[RandomPerson]

Hi, I'm in a biochem course right now, but this is more of a gen chem problem.  This is part of a study set for my class, and I'm very confused on part B. 

The pKa of a glutamic acid sidechain is 4.25.
a) What fraction of this amino acid sidechain is deprotonated at physiological pH (7.4)?
b) What is the delta G of ionization for this amino acid sidechain at 298 K?

I think I've got part a) nailed down, but I'm confused a little bit about part B.  If we have delta G=-RTlnKeq, how does that tie in here?  Am I supposed to somehow use the info from part A to calculate Keq to solve?

[Borek]

What is pKa? What is Keq?

[RandomPerson]

Well, pKa=-logKa and Ka=[H+][A-]/[HA], and Keq is the equilibrium constant for the reaction.

[Borek]

OK, so where is the problem? Just plug and chug.

[RandomPerson]

I think I was just confusing myself...  Thanks!

[RandomPerson]

I feel like I'm getting weird answers, so here's what I'm doing.  Let me know what I'm doing wrong.

So, using the Henderson-Hasselbalch equation:

pH=pka+log([A-]/[HA])

7.4=4.25+log([A-]/[HA])

3.15=log([A-]/[HA])

10^3.15=1412.5  <----Reasonable answer?

Then...

1412.5/(1412.5+1)=0.999x100=99.9%  ---> Reasonable answer?


b)  For part B, I really feel like my answer is off.  I did:

deltaG=-RTlnKa
deltaG=-(8.314)(298)ln(1412.5)=-17970.2

Clearly something is messed up here, I'm just not sure where I'm going wrong.

[ramboacid]

First of all, what is 1412.5 supposed to represent? It's the ratio of the amount of A- and the amount of HA. Thus, there is 1412.5 times as much A- as HA.

For part B, 1412.5 isn't the Keq. The Keq in acid dissociation reactions is the Ka, which happens to be 10^-pKa.

[RandomPerson]

Ahhh, gotcha.  I'm just getting confused with what everything means.  Gen chem was so long ago and I've forgotten a great deal of what everything means!

Thanks so much!