Chemistry - Concentration from known pH and Ka.

[Mholnic-]

Homework Statement

A particular sample of vinegar has a pH of 2.90. If acetic acid is the only acid that vinegar contains (Ka = 1.8 x 10^-5), calculate the concentration of acetic acid in the vinegar.

Homework Equations

Ka = [Products]/[Reactants]
pH = -log[H⁺]

The Attempt at a Solution

I arranged the problem in my usual lazy way:
Acid + Water ---> Conjugate Base + Hydrogen Ions

Assuming that [H⁺] is equal to [Conjugate Base] I calculated the concentration of the conjugate base and hydrogen ions.

pH = -log[H⁺] = 2.90
[H⁺] = 10^-2.90 = [Conjugate Base]

Then I plugged those numbers and the given Ka value into:

Ka = [products]/[reactants]

1.8 x 10^-5 = [10^-2.90]²/[Acid]

[10^-2.90]²/1.8 x 10^-5 = [Acid]

I get 8.8 x 10^-12. The book says the answer is .089 M. Not quite sure where I'm going wrong.. maybe I am not using the correct equations or perhaps it's an overlooked error in algebra. Help!

 

[Borek]

[10^-2.90]²/1.8 x 10^-5 = [Acid]

Equation is correct, but it doesn't yield 8.8x10^-12.

Note that concentration of the acid that you can calculate in this step is not the final answer yet.