Answer: 1.44 × 10^-3 M.
Explanation: To calculate the [H3O+] of the solution, we need to consider the dissociation of HF (hydrofluoric acid) and the subsequent formation of H3O+ ions. Since HF is a weak acid, it partially dissociates in water.
The dissociation reaction of HF can be represented as follows:
HF + H2O ⇌ H3O+ + F-
The equilibrium constant for this reaction, Ka, is given as 7.2 × 10^-4.
Given:
[Molar concentration of HF] = 0.20 M
[Molar concentration of NaF] = 0.10 M
Assuming that the dissociation of HF is limited by the available F- ions from NaF, we can use the concept of the common ion effect to calculate the [H3O+] in the solution.
Since NaF is a salt that dissociates completely into Na+ and F- ions, the [F-] in the solution is equal to the concentration of NaF, which is 0.10 M.
Let's denote the concentration of [H3O+] as x M.
Using the equilibrium expression for the dissociation of HF:
Ka = [H3O+][F-] / [HF]
Substituting the known values:
7.2 × 10^-4 = x * 0.10 / 0.20
Simplifying the equation:
x = (7.2 × 10^-4) * (0.20 / 0.10)
x = 1.44 × 10^-3
Therefore, the [H3O+] of the solution is approximately 1.44 × 10^-3 M.