pH & pOH (College Board AP® Chemistry): Study Guide

The pH scale

At 25 °C, solutions below pH 7 are acidic, pH 7 is neutral and above pH 7 is basic

pH

• The acidity of an aqueous solution depends on the number of H₃O⁺ ions in the solution

• pH is defined as:

pH = −log [H₃O⁺]

• Where [H₃O⁺] is the concentration of H₃O⁺ ions in M

• Similarly, the concentration of H₃O⁺ of a solution can be calculated if the pH is known by rearranging the above equation to:

[H₃O⁺] = 10^−pH

• The pH scale is a logarithmic scale with base 10

  • This means that a solution one pH unit lower has 10 times the [H₃O⁺]

• For example:

  • A pH 5 solution is 10 times more acidic than a pH 6 solution

  • A pH 5 solution has 100,000 times the [H₃O⁺] of a pH 10 solution

• The number of decimal places in a pH equals the number of significant figures in [H₃O⁺]: [H₃O⁺] = 1.6 × 10^-4 M (2 significant figures) gives pH = 3.80

pH and [H₃O⁺] table

pH of acids

• Acidic solutions (strong or weak) always have more H₃O⁺ than OH^- ions

• At 25 °C, [H₃O⁺] in an acidic solution is greater than 1.0 × 10^-7 M, so its pH is below 7

• At other temperatures the neutral point moves, but an acidic solution always has [H₃O⁺] > [OH^-]

• The higher the [H₃O⁺] of the acid, the lower the pH

pH of bases

• Basic solutions (strong or weak) always have more OH^- than H₃O⁺ ions

• At 25 °C, [H₃O⁺] in a basic solution is less than 1.0 × 10^-7 M, so its pH is above 7

• At any temperature, a basic solution has [OH^-] > [H₃O⁺]

• The higher the [OH^–] of the base, the higher the pH

pH of water

• At 25 °C, pure water has equal concentrations of H₃O⁺ and OH^-, each 1.0 × 10^-7 M

• To calculate the pH of water, the following formula should be used:

pH = −log (10^-7) = 7

• Thus, pure water has a pH of 7.00 at 25 °C

• Pure water is always neutral because [H₃O⁺] = [OH^-]

• K_w changes with temperature, so at temperatures other than 25 °C the pH of pure water is not 7.00      

pOH

• The basicity of an aqueous solution depends on the number of hydroxide ions, OH^-, in the solution

• pOH is defined as:

pOH = −log [OH^–]

• Where [OH^-] is the concentration of hydroxide ions in M

• Similarly, [OH^-] can be calculated from the pOH by rearranging the equation above:

[OH^–] = 10^−pOH

• If you are given the concentration of a basic solution and need to find the pH, this can be done by:

[H₃O⁺] = $\frac{{\mathrm{K}}_w}{\left[{\mathrm{OH}}^{-}\right]}$

• Alternatively, if you are given the [OH^-] and calculate the pOH, the pH can be found by:

pH = 14.00 − pOH (at 25 °C)

• pH and pOH are interlinked, and at all temperatures pH + pOH = pK_w (see The Ionic Product of Water)