9.3: Acid Dissociation Constants
- Page ID
- 490588
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Write the acid dissociation constant (\(K_a\)) expression.
- Determine the relative strength of an acid using the (\(K_a\)) value.
The ionization for a general weak acid, \(\ce{HA}\), can be written as follows:
\[\ce{HA} \left( aq \right) \rightleftharpoons \ce{H^+} \left( aq \right) + \ce{A^-} \left( aq \right) \nonumber \]
Because the acid is weak, an equilibrium expression can be written. An acid ionization constant \(\left( K_\text{a} \right)\) is the equilibrium constant for the ionization of an acid.
\[K_\text{a} = \frac{\left[ \ce{H^+} \right] \left[ \ce{A^-} \right]}{\left[ \ce{HA} \right]} \nonumber \]
The acid ionization represents the fraction of the original acid that has been ionized in solution. Therefore, the numerical value of \(K_\text{a}\) is a reflection of the strength of the acid. Weak acids with relatively higher \(K_\text{a}\) values are stronger than acids with relatively lower \(K_\text{a}\) values. Because strong acids are essentially \(100\%\) ionized, the concentration of the acid in the denominator is nearly zero and the \(K_\text{a}\) value approaches infinity. For this reason, \(K_\text{a}\) values are generally reported for weak acids only.
The table below is a listing of acid ionization constants for several acids. Note that polyprotic acids have a distinct ionization constant for each ionization step, with each successive ionization constant being smaller than the previous one.
Name of Acid | Ionization Equation | \(K_\text{a}\) |
---|---|---|
Sulfuric acid |
\(\ce{H_2SO_4} \rightleftharpoons \ce{H^+} + \ce{HSO_4^-}\) \(\ce{HSO_4} \rightleftharpoons \ce{H^+} + \ce{SO_4^{2-}}\) |
very large \(1.3 \times 10^{-2}\) |
Hydrofluoric acid | \(\ce{HF} \rightleftharpoons \ce{H^+} + \ce{F^-}\) | \(7.1 \times 10^{-4}\) |
Nitrous acid | \(\ce{HNO_2} \rightleftharpoons \ce{H^+} + \ce{NO_2^-}\) | \(4.5 \times 10^{-4}\) |
Benzoic acid | \(\ce{C_6H_5COOH} \rightleftharpoons \ce{H^+} + \ce{C_6H_5COO^-}\) | \(6.5 \times 10^{-5}\) |
Acetic acid | \(\ce{CH_3COOH} \rightleftharpoons \ce{H^+} + \ce{CH_3COO^-}\) | \(1.8 \times 10^{-5}\) |
Carbonic acid |
\(\ce{H_2CO_3} \rightleftharpoons \ce{H^+} + \ce{HCO_3^-}\) \(\ce{HCO_3^-} \rightleftharpoons \ce{H^+} + \ce{CO_3^{2-}}\) |
\(4.2 \times 10^{-7}\) \(4.8 \times 10^{-11}\) |
Hydrofluoric acid \(HF_{(aq)}\) reacts directly with glass (very few chemicals react with glass). Hydrofluoric acid is used in glass etching.