Answer
The correct answer is (c) 1/1.8.
Work Step by Step
1. Calculate the pKa value for acetic acid.
$pKa = -log(Ka)$
$pKa = -log( 1.8 \times 10^{- 5})$
$pKa = 4.74$
2. Find the acid/base ratio:
$pH = pK_a + log\frac{[Base]}{[Acid]}$
$5 = 4.74 + log\frac{[Base]}{[Acid]}$
** Mathematically, we can invert a fraction inside a logarithm, as long as we multiply the log by "-1":
$log\frac{[Base]}{[Acid]} = -log\frac{[Acid]}{[Base]}$
$5 - 4.74 = - log\frac{[Acid]}{[Base]}$
$0.26 = - log\frac{[Acid]}{[Base]}$
$\frac{[Acid]}{[Base]} = 10^{-0.26} = 0.55$
There is no "0.55" answer, but, we can do this:
$\frac{[Acid]}{[Base]} = \frac{0.55}{1}$
** Dividing the fraction by 0.55:
$\frac{[Acid]}{[Base]} = \frac{1}{1.8}$
So, the correct answer is (c): 1/1.8
