An approximate equation for the ionization of a weak acid, including consideration of the hydrogen ions from water is

[H⁺]/c^◦ =√K_ac/c◦ + K_w,

where c is the gross acid concentration. This equation is based on the assumption that the concentration of unionized acid is approximately equal to the gross acid concentration. Consider a solution of HCN (hydrocyanic acid) with stoichiometric acid concentration equal to 1.00 × 10⁻⁵ mol l⁻¹. K_a = 4 × 10⁻¹⁰ for HCN. At this temperature, K_w = 1.00 × 10⁻¹⁴.
(a) Calculate [H⁺]/c^◦ using this equation.
(b) Calculate [H⁺]/c^◦ using Eq. (5.9).