer: (a) The equilibrium constant, K, will stay the same.

Step 2: (b) Determining the change in the concentration of B(aq)

Since we are adding HB+(aq) to the solution, the concentration of HB+ will increase, according to Le Châtelier's principle, the equilibrium will shift to the left to counteract this change. As the equilibrium shifts to the left, the concentration of B(aq) will increase. Answer: (b) The concentration of B(aq) will increase.

Step 3: (c) Determining the change in pH

In this reaction, the equilibrium is shifted towards the left when the concentration of HB+ is increased. As the concentration of B(aq) increases, the concentration of OH- ions would decrease since the reaction is moving to the left. A decrease in the concentration of OH- ions will lead to an increase in H+ ions concentration. Therefore, the pH will decrease. Recall the relationship between pH and [H+]: \[ pH = -\log[H+] \] As the concentration of H+ ions increases, the pH value will decrease. Answer: (c) The pH of the solution will decrease.

Key Concepts

Le Châtelier's Principle

Le Châtelier's Principle is a vital concept in understanding how chemical reactions respond to changes in their environment. If a system at equilibrium is disturbed by a change in concentration, temperature, or pressure, the system adjusts to counteract the disturbance. In essence, the system shifts to "balance itself out."

In the given exercise, when a salt containing the product \( \mathrm{HB}^{+} \) is added to the equilibrium reaction \( \mathrm{B}(aq) + \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HB}^{+}(aq) + \mathrm{OH}^{-}(aq) \), it increases the concentration of \( \mathrm{HB}^{+} \) in the solution. According to Le Châtelier's Principle, the equilibrium will shift towards the reactants — to the left — to reduce the added stress from \( \mathrm{HB}^{+} \).

This principle helps explain why certain concentrations increase or decrease when a system is altered.

Equilibrium Constant

An equilibrium constant, denoted as \( K \), is a number that expresses the ratio of concentrations of the products to reactants at equilibrium. Importantly, \( K \) is dependent on temperature and not on the concentrations of the individual reactants or products.

In the exercise, though we add \( \mathrm{HB}^{+} \) to the solution, the equilibrium constant \( K \) remains unchanged because this scenario only involves concentration changes and not a temperature change. The value of \( K \) can be seen as a snapshot — it stays constant unless the temperature changes.

Thus, while the system may shift according to Le Châtelier's Principle, the numerical value of \( K \) remains fixed at a given temperature.

pH Changes

The pH of a solution is a measure of its hydrogen ion concentration, usually given as \( \mathrm{pH} = -\log[\mathrm{H}^+] \). It specifies how acidic or basic the solution is on a scale from 0 (most acidic) to 14 (most basic).

In the present reaction, when the equilibrium is shifted to the left by adding \( \mathrm{HB}^{+} \), the concentration of \( \mathrm{OH}^{-} \) ions decreases as \( \mathrm{HB}^{+} \) forms \( \mathrm{B}(aq) \) and \( \mathrm{H}_{2} \mathrm{O}(l) \). Consequently, fewer \( \mathrm{OH}^{-} \) ions mean a relative increase in \( \mathrm{H}^+ \) ion concentration as equilibrium shifts.

This increase in \( \mathrm{H}^+ \) concentration results in a lower value of pH, indicating the solution becomes more acidic.

Concentration Changes

Changes in concentration are common disturbances that affect equilibria according to Le Châtelier's Principle. Here, adding \( \mathrm{HB}^{+} \) affects the concentration balance of the reaction.

As more \( \mathrm{HB}^{+} \) is added, the system tries to minimize this alteration. The equilibrium shifts towards the left to produce more \( \mathrm{B} \) and \( \mathrm{H}_{2} \mathrm{O} \), thereby increasing the concentration of \( \mathrm{B}(aq) \).

This change in concentration ensures the reaction responds by reducing the impact of the added \( \mathrm{HB}^{+} \) ions — a classic demonstration of concentration's effect on equilibrium.