TBR Gen Chem p269 #19

[circulus vitios]

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Which of the following values most accurately describes the pka for HBrO2 based on table 1?
A. 0.63
B. 1.44
C. 1.92
D. 2.85

Relevant part of table 1:

Acid, pKa
...
HClO3, 0.1
HClO2, 1.9
HOCl, 7.3
...

I answered C. The book says D with the explanation that "...the pka for HBrO2 must be >1.9, so the only answer possible is choice D."

Last time I checked 1.92 > 1.90. I understand the primary trend of acidity increasing with increasing number of electron withdrawing groups (oxygens) and the secondary trend of acidity increasing with electronegativity of the halide and the number of the halides. But how am I supposed to know extrapolate this qualitative data and know that the pka is 2.85 rather than 1.92?

 

[ilovemcat]

You're told that each additional oxygen will lower the pKa of an acid by approximately 5.(passage info). For this question however, the pKa difference is due to the difference in electronegativity of the central atom. To answer this you need to first locate all the oxyacids with same # of oxygens.

The only other oxyacid with 2 oxygens listed is HClO2, which has a pKa of 1.9. Now you must decide whether the pKa is higher or lower than 1.9 and if so by how much. As you pointed out, HBrO2 is a weaker acid than HClO2, so it's pKa should be higher. This rules out A and B. The next question becomes, by how much does the pKa increase: by 0.2 (choice C) or by ~1.0 (choice D).

To answer this question, you need to look at the table in order to establish roughly how much the pKa will differ due to electronegativity.

HClO4: pKa = -8.8
HBrO4: pKa = -4.6
HIO4: pKa = -1.8

HOCl: pKa = 7.3
HOBr: pKa = 8.6
HOI: pKa = 10.8

As you can see, the difference in pKa for any of these oxyacids (different by the central atom only) has a difference must greater than 0.2. This rules out choice C.

 

[circulus vitios]

Durrr. I don't know why I didn't think of looking for halide trends within the table. Oh well, that's me. 🙄 Thanks for the thorough explanation. 👍