Acid-Base Equilibria Problem

[NateG14]

AP Chem student here with some trouble with A/B equilibrium. The problem and what I have done so far given below:

 

1. A solution contains .300 mol of acetic acid and .200 mol of sodium acetate in a total volume of 500 mL. How much 6.0 M NaOH must be added so that the pH of the solution equals the pKa of acetic acid? (Ka of acetic acid = 1.8 * 10^-5)

 

I apologize for not putting this in LaTeX, but the formula I must use, known as the Henderson-Hasselbach equation, goes as such:

 

pH = pKa + log([A-]/[HA])

 

where [HA] = the concentration (M) of the (weak) acid in question and [A-] = the concentration of the conjugate base. I understand that the ratio of

[A-]:[HA] must equal 1, as log(1) equals 0, and hence pH = pKa. However, given that the concentration of acetic acid is .6 M, and the concentration of the conjugate base (acetate ion) is .4 M, I do not understand how to calculate the volume of NaOH to be added without making the calculations unduly complicated. Assistance would be greatly appreciated.

 

P.S. I realized too late that this must go in the Homework Help forum. I would be thankful for a mod to move the thread if the rules require.

[NateG14]

Urgent help requested, please.

[John Cuthber]

Well you have got as far as the ratio of Na to acetate must be 1 to 1.

What is that ratio now and what would you need to do to make it 1 to 1?