TBR Gen Chem 4.22

[SrootsWwings]

So I have entered an idiot cycle and can't get out:

The question:

What is the pH of 0.20 M sodium propionate, if it has Kb = 7.2 * 10^-10?

A. Less than 3
B. Between 3 and 7
C. Between 7 and 11
D. Greater than 11

I understand how to solve the problem by solving for (or estimating) pKb, and then using that to find pOH, and then obviously pH. This leads to the correct answer C.

Here's what I don't understand: on immediate analysis, if Kb = 7.2 * 10^-10, why can't I use Ka * Kb = 10^-14? I thought I could, which meant Ka>Kb, so that the substance is an acid, and it obviously gets contradictory right around there. I am sure there is an obvious reason I am missing, so someone please tell me there is a giant elephant behind that lamp in the corner.

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[SrootsWwings]

I think I just figured it out; pKa + pKb = 14 only applies at 25ºC --> so does Ka * Kb = 10^-14

 

[SrootsWwings]

Aaaaaaand also, more relevantly, I was trying to use it for the same compound, not for the conjugate pair. I feel like that kid in class who gets halfway through a question in class before the light bulb...

 

[Jengreef]

Could you explain it then? I'm not getting it...

I figured the low Kb would imply high Ka, or at least proportionally higher Ka, and thus a lower pH. How did you get C?

 

[SrootsWwings]

The relationship Kacid * Kbase = 10^-14 is actually Kconj.acid * Kconj.base = 10^-14 --> you can't use the Ka of a substance to estimate its own Kb. Does that make sense?

I.e., if the Ka of HX is 10^-10, then its Kb isn't 10^-4; the Kb of its conj. base, X-, is 10^-4 (so that Ka*Kb = 10^-10 * 10^-4 = 10^-14).

So in solving that problem, you can't estimate Ka; the solving progression goes Kb --> pKb --> pOH --> pH.

So Kb = 7.2*10^-10, thefore pKb = -log(Kb) -log(7.2*10^-10) = 10 - log7.2 = 10 - ~.8 = 9.2

pOH = pKb/2 - log[OH-] = 9.2/2 - .5log.2 = 4.6 - (.5*.3) = 4.45

14 - pOH = pH, so 14 - 4.45 ~ 9.55.

It's unnecessary, and unwise, to solve so extensively in test mode, but for understanding it's great practice. Last night I was doing a lot of under-breath cursing at all this, and now it's fast and easy. It has a strong acid-strong base learning curve, not a buffer-zone one (herpa-derp), it'll click!!!

 

[Jengreef]

Ah, thanks.