Calculating the pH of mixed solutions

The pH of solutions that have been prepared by mixing solutions of a strong acid and a strong base depends on

the amounts of strong acid and strong base in the solutions that are mixed
the total volume of the mixed solution

The amount of reaction that occurs between the strong acid and the strong base on mixing and the major species in solution can be deduced by using the given data to construct a table such as shown below for a mixture of 12.0

0.100

NaOH with 20.0

0.100

HCl.

	NaOH	+	HCl	NaCl	+	H₂O
initial (amount added) (n = cV)	0.0012 mol		0.0020 mol	0
change* (+ for products, – for reactants)	-0.0012 mol		-0.0012 mol	+0.0012 mol
final (initial + change)	0		0.0008 mol	0.0012 mol

*The amount of change (reaction) that occurs depends on the limiting reactant (in this case NaOH).

As shown above the major species in the mixed solution are Na⁺, Cl^– and H₃O⁺. Neither Na⁺ nor Cl^– affect the pH of the solution.

The excess amount in moles of H₃O⁺ (or HO^–in other examples) can be used to calculate the pH of the mixed solution.

Calculation of pH mixed solution if H₃O⁺ present in excess

The excess amount in moles of H₃O⁺must be divided by the TOTAL VOLUME to get [H₃O⁺]
Thus [H₃O⁺] for the example is 0.0008 mol divided by 0.032

.
Thus [H₃O⁺] is 0.025

and the pH is 1.6.

Calculation of pH mixed solution if HO^–is present in excess,

Determine [HO^–] as above for [H₃O⁺],
Calculate [H₃O⁺] using K_w.

K_w= [H₃O⁺][OH^–]
K_w(25 °C) = 1.0 × 10^–14