New TBR Ochem 1 - Section 4: Lab Techniques Phase 3 #4

[aurevoir0711]

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According to 2011 Ochem edition, it should be Ochem 2, Section 8, #39

4. What is true about the pK values for the conjugate bases of the benzoic acid and resorcinol?
Benzoic acid pKa = 4.17
Resorcinol pka1 = 9.89 (diol, the compound has two hydroxide groups, diprotic, pKa2 not given)

A. pKb (sodium benzoate) > pKb2 (sodium resorcinoxide) and pKa1 (resorcinol) > pKa2(resorcinol)
B. pKb2 (sodium resorcinoxide) >pKb (sodium benzoate) and pKa1 (resorcinol) > pKa2(resorcinol)
C. pKb (sodium benzoate) > pKb2 (sodium resorcinoxide) and pKa2 (resorcinol) > pKa1(resorcinol)
D. pKb2 (sodium resorcinoxide) >pKb (sodium benzoate) and pKa2 (resorcinol) > pKa1(resorcinol)



The answer is C.
Explanation:
The second proton is by definition less acidic than the first proton, so the second pKa is greater than the first pKa. Choices A and B are eliminated. The value of pKb can be found by subtracting the pKa for the conjugate acid from 14. Because the pKa for benzoic acid is lower than the pKa for the first proton of resorcinol, the pKb for the conjugate base of benzoic acid (benzoate) must be greater than the pKb for the conjugate base of the first acidic proton of resorcinol (pKb2)- The first proton lost by a diprotic acid is the second one gained by the fully deprotonated form of the conjugate base. This makes choice C the best answer.


The highlighted portion from above is what I do not understand. Here's my take on it.
6 pK values since resorcinol is diprotic
Benzoic acid pKa = 4.17, so benzoate (conjugate base) will have pKb = 14-4.17 = 9.83
Resorcinol pKa1 = 9.89, as stated in the explanation, pKa2 of Resorcinoxide should be higher since it's less acidic. I will assign an arbitrary number like pKa2 ~ 12.
Since diprotic, pKa1 + pKb2 = 14, so pKb2 = 14-9.89 = 4.11
Similarly, pKa2 + pKb1 = 14, so pKb1 = 14-12 = 2 (approximation)

Based on this, I get pKa2 (resorcinoxide) > pKa1 (resorcinol) > pKb (benzoate) > pKa (benzoic acid) > pKb2 (resorcinoxide) > pKb1 (resorcinol)

For C, I can't get my head around why pKa2 resorcinol is lower than pKb of benzoate. Can someone please explain why? Thank you for your insight in advance.

 

[aurevoir0711]

Nvm... I thought that "and" was a part of the inequality for some reason. I guess I need to take some break or something.

 

[BerkReviewTeach]

Sorry to be late to respond, but it seems you solved it already. That is always better for learning, so great job!