# If [H_3O^+]-=10^(-10)*mol*L^-1, what is pH of this solution?

Mar 28, 2017

$p H = 10$

#### Explanation:

By definition, $p H = - {\log}_{10} \left[{H}_{3} {O}^{+}\right]$

And thus, here, $p H = - {\log}_{10} \left({10}^{- 10}\right) = - \left(- 10\right) = 10.$

Given the definition of the logarithmic function, ${\log}_{a} b = c$, $c$ is that power to which we raise the base $a$ to get $b$, then ${\log}_{10} {10}^{x} = x$. Logs were introduced in the days BEFORE the advent of cheap electronic calculators; scientists, and economists, and engineers, and A level students, used to use $\text{log tables}$, and $\text{slide rules}$ which made complex calculations a bit less tiresome.

In water, under standard conditions, we can show that $p H + p O H = 14$. What is $\left[H {O}^{-}\right]$ in the given example?

The use of $p H$ and $p O H$ allows the use of buffer solutions to moderate acidity and alkalinity.