Let the acid be HA.
The chemical formula for this acid will be the following:
[tex]HA \rightleftharpoons H^{+}+A^{-}[/tex]
The formula for the acid dissociation constant will be the following:
[tex]K_a= \dfrac{[H^+][A^-]}{[HA]}[/tex]
We know [H+]=0.0001 (it's given).
However, we must find [A-] and [HA] in order to solve for the constant.
We find that [A-]=[H+] by using a electroneutrality equation.
Also, we can create a concentration equation to find [HA].
[tex]0.5M=[A^-]+[HA][/tex]
[tex][HA]=0.5M-[A^-][/tex]
Now, we can find the acid dissociation constant.
[tex]K_a= \dfrac{[H^+][A^-]}{0.5M-[A^-]}[/tex]
[tex]= \dfrac{0.0001*0.0001}{0.5-0.0001} = 2.0*10^{-8}[/tex]
