Question

What is the $pH$ of a $0.5$ M solution of acetic acid, if the $K_a$ of acetic acid is $2\times {10}^{-5}$?

• A. $1.0$
• B. $2.0$
• C. $2.5$
• D. $3.0$
• E. $7.0$

Answer 1

The correct option is C $2.5$

$C{H}_{3}COOH$ <---> $C{H}_{3}CO{O}^{-}+H^{+}$
Inital molarity 0.5 0 0
Equilibrium molarity 0.5-x x x
$K_a=2\times {10}^{-5}=\frac{x^2}{(0.5-x)}$
Because x is too small, so it can be ignored.

$\therefore 0.5-x\approx 0.5$

$2\times {10}^{-5}=\frac{x^2}{0.5}$

$x=0.003162$

$pH=-log\left(0.003162\right)=2.5$

Hence, the correct option is C.