pH is a measure of how acidic or basic a chemical solution is. The pH scale runs from 0 to 14—a value of seven is considered neutral, less than seven acidic, and greater than seven basic.

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 a given hydrogen ion concentration and reverse the sign. See more information about the pH formula below.

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

## Review of Acids and Bases

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

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. If you are given concentration in any other unit than moles (mass percent, molality, etc.), convert it to molarity in order to use the pH formula.

The relationship between pH and molarity can be expressed as:

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

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

- K
_{w}is the dissociation constant of water - 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 more often than not, these have a "log" button. This is not the same as the "ln" button, which refers to the natural logarithm.

### pH and pOH

You can easily use a 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.

## Example Calculation Problems

Try these sample problems to test your knowledge of pH.

### Example 1

Calculate the pH for a specific [H^{+}]. 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

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

### Example 3

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

Here it helps to rewrite the concentration as 1.0 x 10^{-4} M because 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

Usually, you aren't given the hydrogen ion concentration in a problem but have to find it from a chemical reaction or acid concentration. The simplicity of this will depend on whether you have 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 4

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

Remember, 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.

**Answer: **

[H^{+} ]= 0.03 M

pH = - log (0.03)

pH = 1.5

## Check Your Work

When you're performing pH calculations, always make sure your answers make sense. An acid should have a pH much less than seven (usually one to three) and a base should have a high pH value (usually around 11 to 13). While it's theoretically possible to calculate a negative pH, pH values should be between 0 and 14 in practice. This means that a pH higher than 14 indicates an error either in setting up the calculation or the calculation itself.

## Sources

- 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.