# What is the pH of a #3.9*10^-8# #M# #NaOH# solution?

##### 2 Answers

The pH is 7.08.

#### Explanation:

The base is so dilute that we must also consider the

We start by noting that charges must balance.

If the

The

Also,

∴

Solving the quadratic, we get

#### Explanation:

We would predict that as this is such a low concentration the

This is an incredibly low concentration, so we must take into account the

For which:

This means that the concentration of

A tiny amount of

It might be reasoned, therefore, that the total

However this will not be the **at equilibrium.**

By adding those ions we have disturbed a system which is at equilibrium.

Le Chatelier's Principle tells us that the system will respond by opposing that change, thus restoring the equilibrium which represents the lowest energy state.

The reaction quotient

This shows that

To calculate the **ICE** table:

So:

This simplifies to:

This is a quadratic equation which can be solved using the quadratic formula.

Discarding the absurd root we get:

So:

You may see this more generally described as "The Common Ion Effect" .