Calculate pH after combining 5.0 ml of 2.0 M hydrochloric acid (HCl) solution with 50 ml of 1.0 M potassium hydroxide (KOH) solution.

General information:
HCl neutralizes KOH in solution according to the following formula:

HCl + KOH → KCl + H₂O

Therefore,  1 mole of HCl neutralizes 1 mole of KOH.

Number of moles in a given solution = concentration × volume

Calculations:
Volume of HCl solution in liters = 5.0 ml × (0.001 liter/ ml) = 0.005 liter
Volume of KOH solution in liters = 50 ml × (0.001 liter/ mole) = 0.05 liter
Volume of final solution = 0.005 + 0.05 = 0.055 liter

Number of moles of HCl = 2.0 M × 0.005 liter = 0.01 mole
Number of moles of KOH = 1.0  M × 0.05 liter = 0.05 mole

The number of moles of KOH in the combined solution is larger than that of HCl. Therefore, 0.01 mole of KOH will be neutralized by the 0.01 mole HCl present after combination. Therefore,

Number of moles of KOH remaining in solution = 0.05 - 0.01 = 0.04 mole
Concentration of KOH in the combined solution = (0.04 mole)/ (0.055) liter = 0.73 M

pH can be calculated using online pH calculator or by applying the pH equation for a strong base as the following:
pH = 14 + log [OH-]
pH = 14 - 0.14 = 13.86

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