What is the percent ionization?

Question

What is the percent ionization in a 0.460 M solution of formic acid (HCOOH) (Ka = 1.78 × 10⁻⁴)?

Answer 1

HCOOH <--> H⁺ + HCOO^-

To find % ionization, we want to find the [H+] and/or [HCOO-] and then divide that by the original concentration of the non-ionized acid.

Ka = 1.78x10^-4 = [H⁺][HCOO^-] / [HCOOH]

1.78x10^-4 = (x)(x) / 0.460 - x and if we assume x is small relative to 0.460, we can ignore it (see below)

1.78x10^-4 = (x)(x) / 0.460

x2 = 8.19x10^-5

x = 9.05x10^-3 = 0.00905 M compared to 0.460 M is only ~ 2% so it was ok to ignore it above and avoid using the quadratic equation.

Percent Ionization = 0.00905 / 0.460 (x100) = 1.97%