# The [H^+] in a solution is 0.01 M. What is the pH of the solution?

Dec 8, 2016

$\text{pH} = 2$

#### Explanation:

The pH of a given solution is nothing more than the negative log base $10$ of the concentration of hydrogen ions, ${\text{H}}^{+}$, which you'll sometimes see written as ${\text{H"_ 3"O}}^{+}$, the hydronium ion.

You thus have

color(blue)(ul(color(black)("pH" = - log(["H"^(+)]))))

In your case, the problem provides you with the concentration of hydrogen ions

["H"^(+)] = "0.01 M"

This means that the pH of the solution will be

$\text{pH} = - \log \left(0.01\right)$

$\text{pH} = - \log \left({10}^{- 2}\right) = - \left(- 2\right) \cdot \log \left(10\right)$

Since you know that

${\log}_{10} \left(10\right) = \log \left(10\right) = 1$

you can say that

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{pH} = - \left(- 2\right) \cdot 1 = 2}}}$

Because the pH is $< 7$, this solution will be acidic.