What mass of NaOH is needed to make 250 mL of a solution with pH = 13.00? (NaOH = 40.0 g/mol)

Core Concept

A pH of 13.00 gives pOH = 14.00 - 13.00 = 1.00, so [OH-] = 10^-1.00 = 0.100 M. NaOH dissociates completely and supplies one OH- per formula unit, so the moles of NaOH must equal the moles of hydroxide: 0.100 mol/L x 0.250 L = 0.0250 mol. Converting with the given molar mass: 0.0250 mol x 40.0 g/mol = 1.0 g. Every strong-base mass problem follows this chain: pH to pOH, pOH to concentration, concentration times volume to moles, then moles times molar mass.