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")#
