The concentration of the hydronium ions will be equal to 8.8 * 10^(-5)"M".
Hypochlorous acid, HClO, is a weak acid that dissociates in aqueous solution to form hydronium cations, H_3O^(+), and hypochlorite anions, ClO^(-).
You can determine the concentration of the hydronium ions by using an ICE table for the following equilibrium reaction
" "HClO_((aq)) + H_2O_((l)) rightleftharpoons H_3O_((aq))^(+) + ClO_((aq))^(-)
I......0.265......................................0.....................0
C.......(-x).......................................(+x).................(+x)
E.....0.265-x...................................x.....................x
The acid dissociation constant, K_a, will be equal to
K_a = ([H_3O^(+)] * [ClO^(-)])/([HClO]) = (x * x)/(0.265 - x) = x^2/(0.265 - x)
Because K_a has such a small value, you can approximate (0.265 - x) with x to get
K_a = x^2/0.265 = 2.9 * 10^(-8)
This means that x will be equal to
x = sqrt(0.265 * 2.8 * 10^(-8)) = 8.8 * 10^(-5)
Since x is equal to the molarity of the hydronium ions, the answer will be
[H_3O^(+)] = color(green)(8.8 * 10^(-8)"M")
