Here's a quick review of how to calculate pH and what pH means with respect to hydrogen ion concentration, acids, and bases.

### Review of Acids, Bases and pH

There are several ways to define acids and bases, but pH only refers to hydrogen ion concentration and is only meaningful when applied to aqueous (water-based) solutions. When water dissociates it yields a hydrogen ion and a hydroxide.

H_{2}O ↔ H^{+} + OH^{-}

When calculating pH, remember that [] refers to molarity, M. Molarity is expressed in units of moles of solute per liter of solution (not solvent). If you are given concentration in any other unit (mass percent, molality, etc.), convert it to molarity in order to use the pH formula.

Using the concentration of hydrogen and hydroxide ions, the following relationship results:

K_{w} = [H^{+}][OH^{-}] = 1x10^{-14} at 25°C

for pure water [H^{+}] = [OH^{-}] = 1x10^{-7}

Acidic Solution: [H^{+}] > 1x10^{-7}

Basic Solution: [H^{+}] < 1x10^{-7}

### How To Calculate pH and [H^{+}]

The equilibrium equation yields the following formula for pH:

pH = -log_{10}[H^{+}]

[H^{+}] = 10^{-pH}

In other words, pH is the negative log of the molar hydrogen ion concentration. Or, the molar hydrogen ion concentration equals 10 to the power of the negative pH value. It's easy to do this calculation on any scientific calculator because it will have a "log" button. (This is not the same as the "ln" button, which refers to the natural logarithm!)

**Example:**

Calculate the pH for a specific [H^{+}]. Calculate pH given [H^{+}] = 1.4 x 10^{-5} M

pH = -log_{10}[H^{+}]

pH = -log_{10}(1.4 x 10^{-5})

pH = 4.85

**Example:**

Calculate [H^{+}] from a known pH. Find [H^{+}] if pH = 8.5

[H^{+}] = 10^{-pH}

[H^{+}] = 10^{-8.5}

[H^{+}] = 3.2 x 10^{-9} M

**Example:**

Find the pH if the H^{+} concentration is 0.0001 moles per liter.

pH = -log[H^{+}]

Here it helps to rewrite the concentration as 1.0 x 10^{-4} M, because if you understand how logarithms work, this makes the formula:

pH = -(-4) = 4

Or, you could simply use a calculator and take:

pH = - log (0.0001) = 4

Usually you aren't given the hydrogen ion concentration in a problem, but have to find it from a chemical reaction or acid concentration. Whether this is easy or not depends on whether you're dealing with a strong acid or a weak acid. Most problems asking for pH are for strong acids because they completely dissociate into their ions in water. Weak acids, on the other hand, only partially dissociate, so at equilibrium a solution contains both the weak acid and the ions into which it dissociates.

**Example:**

Find the pH of a 0.03 M solution of hydrochloric acid, HCl.

Hydrochloric acid is a strong acid that dissociates according to a 1:1 molar ratio into hydrogen cations and chloride anions. So, the concentration of hydrogen ions is exactly the same as the concentration of the acid solution.

[H^{+} = 0.03 M

pH = - log (0.03)

pH = 1.5

### pH and pOH

You can easily use the pH value to calculate pOH, if you recall:

pH + pOH = 14

This is particularly useful if you're asked to find the pH of a base, since you'll usually solve for pOH rather than pH.

### Check Your Work

When you're performing a pH calculation, it's a good idea to make sure your answer makes sense. An acid should have a pH much less than 7 (usually 1 to 3), while a base has a high pH value (usually around 11 to 13). While it's theoretically possible to calculate a negative pH, in practice pH values should be between 0 and 14. This, a pH higher than 14 indicates an error either in setting up the calculation or else using the calculator.

### Key Points

- pH is a measure of how acidic or basic a chemical solution is.
- Normally, pH runs from 0 to 14.
- A neutral pH value is 7. A value less than 7 is acidic, while a value greater than 7 is basic.
- The formula for pH is pH = -log[H+]. This means pH is the negative base 10 logarithm ("log" on a calculator) of the hydrogen ion concentration of a solution. To calculate it, take the log of the hydrogen ion concentration and reverse the sign to get the answer.