In lecture, we derived expressions for ${}_0,{}_1,$ and ${}_2($ionization fractions$)$ for a diprotic acid in terms of $pH$ and the $K_a$ values. Here, you will consider a monoprotic acid.

a$.$ Derive expressions for ${}_0$ and ${}_1($in terms of $H^{+}$and $K_a)$ for a monoprotic acid $($e$.$g$.,$ HF$).($These equations would be good to put on your equation sheet for the next exam.$)$

b$.$ For a monoprotic acid, ${}_0+{}_1=?$