Refer to:
https://image.slidesharecdn.com/acidbasetable-151107033108-lva1-app6892/95/acid-base-table-1-638.jpg?cb=1446867098
Ka for HNO₂= 7.2 × 10⁻⁴
(You may find other values of Ka for HNO₂ from other sources.)
Consider the dissociation of HNO₂ :
____________ HNO₂(aq) __ ⇌ __ NO₂⁻(aq) __ + __ H⁺(aq) ___ Ka = 7.2 × 10⁻⁴
Initial: ________ 0.5 M _________ 0.5 M ________ 0 M
Change: _______ -y M __________ +y M _______ +y M
At eqm: _____ (0.5 - y) M _____ (0.5 + y) M ______ y M
(Since the initial [H⁺] is 0 M, then the change of [H⁺] must be positive because [H⁺] must not be negative.)
Due to the fact that Ka is small and common ion effect in the presence of 0.5 M NO₂⁻, the dissociation of HNO₂ would be to a very small extent.
It is assumed that 0.5 ≫ y, i.e.
[HNO₂] at equilibrium = (0.5 - y) M ≈ 0.5 M
[NO₂⁻] at equilibrium = (0.5 + y) M ≈ 0.5 M
Ka = [NO₂⁻] [H⁺] / [HNO₂]
7.2 × 10⁻⁴ = 0.5y / 0.5
y = 7.2 × 10⁻⁴
pH = -log[H⁺] = -log(7.2 × 10⁻⁴) = 3.14