What is the pH?

Question

What is the pH of a 0.680 M solution of Ca(NO₂)₂ (Ka of HNO₂ is 4.5 × 10⁻⁴)?

Answer 1

HNO₂ ==> H⁺ + NO₂^-

Ka = 4.5x10^-4 = [H⁺][NO₂^-]/[HNO₂]

4.5x10^-4 = (x)(x)/0.680 - x and if we assume x is small relative to 0.680 we can ignore it (see below)

4.5x10^-4 = x2 / 0.680

x² = 3.06x10^-4

x = 1.75x10^-2 and this is only 2.5% of 0.68 so our assumption above is valid (i.e. it is less than 5%)

[H⁺] = 1.75x10^-2 M

pH = -log [H⁺] = -log 1.75x10^-2

pH = 1.76