Question

Which of the following statements are true for a \(0.10-M\) solution of a weak acid HA? (Choose all that apply.) (a) The pH is 1.00 . (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=\left[\mathrm{A}^{-}\right]\) (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]>>\left[\mathrm{A}^{-}\right]\) (d) The \(\mathrm{pH}\) is less than 1 .

Short answer

Only statement (c) is true.

Step-by-step solution

Understanding Weak Acids

A weak acid partially dissociates in solution. This means it does not completely ionize, and the concentration of hydrogen ions (\[[\mathrm{H}_{3}\mathrm{O}^{+}]\]) in the solution will be less than the initial concentration of the acid.Consequently, for a 0.10 M solution of a weak acid, \[[\mathrm{H}_{3}o^{+}]\] will not be 0.10 M.

Analyze Statement (a)

The statement 'The pH is 1.00' means that \[[\mathrm{H}_{3}O^{+}]\] is 0.10 M (since pH = -log(0.10) = 1). This can only be true if the acid is a strong acid that fully dissociates. Thus, this statement is false for a weak acid.

Analyze Statement (c)

For a weak acid, \[\mathrm{HA}\rightleftharpoons \mathrm{H}^{+} + \mathrm{A}^{-}\], at equilibrium, \[[\mathrm{H}_{3}O^{+}]\] is equal to \[[\mathrm{A}^{-}]\] due to the stoichiometry of the dissociation, assuming no significant common ion effects or interference.

Analyze Statement (b)

The statement '\[[\mathrm{H}_{3}O^{+}]>>[\mathrm{A}^{-}]\]' suggests a scenario where \[[\mathrm{H}_{3}O^{+}]\] is much greater than \[[\mathrm{A}^{-}]\]. Since \[[\mathrm{H}_{3}O^{+}]\] and \[[\mathrm{A}^{-}]\] are equal for weak acid dissociation, this statement is false.

Analyze Statement (d)

The statement 'The pH is less than 1' would imply a highly acidic solution with a high concentration of \[[\mathrm{H}_{3}O^{+}]\]. Since weak acids only partially dissociate, this is unlikely to be the case for a 0.10 M weak acid solution. Hence, this statement is false.

Key concepts

Partial Dissociation

Weak acids are special because they do not completely break apart into ions in a solution. This process is called partial dissociation. When you have a weak acid like HA in water, it doesn't just transform entirely into its ions, \(\mathrm{H}^{+}\) and \(\mathrm{A}^{-}\). Instead, only a part of the acid molecules dissociates, resulting in a mixture of undissociated acid, hydrogen ions, and anions in the solution. A good way to think about this is to imagine a crowd of people at a party, some staying in a group and others branching off to mingle. In a similar manner, some molecules of the acid stay together (HA), while others separate into ions. As a result, the concentration of \[\mathrm{H}_{3}\mathrm{O}^{+}]\] in a solution of a weak acid is lower than if it were a strong acid that dissociates completely.This is crucial for understanding why the pH of weak acids is different compared to strong acids or full dissociation reactions.

pH

Understanding the concept of pH is essential when discussing acids. The pH scale is a way to measure how acidic or basic a solution is. Mathematically, pH is defined as the negative logarithm of the hydrogen ion concentration: \[ \text{pH} = -\log_{10}[\mathrm{H}_{3}\mathrm{O}^{+}] \]For a strong acid, you could find a very low pH, often as low as 1, because it fully dissociates, increasing the concentration of hydrogen ions. However, for weak acids, we have partial dissociation, leading to a higher pH than you might expect with a strong acid of the same concentration.In our case, a 0.10 M solution of a weak acid will have a pH greater than 1 because the hydrogen ion concentration is less than 0.10 M due to the incomplete dissociation. This shows that pH isn't just about the starting concentration of the acid but also how well the acid dissociates in the solution.It's important to remember that the pH scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration.

Equilibrium Concentrations

Equilibrium in chemistry refers to a state where the concentrations of reactants and products remain constant over time. In the case of weak acid dissociation, we're interested in the equilibrium concentrations of \(\mathrm{HA}\), \(\mathrm{H}_{3}\mathrm{O}^{+}\), and \(\mathrm{A}^{-}\). The reaction for a weak acid, HA, dissociating in water can be represented as:\[ \mathrm{HA} + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{A}^{-} \]At equilibrium, the concentration of \[\mathrm{H}_{3}\mathrm{O}^{+}]\] and \[\mathrm{A}^{-}]\] will be equal because for every molecule of HA that dissociates, one \(\mathrm{H}_{3}\mathrm{O}^{+}\) ion and one \(\mathrm{A}^{-}\) ion are produced.This equality is a result of the stoichiometry of the dissociation reaction, meaning it accounts for the ratio of product ions to the original acid molecules in a balanced chemical equation. However, equilibrium does not mean equal concentrations; it means the rate of the forward reaction (dissociation of HA) is equal to the rate of the reverse reaction (reforming HA from ions). This balance maintains consistent concentrations over time.