# What is the pH of a solution with #[OH^-] = 2.0 times 10^-10# #M#?

##### 2 Answers

We find

#### Explanation:

We interrogate the equilibrium:

We know that in aqueous solution under standard conditions that:

We take

But by definition, the logarithmic function is that power to which you raise the base to get the specific answer.........i.e. if

And thus

And so

OR

But we define

And now finally,

4.30

#### Explanation:

Right off the bat, if you don't understand the general concepts of pH and pOH, I suggest you watch this 5-minute video before proceeding to read this answer.

Recall that pH is an index for describing the concentration of hydronium ion. Mathematically, pH is described as:

A common mistake to make in this sort of problem is to move too quickly, and take *hydroxide* ion concentration. Therefore, what you've calculated is really something called the **pOH**, not the pH.

So how do you work this out? Basically, you'll need to know that the product of the concentration of hydroxide and hydronium ions in a solution will always equal

Taking the negative log of both sides of the equation yields:

Given this, there's 2 ways to do this problem. Method one is to use the 1st equation, and solve for

Method 2 (easier, in my opinion) is to solve for the pOH, and then subtract it from 14.

Either way, you should get an answer of **4.30.**

Do a reality check: your concentration of hydroxide is very small. Therefore, your pOH value would be fairly large, meaning that your pH would be small. This aligns with what we got.

Hope that helps :)