# How is acid/base chemistry defined and represented in aqueous solution?

Mar 23, 2017

In water under standard conditions, we know that ${K}_{a} = \left[{H}_{3} {O}^{+}\right] \left[H {O}^{-}\right] = {10}^{-} 14$

(note that ${H}_{3} {O}^{+}$ and ${H}^{+}$ may be used equivalently. They represent the characteristic cation in water, $\text{the acidium ion.}$)

#### Explanation:

We know (i) that $p H = - {\log}_{10} \left[{H}_{3} {O}^{+}\right]$, and (ii) that under standard conditions of $1 \cdot a t m$ and $298 \cdot K$, ${K}_{a} = {10}^{-} 14$.

(i) was by definition, and (ii) was by dint of VERY careful measurement. And these relationships define the very idea of acid/base chemistry in aqueous solution.

A solution is acidic if there there is a preponderance of the characteristic cation, ${H}_{3} {O}^{+}$. That is the solution is acidic if $\left[{H}_{3} {O}^{+}\right] > \left[H {O}^{-}\right]$, i.e. there are more so-called $\text{hydronium ions}$ than $\text{hydroxide ions}$ per unit volume.

The solution is basic if $\left[{H}_{3} {O}^{+}\right] < \left[H {O}^{-}\right]$, i.e. there are LESS so-called $\text{hydronium ions}$ than $\text{hydroxide ions}$ per units volume.

And if $\left[{H}_{3} {O}^{+}\right] = \left[H {O}^{-}\right]$, then the solution is NEUTRAL.

$\text{For undergrads:}$

we know that ${K}_{a} = \left[{H}_{3} {O}^{+}\right] \left[H {O}^{-}\right] = {10}^{-} 14$ under standard conditions of $1 \cdot a t m$ (or whatever they use these days), and $298 \cdot K$. Under non-standard conditions, i.e. $T = 373 \cdot K$, how do you think ${K}_{a}$ would evolve?