# Question df7ec

Oct 17, 2016

$\text{pH} = 1.60$

#### Explanation:

The pH of a solution is simply a measure of the concentration of hydrogen ions, ${\text{H}}^{+}$, which are sometimes called hydronium ions, ${\text{H"_3"O}}^{+}$.

More specifically, the pH of a solution is defined as

color(blue)(bar(ul(|color(white)(a/a)"pH" = - log(["H"^(+)])color(white)(a/a)|)))#

Here $\left[{\text{H}}^{+}\right]$ represents the molarity, or molar concentration, of the hydrogen ions.

This means that all you have to do to find the solution's pH is take the negative log base $10$ of the concentration of hydrogen ions.

In your case, this will get you

$\text{pH} = - \log \left(2.5 \cdot {10}^{- 2}\right)$

Now, you can use the properties of the log function to say that

$\text{pH} = - \left[\log \left(2.5\right) + \log \left({10}^{- 2}\right)\right]$

which gets you

$\text{pH} = - \left[\log \left(2.5\right) + \left(- 2\right) \log 10\right]$

$\text{pH} = - \left[\log \left(2.5\right) - 2\right]$

$\text{pH} = 2 - \log \left(2.5\right)$

You can say for sure that the pH of this solution is lower than $2$. You can play around with this even more to find

$\text{pH} = 2 - \log \left(\frac{10}{4}\right)$

$\text{pH} = 2 - \left(\log 10 - \log 4\right)$

$\text{pH} = 2 - 1 + \log 4$

$\text{pH} = 1 + \log 4$

You can now say that the pH is higher than $1$. Finally, you can use a calculator to get the exact value

$\textcolor{g r e e n}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{pH} = 1 + \log 4 = 1.60} \textcolor{w h i t e}{\frac{a}{a}} |}}}$