# Question 8eff7

Oct 8, 2016

$\text{pH} = 2.20$

#### Explanation:

Well, all you really have to do here is use the equation given to you. The pH of a solution can be calculated by using

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

Before plugging in the value given to you for the concentration of hydrogen ions, it's worth mentioning that because you're dealing with the negative log, a higher concentration of hydrogen ions will result in a lower pH.

Likewise, a lower concentration of hydrogen ions will result in a higher pH.

In your case, you know that

["H"^(+)] = 6.3 * 10^(-3)"M"#

The pH of the solution will be

$\text{pH} = - \log \left(6.3 \cdot {10}^{- 3}\right)$

$\text{pH} = 2.20$

Here's a cool thing to remember about logs and pH. You can manipulate the above equation to write

$\text{pH} = - \left[\log \left(6.3\right) + \log \left({10}^{- 3}\right)\right]$

$\text{pH} = - \left[\log \left(6.3\right) + \left(- 3\right) \cdot \log \left(10\right)\right]$

$\text{pH} = - \left[\log \left(6.3\right) - 3\right]$

$\text{pH} = 3 - \log \left(6.3\right)$

$\text{pH} = 2.20$

Notice that for

$\left[{\text{H}}^{+}\right] = 6.3 \cdot {10}^{- \textcolor{b l u e}{3}}$

you have

$\text{pH} = \textcolor{b l u e}{3} - \log \left(6.3\right)$

This allows you to estimate the pH of a solution just by looking at the concentration of hydrogen ions. For example, if

$\left[{\text{H}}^{+}\right] = 1.5 \cdot {10}^{- \textcolor{red}{4}}$

you can say that you have

$\text{pH} = \textcolor{red}{4} - \log \left(1.5\right) < 4$