Answer
(c) initial [HA]= 0.0100 M; $K_a$ = $1.0 \times 10^{-3}$
Work Step by Step
The $x \space is \space small$ approximation is least likely to work in solutions with lower initial acid concentration and "big" $K_a$ values.
This happens because the approximation depends on the percent ionization of the acid (it must be low). This percent ionization increases when the inital acid concentration decreases and the $K_a$ of the acid increases.
(c) is the alternative with the lowest initial concentration and the greatest $K_a$, so it is definitely the least likely to work with this approximation.
