Final answer:
In a 0.54 M solution of nitrous acid, the concentration of H₃O⁺ is 0.54 M, the concentration of NO₂⁻ is 0.54 M, and the concentration of OH⁻ is 1.85 x 10⁻¹⁴ M.
Step-by-step explanation:
In a 0.54 M solution of nitrous acid, HNO₂, we can determine the concentration of H₃O⁺, NO₂⁻, and OH⁻ by considering the dissociation of nitrous acid. The equation for the dissociation of nitrous acid is as follows:
HNO₂ + H₂O → H₃O⁺ + NO₂⁻
From this equation, we can see that the concentration of [H₃O⁺] is equal to the concentration of nitrous acid, which is 0.54 M. So [H₃O⁺] = 0.54 M. Since nitrous acid is a weak acid, we can assume that the concentration of [NO₂⁻] is equal to the concentration of [HNO₂], which is also 0.54 M. So [NO₂⁻] = 0.54 M. Lastly, the concentration of [OH⁻] can be determined using the equation Kw = [H₃O⁺][OH⁻], where Kw is the ion product of water (1.0 x 10⁻¹⁴). From this equation, we can solve for [OH⁻]: [OH⁻] = Kw / [H₃O⁺]. Plugging in the values, we get [OH⁻] = (1.0 x 10⁻¹⁴) / (0.54) = 1.85 x 10⁻¹⁴ M.