# How much more acidic is a solution of pH 3 compared with a solution of pH 6?

Oct 24, 2016

The solution whose $p H = 3$ is $1000$ times as acidic as the solution whose $p H = 6$.

#### Explanation:

By definition, $p H = - {\log}_{10} \left[{H}_{3} {O}^{+}\right]$. A solution whose $p H = 1$ is ten times more acidic than the solution whose $p H = 2$.

Given the logarithmic scale, if $p H = 3$ this is ${10}^{3}$ times as acidic as the solution whose $p H = 6$.

To give numbers, $p H = 3$, $\left[{H}_{3} {O}^{+}\right] = {10}^{-} 3 \cdot m o l \cdot {L}^{-} 1$.

$p H = 6$, $\left[{H}_{3} {O}^{+}\right] = {10}^{-} 6 \cdot m o l \cdot {L}^{-} 1$. And clearly the former is ${10}^{3}$ as acidic.

Back in the day, students routinely used log tables before the advent of electronic calculators to perform mulitplications and divisions. I can't say say that I really miss it; there was far too much arithmetic.