In a laser photolysis reaction $\ce{C6H5NH2}$ $(C_0 = \pu{60 µM})$ is oxidized to its radical cation. The disappearance of the cation can follow three pathways: (1) Dimerzing of the cation, (2) Reaction between the cation of the initial substance, (3) Reaction between the cation and the solvent. Decide which pathway is most likely to occur.
$$ \begin{array}{l|cccccccc} \hline t/\pu{µs}~(\text{efter puls}) & 0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 \\ \hline [\text{Radikalkatjon}]/\pu{µM} & 20 & 11.12 & 6.86 & 4.47 & 3.00 & 2.06 & 1.43 & 1 \\ \hline \end{array} $$
I first checked for the dimerizing of the cation by assuming it to be a second order reaction with the same reactants and plotting $1/[\mathrm{cation}]$ against $t,$ which didn't give a good fit. So I wanted to plot it as a second order reaction with different reactants $(\ce{A + B -> products})$ but I don't understand how that is done.
I should plot $\displaystyle\ln\frac{a-x}{b-x}$ against $t,$ but what exactly is $(a-x)$ and $(b-x)?$
I know that I should set up a reaction like:
$$ \begin{array}{l|ccc} \hline & \text{A} & \text{B} & \text{product} \\ \hline t=0 & a & b & 0 \\ t=t & a-x & b-x & x \\ \hline \end{array} $$
And I would assume that my $a = \pu{20 µM}$ and $b = \pu{60 µM}.$ But where do I go from there? All help is appreciated!