Answer is: concentration of hydronium ions is 8.13·10⁻⁴ M.
c(HNO₂) = 0.055 M.
c(NaNO₂) = 0.10 M.
Ka(HNO₂) = 4.5·10⁻⁴.
This is buffer solution, so use Henderson–Hasselbalch equation:
pH = pKa + log(c(NaNO₂) ÷ c(HNO₂)).
pH = -log(4.5·10⁻⁴) + log(0.055 M ÷ 0.10 M).
pH = 3.35 - 0.26.
pH = 3.09.
[H₃O⁺] = 10∧(-3.09).
[H₃O⁺] = 8.13·10⁻⁴ M.