PKa Problem (Am I not correct)

[The8]

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Ok, so look at the attachments. In my opinion, nothing can be said about the pka of the last two acids because the pkb only gives this information when it is of the CONJUGATE base of the acid. The pkb of an acid will give information regarding the protonated form of the acid itself, or the doubly protonated acid.

Correct answer is apparently D, but I don't see how you can get access to this information.

 

[theonlytycrane]

pKa + pKb = 14, so we can find pKa of the acid form given the pKb of the base form.

 

[bobeanie95]

You can't really use pKa + pKb =14 for this problem. In reality, this equation is used to compared the conjugate acid to the conjugate base.

For example, assume you have RCOO-H <----> COO- + H+. I'm making up these numbers, but if the pKa of RCOO-H is 4 then the equation can be used to calculate the basicity strength of COO- (pKb=14-4=10). In other words, you cannot use the pKa of RCOO-H to calculate the pKb of RCOO-H, it could only be used for conjugates.

As far as this problem goes, I would suggest finding the dissociation constants.
-For A, the Ka would be around 1 x 10^-4 = [X-][H+]/[HX]
-Meanwhile D will have a Kb of around 1x10^-11 = [HX+][OH-]/[X]

The Ka tells you the strength of the acid, while the Kb tells you the strength of the base. The larger the Kb/Ka, the stronger the base/acid. In this case, D has a very, very small (10^-11) Kb so it's indicating that its a very weak base and most likely a stronger acid. Meanwhile, A has a Ka of 10^-4 and usually strong acids have a Ka > 1, so its most likely a weaker acid. So I'd most likely go with D.

In my opinion, I think this is a poor question, I don't think the test writers wrote it well since you cannot truly compare the acidity of molecules with different pKa/pKb, especially with monoprotic molecules.

 

[theonlytycrane]

^ When they say pKb of Acid C, they implicitly mean the pKb of the base form. This allows you to find the pKa of the conjugate acid.

 

[bobeanie95]

You could assume that, though its still vague, which is why I think its a bad question. But yes, with your reasoning then you'd be correct.

 

[laczlacylaci]

We know weakest H-X bonds=more willing to release the proton=stronger acid. We also know that as pKa increases, pH increases. To find the strongest acid, we need to find the one that has the lowest pKa or highest pKb.

you could have eliminated B and C at the beginning because to find the weak/strongEST (extreme) you can eliminate the middle ones.
Using pKa+pKb=14

A) Acid A: pKa=4.1; pKb=9.9
B) Acid B: pKa=4.75; pKb=9.25
C) Acid C: pKa=4.37; pKb=9.63
D) Acid D: pKa=3.10; pKb=10.9

D fulfills the lowest pKa and highest pKb.

I feel like the Ka/Kb way by bobeanie95 and pKa/pKb by theonlytycrane are both correct. Though, I feel like the pKa/pKb way is faster.

 

[The8]

Well, in my opinion you can't assume that! Anyways, I'll give you a great example, METHANE. TERRIBLE base, super low pkb, but hell, it's pka is not very high either.... TERRIBLE QUESTION.... correct me if I'm wrong...... and why should I assume they are talking about the conjugate base and not trying to trick me with the question.... what a scumbag TPR can be.

 

[laczlacylaci]

Well, in my opinion you can't assume that! Anyways, I'll give you a great example, METHANE. TERRIBLE base, super low pkb, but hell, it's pka is not very high either.... TERRIBLE QUESTION.... correct me if I'm wrong...... and why should I assume they are talking about the conjugate base and not trying to trick me with the question.... what a scumbag TPR can be.

Yeah, I guess so since the formula is really pKa of HX+pKb of X-=pKw and not pKa of HX + pKb of HX=pKw. But like theonlytycrane said, I think you should just assume that the pKb is the pKb of the conjugate base and not the acid.

Good point though.

 

[BerkReviewTeach]

Well, in my opinion you can't assume that! Anyways, I'll give you a great example, METHANE. TERRIBLE base, super low pkb, but hell, it's pka is not very high either.... TERRIBLE QUESTION.... correct me if I'm wrong...... and why should I assume they are talking about the conjugate base...

You make an excellent point with methane. It has a very high pKa but does have a pKb. It's conjugate has a pKb, but not that compound.

For the question, there is no way you can draw any conclusion about the strength of the acid from its pKb (only from the pKb of its conjugate base). A great example is NH3, which has a pKb of 4.7 and a pKa of roughly 33. They DO NOT add to 14 because they are not the pKa and pKb of a conjugate pair.

The key point here is that you have a good understanding of the concepts, so no matter what you feel about the question, you will do fine on realistic MCAT questions.