# Why is lower pH more acidic?

Jun 21, 2016

Because of the very definition of $p H$;

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

#### Explanation:

Because of the way the $p$ function is defined, we take the negative logarithm. Concentrated hydrochloric acid (36% w/w) is approx. $10 \cdot m o l \cdot {L}^{-} 1$. Given the definition, $p H = - 1$ for this solution, because ${\log}_{10} 10 = 1$.
Remember, when I write ${\log}_{a} B = c$, I ask to what power I raise the base $a$ to get $B$, here ${a}^{c} = B$. Can you tell me the values of ${\log}_{10} 100$, ${\log}_{10} 1 , 000$, ${\log}_{10} 1 , 000 , 000$? The values are simple whole numbers.