What is the mass percentage of acetic acid in the solution?

Question

The pH of white vinegar solution is 2.45. This vinegar is an aqueous solution of acetic acid with a density of 1.09 g/mL. What is the mass percentage of acetic acid in the solution?

Can someone explain the process of determining the answer - I don't know where to start. How do I solve it? Hint: The answer is 4.1%.

Answer 1

Let [HAc] represent the concentration of acetic acid. Since the pH of white vinegar solution is 2.45, we have [H+] = [Ac-] = 10^(-2.45) = 0.0035.
You have to find a constant from your book--the pKa of acetic acid is 4.76 at 25 °C. That means:
10^(-4.76) = [H+]*[Ac-]/ [HAc] = {10^(-2.45)}^2/ [HAc]
So [HAc] = {10^(-2.45)}^2/10^(-4.76) = 0.724(M)
The total acetic acid concentration is [HAc] + [Ac-] = 0.728M
The molar mass of acetic acid is 60. thus the total mass of acetic acid is 60*0.728 = 43.68. here we considered 1L of the solution , thus the mass of the solution is 1044. The mass percentage of acetic acid is 43.68/1044 = 4.2%
< I would guess 4.1% does not include the [Ac-] in the final result.>

Answer 2

You need to go back through your book and look for a constant I bet that's what U are missing look at examples usually displays the constant