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 \(\mathrm{pH}\) of the solution increase, decrease, or stay the same?

Short answer

In summary, when a salt of HB+ is added to the equilibrium system: (a) The equilibrium constant will stay the same, as it is only dependent on temperature; (b) The concentration of B will increase, as the reaction shifts in the reverse direction to consume HB+ and OH-; and (c) The pH of the solution will decrease, due to a decrease in OH- concentration and an increase in H3O+ concentration.

Step-by-step solution

Equilibrium constant

Le Chatelier's principle helps us predict the effect of a change in conditions on a chemical equilibrium. According to this principle, when a change is applied to a system at equilibrium, the system shifts in a direction that opposes the change to re-establish the equilibrium. However, the equilibrium constant does not change in this case since the equilibrium constant is only dependent on temperature. Therefore, adding a salt of HB+ will not change the equilibrium constant. Answer (a): The equilibrium constant will stay the same.

Reactant concentration

When a salt of HB+ is added to the equilibrium system, the concentration of HB+ increases. According to Le Chatelier's principle, the system will shift in a direction that reduces the impact of this change. As a result, the reaction will shift in the reverse direction, consuming HB+ and OH- and producing more B and H2O. Thus, the concentration of B will increase. Answer (b): The concentration of B will increase.

pH changes

From the previous analysis, we know that the reaction will shift in the reverse direction, producing more B and consuming OH-. The decrease in OH- concentration will cause a rise in the concentration of H3O+ (hydronium ions) since the product of H3O+ and OH- concentrations is always equal to Kw (the ion product of water), \(K_w= [H_3O^+][OH^-]\). Since the pH is defined as -log[H3O+], if the concentration of H3O+ increases, then the pH will decrease. Answer (c): The pH of the solution will decrease.

Key concepts

Le Chatelier's Principle

When a system at equilibrium experiences a change, it adjusts to counteract that change. This is Le Chatelier's Principle in action.
Think of it like a seesaw that balances itself when someone changes position. It's nature’s way of maintaining balance.
For example, if more of a product is added to a system at equilibrium, the reaction shifts to reduce that product, moving in the reverse direction. This helps re-establish the equilibrium without changing the equilibrium constant itself.
It's important to note that the equilibrium constant only changes with temperature, not with changes in concentration or pressure.

Equilibrium Constant

The equilibrium constant, denoted by \( K \), is a measure of the ratio of the concentrations of products to reactants at equilibrium. It shows the extent to which a reaction will proceed.
It's a fixed value for a given reaction at a specific temperature and doesn't change with the addition of reactants or products.
In our case, when a salt containing \( \mathrm{HB}^{+} \) is added, the constant remains unchanged, since it's only temperature-sensitive.
Understanding \( K \) helps in predicting how changes will affect the equilibrium position, but not the constant itself.

pH Changes

The pH is the measure of acidity or basicity of a solution, calculated as \( -\log[\mathrm{H_3O^+}] \). It's crucial in determining the chemical environment within a solution.
When a system shifts to counter a change, like the addition of compounds, it may affect ion concentrations.

• For example, if \( \mathrm{OH}^{-} \) is consumed, the concentration of \( \mathrm{H_3O^+} \) may rise.
• An increase in \( \mathrm{H_3O^+} \) means a decrease in pH, making the solution more acidic.

Therefore, monitoring pH changes can reveal shifts in equilibrium and indicate the balance between acids and bases.

Equilibrium Shift

An equilibrium shift occurs when a system responds to changes in concentrations, pressure, or volume. This can result in an increase or decrease in reactants or products.
Applying Le Chatelier's Principle, when you add more \( \mathrm{HB}^{+} \), the equilibrium shifts left to convert it back to \( \mathrm{B} \) and \( \mathrm{H_2O} \).
This shift helps reduce the added species, rebalancing the system.
Understanding these shifts is essential in chemical reactions, influencing concentration changes and reaction rates.