Given a total chlorine concentration and the pH and pKa of $\ce{HOCl}$, how would you find the concentration of $\ce{OCl-}$ and $\ce{HOCl}$ disinfectants?
If the given total chlorine concentration is $c(\ce{Cl})_\text{tot}= 0.1~\mathrm{M}$, with $\text{pH}(\ce{Cl}) = 8$ and $\text{p}K_\text{a}(\ce{HOCl}) = 7.5$, how does one go about doing so?
So far I think that I should start this way:
$K_\text{a} (\ce{HOCl}) = 10^{-7.5}=3.16\cdot 10^{-8}$
I wrote up the reactions:
$$\ce{H2O + 2e- + OCl <=> Cl- + 2OH-}$$
Where $\ce{OCl-}$ is the conjugate acid and $\ce{OH-}$ the conjugate base.
$$\ce{HOCl<=> OCl- + H+}$$
The conjugated acid is $\ce{HOCl}$, the conjugated base $\ce{OCl-}$.
Now I use $$\text{pH}=\text{p}K_\text{a} + \log\left(\frac{[\text{conj base}]}{[\text{conj acid}]}\right)$$
and/or for weak acids $$K_\text{a}= [\text{products}]/[\text{reactants}]$$
But I'm not sure if this is correct and what values to use.