Calculating the pH of a weak acid

[--whiteskies]

How do you calculate the pH of 1.0 M acetic acid in water, using the pKa of acetic acid?
Thanks!

[lzxnl]

How do you calculate the pH of 1.0 M acetic acid in water, using the pKa of acetic acid?
Thanks!

Ka of acetic acid is around 1.8 * 10^-5

Initially, you have 1.0 M acetic acid reacting to form x M of acetate and x M of H+ (assume no acid initially)
This leaves you with 1 - x M acetic acid at equilibrium
So 1.8 * 10^-5 = [H+][acetate]/[acetic acid] = x^2 / (1-x)
Acetic acid is weak => assume x << 1, so 1-x is about 1
Then we have x^2 = 1.8*10^-5
x = around 4.2*10^-2 M
pH around 2.4