In chemistry, pH is a number that acidity or basicity (alkalinity) of an aqueous solution. The pH scale normally runs from 0 to 14. A pH value of 7 is neutral. This is the pH of pure water. Values less than 7 are acidic, while those greater than 7 basic. Here is a quick review of how to calculate pH. It includes formulas for finding pH and examples showing how to use them.

### pH Calculation Formula

The formula to calculate pH is:

**pH = -log[H ^{+}]**

The brackets [] refer to molarity, M. Molarity is given in units of moles per liter of solution. In a chemistry problem, you may be given concentration in other units. To calculate pH, first convert concentration to molarity. The easiest way to perform the calculation on a scientific calculator is to enter the hydrogen ion concentrations, press the log key (*not* the ln key, which is natural logarithm), and then take the negative of the value. While negative pH is possible, your answer will almost always be a positive number.

### Simple pH Calculation Examples

Here are simple example problems showing how to calculate pH when given hydrogen ion concentration.

#### Example 1

Calculate pH given [H^{+}] = 1.4 x 10^{-5} M

**Answer:**

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

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

pH = 4.85

#### Example 2

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

Here it helps to rewrite the concentration using scientific notation as 1.0 x 10^{-4} M. This makes the formula: pH = -(-4) = 4. Or, you could just use a calculator to take the log. This gives you:

**Answer:**

pH = – log (0.0001) = 4

### Calculate the pH of a Strong Acid

Sometimes you aren’t given the hydrogen ion concentration, so you have to figure it out from the chemical reaction or concentration of the reactants or products. If you have a strong acid, this is easy because strong acids completely dissociate into their ions. In other words, the hydrogen ion concentration is the same as the acid concentration.

#### Example

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

**Answer:**

Hydrochloric acid is a strong acid, so:

[H^{+} ]= 0.03 M

pH = – log (0.03)

pH = 1.5

For bases, weak acids, and weak bases, the calculation is slightly more involved. Here, you use pOH, pK_{a}, and pK_{b}.

### Find [**H**^{+}] From pH

^{+}

You can rearrange the pH equation to find hydrogen ion concentration [H^{+}] from pH:

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

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

#### Example

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

**Answer:**

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

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

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

### pH and K_{w}

pH stands for “power of hydrogen” because the strength of an acid depends on the amount of hydrogen ion (H^{+}) it releases in aqueous (water-based) solutions. In a way, water acts as both an acid and a base because it dissociates to produce a hydrogen ion and a hydroxide ion:

H_{2}O ↔ H^{+} + OH^{–}

K_{w} is the dissociation constant of water.

K_{w} = [H^{+}][OH^{–}] = 1×10^{-14} at 25°C

For pure water:

[H^{+}] = [OH^{–}] = 1×10^{-7}

So, you can use K_{w} value to predict whether a solution is an acid or a base:

- Acidic Solution: [H
^{+}] > 1×10^{-7} - Basic Solution: [H
^{+}] < 1×10^{-7}

### Check Your Work

Avoid common pitfalls when calculating pH:

- Use the correct number of significant figures. In chemistry, using the wrong number of digits may be counted as an incorrect answer, even if you set up the problem correctly.
- Expect an answer between 0 and 14. Values slightly less than 0 and greater than 14 may occur, but you’ll never see a pH of -23 or 150, for example.
- Think about whether the answer makes sense. An acid should have a value less than 7, while a base should have a pH greater than 7.

### References

- Covington, A. K.; Bates, R. G.; Durst, R. A. (1985). “Definitions of pH scales, standard reference values, measurement of pH, and related terminology”.
*Pure Appl. Chem*. 57 (3): 531–542. doi:10.1351/pac198557030531 - International Union of Pure and Applied Chemistry (1993).
*Quantities, Units and Symbols in Physical Chemistry*(2nd ed.) Oxford: Blackwell Science. ISBN 0-632-03583-8. - Mendham, J.; Denney, R. C.; Barnes, J. D.; Thomas, M. J. K. (2000).
*Vogel’s Quantitative Chemical Analysis*(6th ed.). New York: Prentice Hall. ISBN 0-582-22628-7.