6.23: Acids, Bases, and Dissociation

Acids and bases

In lecture, we talked about Brønsted-Lowry acids and bases as well as Lewis acids and bases. The BrønstedLowry definition of acids and bases is more narrow: a Brønsted-Lowry acid is a proton donor, while a Brønsted-Lowry base is a proton acceptor: to be clear here, the proton is a hydrogen ion, \(\mathrm{H}^{+}\). More generally, a Lewis acid is an electron acceptor, while a Lewis base is an electron donor. Water is amphoteric: it can be either an acid or a base. Water serves as the solvent for many acid-base reactions. Consider adding a generic acid to water:

\[H A(a q)+H_2 O(l) \rightarrow H_3 O^{+}(a q)+A^{-}(a q) \nonumber\]

Similarly, consider adding a generic base to water:

\[B^{-}(a q)+H_2 O(l) \rightarrow H B(a q)+O^{-}(a q) \nonumber\]

These serve as prototypical acid-base reactions: we can identify conjugate acid-base pairs to relate species that lost/gained a proton (or electron) on either side of the reaction.

Example: Identify the conjugate acid-base pairs in the following reaction:

\(\mathrm{CH}_3\mathrm{CO}_2\mathrm{H} (aq) + \mathrm{NH}_3 (aq) \rightarrow \mathrm{CH}_3\mathrm{CO}_2^{-} + \mathrm{NH}_4^{+}\)

Answer

Dissociation

In the same way we wrote a general equilibrium constant, we can write an acid/base specific equivalent. The equilibrium constant for our acid dissociation reaction above would be

\(K_{e q}=\dfrac{\left[\mathrm{H}_3 \mathrm{O}^{+}\right]\left[\mathrm{A}^{-}\right]}{\left[\mathrm{H}_2 \mathrm{O}\right][\mathrm{HA}]}\)

However, since the water is acting as a solvent and is present in excess, it has a constant concentration: we therefore define the acid constant as

\(K_a=K_{e q}\left[H_2 O\right]=\dfrac{\left[H_3 O^{+}\right]\left[A^{-}\right]}{[H A]}\)

Similarly, the base dissocation constant is

\(K_b=\dfrac{[H B]\left[O H^{-}\right]}{[B-]}\)

The stronger the acid or base, the more readily it dissolves in solution, and the greater the magnitude of \(K_a\) or \(K_b\). There are only a few strong acids- acids that fully dissociate into their constituent ions. These include \(\mathrm{HCl}, \mathrm{HBr}, \mathrm{HI}, \mathrm{HNO}_3, \mathrm{HClO}_3, \mathrm{HCLO}_4\), and \(\mathrm{H}_2 \mathrm{SO}_4\). The strong bases are mostly alkali salts, including \(\mathrm{LiOH}, \mathrm{NaOH}, \mathrm{KOH}, \mathrm{RbOH}, \mathrm{CsOH}, \mathrm{Ca}(\mathrm{OH})_2, \mathrm{Sr}(\mathrm{OH})_2, \mathrm{Ba}(\mathrm{OH})_2\). Of course, the strength of an acid or base is related to its bond energy: polar acids with big differences in electronegativity have a low bond energy rapidly dissociate when placed in water, for example.

Example: Write an expression for the dissociation and for the acid or base dissociation constants for these acids \(\left(\mathrm{HF}, \mathrm{CH}_3 \mathrm{CO}_2 \mathrm{H}\right)\) and bases \(\left(\mathrm{NH}_3, \mathrm{NaOH}\right)\).

Answer

Hydrofluoric acid, \(\mathrm{HF}\), is a strong acid. In water, the proton dissociates:

\[H F(a q)+H_2 O(l) \rightarrow H_3 O^{+}(a q)+F^{-}(a q) \nonumber\]

Its acid dissociation constant is

\[K_a=\dfrac{\left[\mathrm{H}_3 \mathrm{O}^{+}\right]\left[\mathrm{F}^{-}\right]}{[H F]} \nonumber\]

We can take a similar approach for acetic acid, a weak acid.

\[\mathrm{CH}_3 \mathrm{CO}_2 \mathrm{H}(a q)+\mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{H}_3 \mathrm{O}^{+}(a q)+\mathrm{CH}_3 \mathrm{CO}_2^{-}(a q) \nonumber\]

The acid dissociation constant is

\[K_a=\dfrac{\left[\mathrm{H}_3 \mathrm{O}^{+}\right]\left[\mathrm{CH}_3 \mathrm{CO}_2^{-}\right]}{\left[\mathrm{CH}_3 \mathrm{CO}_2 \mathrm{H}\right]} \nonumber\]

For ammonia, the base gains a proton when placed in water:

\[\mathrm{NH}_3(a q)+\mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{NH}_4^{+}(a q)+\mathrm{OH}^{-}(a q) \nonumber\]

The base dissociation constant for ammonia is

\[K_b=\dfrac{\left[\mathrm{NH}_4^{+}\right]\left[\mathrm{OH}^{-}\right]}{\left[\mathrm{NH}_3\right]} \nonumber\]

Finally, sodium hydroxide fully dissociates:

\[\mathrm{NaOH}(a q)+\mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{Na}^{+}(a q)+\mathrm{OH}^{-}(a q) \nonumber\]

The base dissociation constant is

\[K_b=\dfrac{[N a+]\left[\mathrm{OH}^{-}\right]}{[N a O H]} \nonumber\]

Example: Which of these acids is the strongest? sulfurous acid \(\left(\mathrm{H}_2 \mathrm{SO}_3 ; \mathrm{K}_a=1.54 \times 10^{-2}\right)\), phosphoric \(\operatorname{acid}\left(\mathrm{H}_2 \mathrm{PO}_4^{-} ; \mathrm{K}_a=6.23 \times 10^{-8}\right)\), citric acid \(\left(\mathrm{H}_3 \mathrm{C}_6 \mathrm{H}_5 \mathrm{O}_7 ; \mathrm{K}_a=8.4 \times 10^{-4}\right)\)

Answer

Stronger acids have larger acid dissociation constants, so sulfurous acid is stronger than citric acid and phosphoric acid.