Hydrolysis of a salt question

[pch]

I'm confused about how to find the correct answer to this question:

Acetic acid has a pKa of 4.8. What is the pH of a 0.1M solution of sodium acetate?
a) 2.9
b) 7
c) 8.9
d) 13

I don't really know where to begin. When I first saw the question, I thought I'd be using the Henderson Hasselbach equation because we are dealing with an acid and it's salt but after reading the answer, they used a whole different approach and did the question by looking at the dissociation of the sodium acetate and I got confused.. can someone please explain their train of thought when looking at this question? Thank you!

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[wizzed101]

Since acetate is weak base, my baseless (lol) guess is c) 8.9

 

[LIC2015]

What was their approach, and what is the answer?

 

[BerkReviewTeach]

There are two ways to get the best answer.

(1) Intuitive Reasoning: The solution is made from a weak base and water, so the solution is basic. The pH must be greater than 7, so choices A and B are eliminated. If it were a strong base, then the pOH would be -log 0.1 = 1, making the pH = 13. It is not a strong base, so it only partially reacts. The pH must be less than 13, so choice D is eliminated. Only choice C is greater than 7 and less than 13.

(2) The Berkeley Review Weak Base EquationTM: pOH = 1/2 (pKb + pOHif it fully reacted) = 1/2(9.2 + 1.0) = 1/2(10.2) = 5.1. If the pOH is 5.1, then the pH is 8.9.

Both methods work well and can be done in less than 15 seconds.

 

[pch]

There are two ways to get the best answer.

(1) Intuitive Reasoning: The solution is made from a weak base and water, so the solution is basic. The pH must be greater than 7, so choices A and B are eliminated. If it were a strong base, then the pOH would be -log 0.1 = 1, making the pH = 13. It is not a strong base, so it only partially reacts. The pH must be less than 13, so choice D is eliminated. Only choice C is greater than 7 and less than 13.

(2) The Berkeley Review Weak Base EquationTM: pOH = 1/2 (pKb + pOHif it fully reacted) = 1/2(9.2 + 1.0) = 1/2(10.2) = 5.1. If the pOH is 5.1, then the pH is 8.9.

Both methods work well and can be done in less than 15 seconds.

I'm wondering why you used [OH] = 0.1 and the pOH=1?

 

[BerkReviewTeach]

I'm wondering why you used [OH] = 0.1 and the pOH=1?

That's how you do it using the BR's method. The full explanation is long, and I don't feel right typing it here. Hopefully you can find it in the BR book (pages 62 through 64 of Book 2, which includes examples of how to apply the shortcut equation). For acids and bases, there are no better methods than those in BR, so it's very beneficial to do the two chapters.