Properties of acids and bases in aqueous solution

Water is an unusual (and important) solvent, in that it can act both as an acid and a base in the same reaction:

$${\rm H}_2{\rm O}(l) + {\rm H}_2{\rm O}(l)\rightleftharpoons {\rm H}_3{\rm O}^+(aq) + {\rm OH}^-(aq)$$

This is a simple reaction that the pure solvent can undergo. One of the waters acts as an acid, donating a proton (in the BL sense) and the other acts as a base accepting a proton. In both cases, the water also acts as a solvent. This reaction is called the autoionization of water. The expression for the equilibrium constant is

$$K = [{\rm H}_3{\rm O}^+][{\rm OH}^-] \equiv K_w$$

Note that the concentration of H$_2$O is omitted from this expression. The reason for this will become clearer in Chapter 11, however, for now, suffice it to say that the density of water is essentially constant, so it is excluded rather than carrying around the (nearly) constant value of $[{\rm H}_2{\rm O}]$ in all equilibrium constant expressions. $K_{\rm w}$ is called the ion product constant for water and has the numerical value

$$K_{\rm w}= 1.0\times 10^{-14}$$

at 25 $^{\rm o}{\rm C}$. Finally, since water is electrically neutral, $[{\rm H}_3{\rm O}^+]$ and $[{\rm OH}^-]$ must be the same, so that

$$[{\rm H}_3{\rm O}^+]= [{\rm OH}^-] = 1.0\times 10^{-7}$$

at 25 $^{\rm o}{\rm C}$.

Now, suppose we make a 0.1 M solution of HCl. The reaction that occurs when HCl is dissolved in water is

$${\rm HCl}(aq) + {\rm H}_2{\rm O}(l) \rightleftharpoons {\rm H}_3{\rm O}^+(aq) + {\rm Cl}^-(aq)$$

Thus, the concentration of ${\rm H}_3{\rm O}^+$ will be 0.1 M. The concentration of ${\rm OH}^-$ will then be

$$[{\rm OH}^-]= {K_{\rm w}\over [{\rm H}_3{\rm O}^+]} = {1.0\times 10^{-14} \over 0.1} = 1.0\times 10^{-13}$$

The contribution to $[{\rm H}_3{\rm O}^+]$ from the autoionization of water is negligible compared to that from the HCl dissolution. Also, since the only source of ${\rm OH}^-$ is the autoionization, we see that this reaction is suppressed in the presence of a strong acid.

By similar reasoning, a strong base can be seen to suppress the ${\rm H}_3{\rm O}^+$ concentration and give rise to a large concentration of ${\rm OH}^-$.

Typically the concentration of ${\rm H}_3{\rm O}^+$ can range from 10 M to 10$^{-13}$ M, which constitutes 14 order of magnitude. It is convenient to define a logarithmic scale for the ${\rm H}_3{\rm O}^+$ concentration, which will be compressed down to 1 order of magnitude. This is the pH scale defined by

$${\rm pH}=-\log_{10}[{\rm H}_3{\rm O}^+]$$

Thus, the pH of pure water at 25 $^{\rm o}{\rm C}$ is

$${\rm pH}=-\log_{10} (1.0\times 10^{-7}) = 7.00$$

while that of a 0.1 M HCl solution is

$${\rm pH}=-\log_{10} (0.10) = 1.00$$

Thus, we see that the more acidic a solution, the lower will be its pH.