.151 M Sodium Acetate + .082 M Acetic Acid, find the pH

[Grimm]

Hi everyone. I'm sure you're all glad I'm back with another chemistry problem giving me problems. You can see below is the attached question. Here is the work I have for it.

 

kb = kw/ka = 1 E-14 / 1.8 E-5 = 5.55 E-10

 

NaC2H3O2 .151 M HC2H3O2 .082 M

 

C2H3O2- + H2O <--> HC2H3O2 + OH-

I .151 .082 0

C -x +x +x

E .151-x .082+x x

 

kb = [HC2H3O2][OH-] / [C2H3O2-]

 

5.55 E-10 = [.082 + x][x] / [.151 - x]

 

Since the kb is so low we can make assumptions and use the 5% rule.

 

5.55 E-10 = [.082][x] / [.151]

 

x = 1.023 E-9 = [OH-]

 

-log[OH-] = 8.990 = pOH

 

14 - pOH = 5.010 = pH

 

Someone please help me. I already have it marked wrong so right now my main concern is just making sure that I know it for the exam. Please let me know where I went wrong here.

[John Cuthber]

Have you met this?

https://en.wikipedia.org/wiki/Henderson%E2%80%93Hasselbalch_equation

[Grimm]

Have you met this?

https://en.wikipedia.org/wiki/Henderson%E2%80%93Hasselbalch_equation

 

I don't think I've tried that. So I wasn't using the correct set up then? The question tells me to use a specific method.

 

I will try it though, thanks.

The ka of Acetic Acid is 1.75 E-5 -log(ka) = pka = 4.757

 

[A-] = [C2H3O2-] = .151 M [HA] = HC2H3O2 = .082 M

 

pH = 4.757 + log(.151/.082)

 

pH = 1.261

 

Do I have this right?

[John Cuthber]

Check your arithmetic.

[hypervalent_iodine]

 

I don't think I've tried that. So I wasn't using the correct set up then? The question tells me to use a specific method.

 

I will try it though, thanks.

The ka of Acetic Acid is 1.75 E-5 -log(ka) = pka = 4.757

 

[A-] = [C2H3O2-] = .151 M [HA] = HC2H3O2 = .082 M

 

pH = 4.757 + log(.151/.082)

 

pH = 1.261

 

Do I have this right?

 

 

Doesn't the question tell you the Ka of acetic acid is 1.8 x 10^-5 ?

 

As for telling you to use a specific method, I wouldn't worry about it. The question is clearly primed for use in the HH equation. Anything else (particularly if you've been taught HH) is overcomplicating it and wasting your time. Since this is through Wiley Plus (which I assume is being used as a supplementary form of assessment with questions not written by your course providers), I wouldn't stress about the way they tell you to approach it and instead focus on methods you've learned yourself in class.

 

That being said, some notes on the method you originally took and that they suggest. You were actually quite close, but I think you were killed by rounding errors resulting from not including the + and - x terms. The equation does get a bit tricky to solve, but it's best to keep them in these cases, unless you're using the HH equation as you probably should be.