According Broenstedt, the neutralization reaction (acid-base reaction; protolysis) between an acid $HB_1$ and a base $B_2$ is the exchange of a proton:
Neutralisation (Protolysis): $HB_1$ $+$ $B_2$ $\rightleftarrows$ $HB_2$ $+$ $B_1$
Examples: $HCl$ $+$ $CH_3COO^-$ $\rightleftarrows$ $CH_3COOH+Cl^-$ $HCO_3^-$ $+$ $OH^-$ $\rightleftarrows$ $CO_3^{2-}$ $+$ $H_2O$
The equilibrium constant for the protolysis reaction depends upon the acidity constants in question (in the case of strong acids or strong bases, one consideres constants of couples $H_3O^+/H_2O$ of $pK_a=-1,74$ respectively $H_2O/OH^-$ of $pK_a=15,74$ ), indeed: $K$ $=$ $\frac{[HB_2][B_1]}{[HB_1][B_2]}$ = $\frac{[HB_2]}{[H_3O^+][B_2]}\cdot \frac{[H_3O^+][B_1]}{[HB_1]} $ = $\frac{K_{a1}}{K_{a2}}$
Equilibrium constant of a protolysis reaction $K$ $=$ $\frac{K_{a1}}{K_{a2}}$
We can look (see exercises) in which case the protolysis reaction is (almost) complete ( $\rightarrow $ instead of $\rightleftarrows$):
The reaction between a strong acid and a strong base is always complete.
Example: $2\;L\;HCl\; 0.1 M$ are mixed with $1\;L\;NaOH \;0.1 M$: Record of moles :
| $H_3O^+$ | + | $OH^- $ | $\rightarrow$ | $2H_2O$ | |
| Before: | 0.2 | 0.1 | |||
| After: | 0.1 | 0 |
Finally ($Na^+$ et $Cl^-$ do not influence the pH): $pH$ $=$ $-log\frac{n_{H_3O^+}}{V}$ = $-log\frac{0,1}{3}$ $=$ $ 0.48$
The reaction between a weak acid 1 and a strong base 2 is complete ($\rightarrow$), if $pK_{a1}\lt 11$
Example: $1\;L\;CH_3COOH\; 0.1 M$ are mixed with $2\;L\;NaOH \;0.1 M$: Record of moles :
| $CH_3COOH$ | + | $OH^- $ | $\rightarrow$ | $CH_3COO^-$ | + | $H_2O$ | |
| Before: | 0.1 | 0.2 | 0 | ||||
| After: | 0 | 0.1 | 0.1 |
Finally ($Na^+$ does not influence the pH), we are in the presence of a mixture of weak base/strong base: $pH$ $=$ $14$ $+$ $log\frac{n_{OH^-}}{V}$ $=$ $14$ $+$ $log\frac{0,1}{3}$ $=$ $ 13,52$
The reaction between a strong acid 1 and a weak base 2 is complete ($\rightarrow$), if $pK_{a2}\gt 3$
Example: $2\;L\;HCl\; 0,1 M$ are mixed with $1\;L\;NH_3 \;0,1 M$: Record of moles :
| $H_3O^+$ | + | $NH_3 $ | $\rightarrow$ | $NH_4^+$ | + | $H_2O$ | |
| Before: | 0.2 | 0.1 | 0 | ||||
| After: | 0.1 | 0 | 0.,1 |
Finally ($Na^+$ does not influence the pH), we are in the presence of a mixture of weak acid/strong acid: $pH$ $=$ $-log\frac{n_{H_3O^+}}{V}$ = $-log\frac{0,1}{3}= 0,48$
(1) The reaction between a weak acid 1 and weak base 2 is complete ($\rightarrow $), if $pK_{a2}$ $-$ $pK_{a1}\gt 3$ (2) The reaction between a weak acid and weak base 1 2 is incomplete ($\rightleftarrows$) if $-3\lt pK_{a2}$ $-$ $pK_{a1}\lt 3$ (3)There is no reaction between a weak acid 1 and weak base 2 ($\leftarrow), if $ pK_{a2}$ $-$ $pK_{a1}\lt -3$
Justifications: (1) $K$ $=$ $\frac{K_{a1}}{K_{a2}}\gt 10^3$ (2) $10^{-3}\lt K$ $=$ $\frac{K_{a1}}{K_{a2}}\lt 10^3$ (3) $ K$ $=$ $\frac{K_{a1}}{K_{a2}}\lt 10^{-3}$
Examples: The reaction between chloric acid ($pK_{a1}$ $=$ $-1$) and ammonia ($pK_{a2}$ $=$ $9,2$) is complete, because $9,2-(-1)\gt3$ $HClO_3$ $+$ $NH_3$ $\rightarrow$ $ NH_4^+$ $+$ $ClO_3^-$ The reaction between acetic acid ($pK_{a1}$ $=$ $4,75$) and methanoate ($pK_{a2}$ $=$ $3,75$) is incomplete, because $3,75-4,75\lt3$ $CH_3COOH$ $+$ $HCOO^-$ $\rightleftarrows$ $ CH_3COO^-$ $+$ $HCOOH$