# When the pH of a solution decreases by 1, say from pH = 3 to pH = 2, by what factor does the hydronium ion concentration increase? Why?

Jan 21, 2017

The concentration increases TENFOLD.............

#### Explanation:

By definition, $p H$, $\text{pouvoir hydrogene}$ $\equiv$ $- {\log}_{10} \left[{H}_{3} {O}^{+}\right]$.

$1$ $p H$ unit therefore represents a 10-fold increase or decrease in hydrogen ion concentration.

Students tend to have problems with the logarithmic function, because it is here where they are introduced to the function for the first time. All I can say is do not be intimidated by it. Back in the day, before the advent of electronic calculators, everyone used logs for complex calculation. When I write ${\log}_{a} b = c$, I ask to what power I raise the base $a$ to get $c$. Here, ${a}^{c} = b$. And thus ${\log}_{10} 10 = 1 ,$, ${\log}_{10} 100 = 2 ,$${\log}_{10} {10}^{- 1} = - 1$. And ${\log}_{10} 1 = 0$. $p H$ and $p O H$ exploit this logarithmic function, utilizing the autoprotolysis of water:

$2 {H}_{2} O r i g h t \le f t h a r p \infty n s {H}_{3} {O}^{+} + H {O}^{-}$, where $p {K}_{a} = {10}^{-} 14$.

And thus if $p H = 2$, [H_3O^+]=10^(-2)*mol*L^-1=??

And if $p H = 3$, [H_3O^+]=10^(-3)*mol*L^-1=??; thus here hydrogen ion concentration is TENFOLD decreased compared to former concentration. Capisce?