Two TBR GChem Questions (Acids/Bases)

[Synapsis]

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Question 88 in chapter 4 says aspartic acid has a shorter carbon chain in it's side chain than glutamic acid, which results in what?

The two answers of interest are:
A. Stronger inductive effect, making aspartic acid more acidic
B. Weaker inductive effect, making aspartic acid more acidic

My question is more so for clarity's sake. The answer was A, because apparently with the shorter carbon chain, the carboxylic acid in the side chain can be closer to the electron withdrawing NH3+ group. This makes that inductive electron withdrawing effect stronger. That makes total sense.

But with the way this question was phrased, I thought they were referring to the inductive effect of the carbon chain itself. That is, with a shorter carbon chain, you have a smaller electron-donating alkyl group that would be destabilizing the anion in the conjugate base. So I used that logic and said that the inductive effect would be weaker. My issue isn't with understanding why the answer is what it is so much as it's understanding what exactly they're testing me on. When they mentioned a shortened carbon chain, I thought they were trying to get me to consider only the inductive effect associated with the length of the carbon chain rather than that of the amine, which is common for all isolated amino acids. How would I have known that they wanted me to consider the inductive effect of the amine rather than simply the carbon chain alone?

A second question - for question 92 of the same chapter, part of the answer explanation says that the pH of 0.10 M HF (pKa 3.3) is half the pKa +0.5. This "shortcut" is introduced in the chapter but I didn't really understand it. Can someone explain how to use it and when I can use it? I assume for any weak acid?

 

[rguil15]

Question 88 in chapter 4 says aspartic acid has a shorter carbon chain in it's side chain than glutamic acid, which results in what?

The two answers of interest are:
A. Stronger inductive effect, making aspartic acid more acidic
B. Weaker inductive effect, making aspartic acid more acidic

My question is more so for clarity's sake. The answer was A, because apparently with the shorter carbon chain, the carboxylic acid in the side chain can be closer to the electron withdrawing NH3+ group. This makes that inductive electron withdrawing effect stronger. That makes total sense.

But with the way this question was phrased, I thought they were referring to the inductive effect of the carbon chain itself. That is, with a shorter carbon chain, you have a smaller electron-donating alkyl group that would be destabilizing the anion in the conjugate base. So I used that logic and said that the inductive effect would be weaker. My issue isn't with understanding why the answer is what it is so much as it's understanding what exactly they're testing me on. When they mentioned a shortened carbon chain, I thought they were trying to get me to consider only the inductive effect associated with the length of the carbon chain rather than that of the amine, which is common for all isolated amino acids. How would I have known that they wanted me to consider the inductive effect of the amine rather than simply the carbon chain alone?

Because by definition, induction implies something electronegative withdrawing charge. If you know carbon can only donate charge then find the next logical thing in the molecule that would make sense of the question.