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Homework Help: Chemistry - Concentration from known pH and Ka.

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    Ka = [Products]/[Reactants]
    pH = -log[H+]

    3. 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!
  2. jcsd
  3. Mar 13, 2012 #2


    User Avatar

    Staff: Mentor

    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.
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