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Mholnic-
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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!