H^{+} concentrations are typically very small for many solutions, and hence it is often difficult to easily know if a substance is an acid or a base.

So a scale, called a pH scale was invented to make it easy to tell!
pH is just a number that tells us whether a solution is an acid or a base.
(This is similar to giving a movie a review out of 10.)

The pH scale is actually a range from 0 to 14.
pH has no units. Yeah, 14! Later, we will learn why.

Study the pH diagram.

This range is valid at 25^{0}C.

If a solution has a pH of 5, it must be an acid.

If a solution has a pH of 7, it is neutral.

If a solution has a pH of 9, it must be a base.

Essentially, any solution with a pH from 0 to just under 7 is an acid solution.
A solution with a pH of 7 is neutral, which means it is neither acid nor base.
Any solution with a pH from just above 7 to 14, is a base solution.

pH Calculations

Notice that pH is about the H^{+} ions, and NOT the acid from where they come.
It is NOT pACID.

Example 1

Assume that a solution of H_{2}SO_{4} acid has a concentration of 0,002mol.dm^{-3}.
Calculate it's pH at 25^{0}C.

Solution 1 You would need to first determine the concentration of the actual H^{+} ions. H_{2}SO_{4} is a strong acid, and is also DIPROTIC.
(for every ONE mole of acid that reacts, TWO mols of H^{+} are produced)

The concentration of the H^{+} is 0,004M.

Now to calculate the actual pH you use this equation: Seems scary the first time you use this equation. But it is just a button on your calcuator called log. I am using the simplified form here.

Example 2

The H^{+} concentration in a solution is 3 x 10^{-9} M at 25^{0}C. Determine whether the solution is acidic or basic.

Solution 2

Since the pH > 7, the solution is basic according to the pH scale.
So how will you calculate the pH if you had a base? Bases produce OH^{-} ions, not H^{+} ions.

Example 3

Calculate the pH of a solution of NaOH of concentration 0,02M.

Solution 3

Now you cannot use the OH^{-} in the pH. So you have to convert it to a corresponding H^{+} ion concentration. Use this formula to change OH^{-} to H^{+}

Scary? Nah!

Substitute the OH^{-} value of 0,02M in this equation, and solve for the H^{+} ion concentration.

Now use the pH formula.

By the way, this formula :

is called the K_{w} and you will learn more about it later.
It is always equal to 1 x 10^{-14} at 25^{0} C.

pH Calculations Backwards

Example 4

You have a solution of H_{2}SO_{4} that has a pH of 1,2. Calculate the concentration of the acid.

Solution 4

Example 5

A solution of Ba(OH)_{2} has a pH of 11,4. Calculate the concentration of this barium hydroxide solution.

Solution 5

Please note that in scientific notation, this is also :
[OH^{-}] = 2,5 x 10^{-3} M