Question

Question #0059f

Answer 1

Here's how you can do that.

Explanation:

As you know, the `"pH"` of a solution is calculated by taking the negative log base `10` of the concentration of hydrogen ions, `"H"^(+)`, which you'll sometimes see referred to as hydronium ions, `"H"_3"O"^(+)`

`"pH" = - log_10(["H"^(+)])`

or, more simply

`"pH" = - log(["H"^(+)])`

In your case, the `"pH"` of the solution is equal to `9.7`. Right from the start, the fact that you have

`"pH" > 7`

tells you that you're dealing with a basic solution, which, at room temperature, is a classification given to any solution that has

`["H"^(+)] < 10^(-7)` `"M"`

To find the actual concentration of hydrogen ions, rewrite the equation as

`log(["H"^(+)]) = - 9.7`

Now use both sides as exponents for `10` to say that

`10^log(["H"^(+)]) = 10^(-9.7)`

By definition, you have

`a^(log_ax) = x" "(AA)color(white)(.) a>0, x>0, a, x in RR`

This means that

`10^log(["H"^(+)]) = ["H"^(+)]`

which gets you

`["H"^(+)] = 10^(-9.7)`

`["H"^(+)] = 2.0 * 10^(-10)` `"M"`

As predicted, the concentration of hydrogen ions is `< 10^(-7)` `"M"`, which is what you should expect to see for a basic solution.