What is the pH of a $1.0 ext{ M}$ solution of acetic acid? Given: $K_a = 1.8 imes 10^{-5}$. Take

Question

What is the pH of a $1.0	ext{ M}$ solution of acetic acid? Given: $K_a = 1.8 	imes 10^{-5}$. Take $\log(1.8) = 0.25$, $\sqrt{1.8} = 1.34$, $\log(1.34) = 0.13$.

Professor PC Thomas Classes · Answer

For a weak acid $	ext{HA}$, $[	ext{H}^+] = \sqrt{K_a C}$.
Here $C = 1.0	ext{ M}$, $K_a = 1.8 	imes 10^{-5}$.
$[	ext{H}^+] = \sqrt{1.8 	imes 10^{-5} 	imes 1} = \sqrt{18 	imes 10^{-6}} = 4.24 	imes 10^{-3}	ext{ M}$.
Or better, $[	ext{H}^+] = \sqrt{1.8 	imes 10^{-5}} = 1.34 	imes 10^{-2.5} = 10^{0.13} 	imes 10^{-2.5} = 10^{-2.37}$.
$	ext{pH} = -\log[	ext{H}^+] = -\log(\sqrt{1.8} 	imes 10^{-2.5}) = 2.5 - \log(\sqrt{1.8}) = 2.5 - \frac{1}{2}\log 1.8 = 2.5 - \frac{1}{2}(0.26) = 2.37$.