# Equivalence point

Discussion in 'MCAT Study Question Q&A' started by chiddler, 04.22.12.

1. ### chiddler

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I know equivalence point is pKa1 + pKa2 / 2

I don't remember why this is though. Can I please have a proof?

thanks.
2. ### pfaction

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Do you mean pI?

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I have never seen that equation before.
4. ### pfaction

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Amino acid pI. Zwitterionic point.
5. ### chiddler

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yes it does mean pI. but i meant equivalence point! is that incorrect?

i'm trying to translate this concept to, say, carbonic acid a diprotic buffer.

what does pKa1 + pKa2 / 2 tell us about carbonic acid? to help visualize, pKa 1 is 6.3, pKa2 is 10.3. both / 2 = 8.3
6. ### pfaction

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At 8.3, the molecule will be 100% HCO3-.
<6.3: majorly or all H2CO3.
Above 10.3: Majorly or all CO32-
7. ### chiddler

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there we go. it is the first equivalence point.

thanks.

wait, i still need proof lol
8. ### typicalindian

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better go make a trip to your nearest lab then
9. ### pfaction

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No, it's not the first equivalence point, that's H2CO3->HCO3- at 50/50. pH = pKa1 at that point. Equivalence point is when [H]=[OH].
10. ### chiddler

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when it's 50/50, then it's pH = pKa1 which is 6.3. we're looking at 8.3.

equivalence point is when you add one equivalent of base to the acid. since carbonic acid is weak, it becomes slightly basic which is observed with 8.3.
11. ### chiddler

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oh man. i have to break in again?!

12. ### pfaction

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You know I think you're right, I may have been translating a monoprotic acid into diprotic acid.
13. ### typicalindian

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Rookie mistake. My PI likes me enough to give me the keys to our lab and 24/7 access ID badge
14. ### chiddler

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i am so jealous! you get to go to lab at NIGHT?

all the fun i'm missing out on! *swoon*
15. ### typicalindian

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16. ### chiddler

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lol
17. ### rjosh33

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The pH of the equivalence point between the pKa1 and pKa2 of a diprotic acid is actually computed from a pretty complicated formula:

[H+] = [(Ka1Ka2F x Ka1Kw) / Ka1 + F]^1/2

You need to know the starting concentration of the acid as well as the base (in order to get the formal concentration, F) along with the Ka's (both 1 and 2) and the water dissociation constant.

Was a problem asking you for the pH at the equivalence point of a diprotic acid??
18. ### SaintJude

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Ok, so,

So pH of the 1st equivalence point = pKa1 + pKa2 / 2 . And this equals the pI for an amino acid that has a neutral R group, yeah?
19. ### chiddler

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no i was just trying to find a better way of remembering the equation. i thought understanding its derivation would help.

if it is indeed this complicated, then thanks and nevermind. i must have remembered incorrectly that i had known the proof before.

for acidic amino acids. for basics, it is pKa2 + pKa3 / 2.

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Ah, well I know absolutely nothing about that. Glad I wasn't just forgetting something...
21. ### rjosh33

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Nm
Last edited: 04.22.12
22. ### rjosh33

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Ok, I just went back and looked it up, and you're right. Turns out the equation I wrote earlier can be further simplified to what you said, pH = pKa1 + pKa2 / 2. Sorry about the confusion.
23. ### chiddler

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that equation is complicated enough that it won't really help, anyway.

is ok. thanks for the responses. discussion about the equation will have helped memorizing it so i'm satisfied.