Acid-Base Equilibria

In the Brønsted-Lowry model, an acid is a proton donor (it gives away ${\text{H}}^{+}$) and a base is a proton acceptor. A bare proton does not float around in water; it attaches to a water molecule to form the hydronium ion, ${\text{H}}_3{\text{O}}^{+}$. When an acid donates a proton, what is left is its conjugate base. When a base accepts a proton, it becomes its conjugate acid. A conjugate pair differs by exactly one ${\text{H}}^{+}$.

Water is amphiprotic: it acts as a base toward acetic acid, but as an acid toward ammonia, ${\text{NH}}_3+{\text{H}}_2\text{O}\rightleftharpoons {\text{NH}}_4^{+}+{\text{OH}}^{-}$. Hydrogen carbonate, ${\text{HCO}}_3^{-}$, is another amphiprotic species. Because water can do both, it even reacts with itself in tiny amounts, which is where Kw comes from.

In pure water, $[{\text{H}}_3{\text{O}}^{+}]=[{\text{OH}}^{-}]=1.0\times 10^{-7}\text{ mol/L}\text{.}$ Adding acid raises $[{\text{H}}_3{\text{O}}^{+}]$, and the equilibrium shifts so $[{\text{OH}}^{-}]$ drops, keeping the product at $1.0\times 10^{-14}$. Because these concentrations span many powers of ten, we use logarithms: $\text{pH}=-\log [{\text{H}}_3{\text{O}}^{+}]$ and $\text{pOH}=-\log [{\text{OH}}^{-}]$. Taking the negative log of the Kw expression gives $\text{pH}+\text{pOH}=14.00$ at 25 °C. A pH below 7 is acidic, 7 is neutral and above 7 is basic. For significant figures, the number of decimal places in a pH equals the number of significant figures in the concentration.

For a weak acid with initial concentration $c$, the ICE table gives $K_a=\frac{x^2}{c-x}$, where $x=[{\text{H}}_3{\text{O}}^{+}]$. When the acid is weak, $x$ is tiny compared with $c$, so we approximate $c-x\approx c$ and get $x=\sqrt{K_{a}c}$. Check the approximation afterward with percent ionization, $\frac{x}{c}\times 100\%$. If it is below 5%, the approximation is acceptable (the 5% rule); if not, solve the quadratic instead. A useful shortcut: the approximation is usually safe when $c/K_a$ is greater than about 400. For a conjugate acid-base pair in water, $K_a{K}_b=K_w$, so the stronger an acid is, the weaker its conjugate base.