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Chapter 44: Problem 18

For a weak acid, why is \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=\left[\mathrm{A}^{-}\right] ?\)

Short Answer

Expert verified
The concentration of hydronium ions \([\mathrm{H}_{3}\mathrm{O}^{+}]\) equals the concentration of the anion \([\mathrm{A}^{-}]\) in a weak acid solution because weak acids do not fully dissociate. When the weak acid begins to dissociate, a state of equilibrium is established where the rate of dissociation of the acid is equal to the rate of association of the ions, leading to an equivalent concentration of hydronium ions and the anion.

Step by step solution

01

Understanding Weak Acid Dissociation

A weak acid is one that does not dissociate fully into its ions in a solution. This is often represented by the equation \[HA \rightleftharpoons \mathrm{H}^{+} + \mathrm{A}^{-}\] where \(HA\) represents a weak acid, and \(\mathrm{H}^{+}\) and \(\mathrm{A}^{-}\) are the ions it dissociates into. Note that in aqueous solution, \(\mathrm{H}^{+}\) often exist as \(\mathrm{H}_{3}\mathrm{O}^{+}\) (hydronium ions).
02

Understanding the Equation

At the beginning of the reaction, all the acid exists in the form \(HA\). But as the acid begins to dissociate, an equilibrium is established between \(HA\), \(\mathrm{H}^{+}\), and \(\mathrm{A}^{-}\). The rate at which \(HA\) dissociates to \(\mathrm{H}^{+}\) and \(\mathrm{A}^{-}\) is equal to the rate at which \(\mathrm{H}^{+}\) and \(\mathrm{A}^{-}\) associate to form \(HA\). Therefore, the concentrations of \(\mathrm{H}^{+}\) (or \(\mathrm{H}_{3}\mathrm{O}^{+}\) in water) and \(\mathrm{A}^{-}\) are equivalent, hence \([\mathrm{H}_{3}\mathrm{O}^{+}]=[\mathrm{A}^{-}]\)

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Most popular questions from this chapter

A \(0.50 \mathrm{M}\) solution of \(\mathrm{CH}_{3} \mathrm{COOH}\) has \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]=3.0 \times 10^{-3} \mathrm{M}\). What are the values of: \(\begin{array}{lr}\left(\mathrm{CH}_{3} \mathrm{COOH}\right)_{0} & = \\\ {\left[\mathrm{CH}_{3} \mathrm{COOH}\right]} & = \\ {\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]} & = \\ K_{\mathrm{a}} & =\end{array}\)

Explain why the equilibrium concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) is equal to the equilibrium concentration of \(\mathrm{OCl}^{-}\)

Complete and balance the following reaction for the weak base pyridine: $$ \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons $$ Write the equilibrium expression for the \(K_{\mathrm{b}}\) of \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\).
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