Question

use the following information to answer the next question.
consider the dissociation of an acid in water as
ha(aq) + h₂o(ℓ) → h₃o⁺(aq) + a⁻(aq)
which of the following statements about the above ionization reaction is correct?
○ the greater the value of the ionization constant, the higher the concentration of h₃o⁺(aq) and the stronger the acid.
○ the lower the value of the ionization constant, the higher the concentration of h₃o⁺(aq) and the stronger the acid.
○ the greater the value of the ionization constant, the lower the concentration of h₃o⁺(aq) and the weaker the acid.
○ the lower the value of the ionization constant, the lower the concentration of h₃o⁺(aq) and the stronger the acid.
○ there is no relationship between the ionization constant and the concentration of h₃o⁺(aq).

Explanation:

To determine the correct statement, we analyze the relationship between the acid ionization constant (\(K_a\)) and acid strength. The ionization constant expression for \(HA(aq) + H_2O(\ell)
ightarrow H_3O^+(aq) + A^-(aq)\) is \(K_a=\frac{[H_3O^+][A^-]}{[HA]}\). A larger \(K_a\) means the reaction favors the products more, resulting in a higher concentration of \(H_3O^+(aq)\). Stronger acids ionize more, so a greater \(K_a\) corresponds to a stronger acid.

• For the first option: A greater \(K_a\) implies more product formation (\(H_3O^+\) and \(A^-\)), so higher \(H_3O^+\) concentration and a stronger acid. This matches the relationship.
• The second option is incorrect because a lower \(K_a\) means less ionization, so lower \(H_3O^+\) and a weaker acid.
• The third option is incorrect as a greater \(K_a\) should increase, not decrease, \(H_3O^+\) concentration and indicate a stronger (not weaker) acid.
• The fourth option is incorrect because a lower \(K_a\) gives lower \(H_3O^+\) and a weaker (not stronger) acid.
• The fifth option is incorrect because there is a clear relationship between \(K_a\) and \(H_3O^+\) concentration (from the \(K_a\) expression).

Answer:

The greater the value of the ionization constant, the higher the concentration of \(H_3O^+(aq)\) and the stronger the acid.