Calculating H3O+ Concentration Using Buffer Solution

[Hockeystar]

Homework Statement

What is the H3O+ concentration with the following scenario

5.3e^-2M HCl and 7.70e^-2 M NaC₂H₃O₂

Homework Equations

Kw = Kb(Ka) ICE tables

The Attempt at a Solution

Both solutions 100% dissociation

The HCl should be fully neutralized giving 7.70e^-2 - 5.3e^-2 = 0.024M of the acetate left. Knowing the Kb of acetic acid is 5.56e^-10 I set up an ICE table (5.56e^-10*0.024)^1/2 to find [OH-] to be 0.0000037. Convert that to what H+ concentration by taking 1e^-14/0.0000037 = 3e^-9. This answer is wrong. Could somebody point out where I went wrong.

 

[Borek]

Why do you solve buffer problem using ICE table instead of Henderson-Hasselbalch equation?

 

[Hockeystar]

The problem is I used the HH equation in my last question and failed. Should I just use the HH equation with the acetic ion concentration being the concentration of HCl and the acetate ion concentration is just the original concentration subtract HCl concentration?

 

[Borek]

That's the correct approach here.

What was the previous question? I guess there was a reason why HH was not applicable.

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[Hockeystar]

Thanks for your help just solved this question.

The previous question was 0.1 M NaNO2 and 0.05 HNO2. The Ka was 4e-4. I kept on getting 3.70 to be the pH which meant [H+] was 0.0002 but the answer was 3.6e-4.

EDIT. Masteringchemistry wanted we to assume their Ka value in their textbook which was twice as big of a value everywhere else on the internet grrrrrrrrrrrrrrrrrrrrrrr.