Problem 14 - Chemistry The Central Science In Si Units

Question

Consider the equilibrium $$ \mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(I) \rightleftharpoons \mathrm{HB}^{+}(a q)+\mathrm{OH}^{-}(a q) . $$ 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) Stays the same; (b) Increases; (c) Decreases.

Step 1: Understand the Equilibrium Reaction

The equilibrium reaction given is balanced and involves the base \( \mathrm{B}(aq) \) reacting with water to form its conjugate acid \( \mathrm{HB}^{+}(aq) \) and \( \mathrm{OH}^{-}(aq) \). The equilibrium expression for this reaction is based on the concentrations of products over reactants.

Step 2: Determine the Effect on Equilibrium Constant (Part a)

The equilibrium constant \( K \) is a function of temperature. Since no temperature change is mentioned, the equilibrium constant will remain the same even after adding \( \mathrm{HB}^{+}(aq) \). Hence, the equilibrium constant stays the same.

Step 3: Analyze Changes in Reactant Concentration (Part b)

Le Chatelier's principle states that adding \( \mathrm{HB}^{+}(aq) \) shifts the equilibrium left to counteract the change, which will increase the concentration of \( \mathrm{B}(aq) \). Thus, the concentration of base \( \mathrm{B}(aq) \) will increase.

Step 4: Evaluate pH Changes (Part c)

The equilibrium shift to the left due to added \( \mathrm{HB}^{+}(aq) \) results in decreased \( \mathrm{OH}^{-}(aq) \) concentration, leading to a decreased pH. Hence, the pH of the solution will decrease.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a key concept in chemistry that helps us predict how a change will affect a system at equilibrium. If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change.
In the given reaction, the addition of a salt containing \( \mathrm{HB}^{+} \) introduces more products into the system. According to Le Chatelier's Principle, the equilibrium will shift towards the reactants, increasing the concentration of \( \mathrm{B}(aq) \).
This response acts to partially counterbalance the increase in products and reestablishes the equilibrium. Le Chatelier's Principle is crucial for understanding how systems react to various stresses.

Equilibrium Constant

The equilibrium constant, represented as \( K \), is a numerical expression of the ratio of product concentrations to reactant concentrations in an equilibrium state. It is a constant for a given reaction at a specific temperature.
For the reaction \( \mathrm{B}(aq) + \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HB}^{+}(aq) + \mathrm{OH}^{-}(aq) \), the equilibrium constant expression is:
\[ K = \frac{[\mathrm{HB}^{+}][\mathrm{OH}^{-}]}{[\mathrm{B}]} \]
Even if substances are added or removed from the equilibrium system, \( K \) does not change unless the temperature changes. In this exercise, adding \( \mathrm{HB}^{+} \) does not alter the equilibrium constant because the temperature remains constant.

pH Changes

The pH of a solution is a measure of its acidity or basicity and is calculated from the concentration of hydrogen ions (\( \mathrm{H}^{+} \)) in the solution.
In the basic equilibrium reaction provided, the addition of \( \mathrm{HB}^{+} \) causes a shift in equilibrium to the left, reducing \( \mathrm{OH}^{-} \) levels.
Since \( \mathrm{OH}^{-} \) ions are neutralizers of acids, a decrease in \( \mathrm{OH}^{-} \) concentration means a less basic or more acidic solution, resulting in a lower pH.
This change is indicative of an increase in acidity due to the shift in the equilibrium position.

Acid-Base Equilibria

Acid-base equilibria involve the transfer of protons (\( \mathrm{H}^{+} \) ions) between substances. Bases like \( \mathrm{B}(aq) \) accept protons, while acids like \( \mathrm{HB}^{+}(aq) \) donate them.
In the reaction \( \mathrm{B}(aq) + \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HB}^{+}(aq) + \mathrm{OH}^{-}(aq) \), \( \mathrm{HB}^{+} \) is the conjugate acid of the base \( \mathrm{B} \).
This equilibrium process illustrates a common acid-base equilibrium where an acid and a base exist in balance. The equilibrium can shift to either direction based on changes in concentration, impacting pH and reacting species.