# Equivalence point

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#### chiddler

##### Full Member
10+ Year Member
I know equivalence point is pKa1 + pKa2 / 2

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

thanks.

#### pfaction

10+ Year Member
Do you mean pI?

##### MD
Moderator Emeritus
10+ Year Member
I have never seen that equation before.

#### pfaction

##### Full Member
10+ Year Member
I have never seen that equation before.

Amino acid pI. Zwitterionic point.

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#### chiddler

##### Full Member
10+ Year Member
Do you mean pI?

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

#### pfaction

##### Full Member
10+ Year Member
At 8.3, the molecule will be 100% HCO3-.
<6.3: majorly or all H2CO3.
Above 10.3: Majorly or all CO32-

#### chiddler

##### Full Member
10+ Year Member
At 8.3, the molecule will be 100% HCO3-.
<6.3: majorly or all H2CO3.
Above 10.3: Majorly or all CO32-

there we go. it is the first equivalence point.

thanks.

wait, i still need proof lol

#### typicalindian

##### Full Member
10+ Year Member
there we go. it is the first equivalence point.

thanks.

wait, i still need proof lol

better go make a trip to your nearest lab then

#### pfaction

##### Full Member
10+ Year Member
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].

#### chiddler

##### Full Member
10+ Year Member
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].

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.

#### chiddler

##### Full Member
10+ Year Member
better go make a trip to your nearest lab then

oh man. i have to break in again?!

#### pfaction

##### Full Member
10+ Year Member
You know I think you're right, I may have been translating a monoprotic acid into diprotic acid.

#### typicalindian

##### Full Member
10+ Year Member
oh man. i have to break in again?!

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

#### chiddler

##### Full Member
10+ Year Member
Rookie mistake. My PI likes me enough to give me the keys to our lab and 24/7 access ID badge

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

all the fun i'm missing out on! *swoon*

#### typicalindian

##### Full Member
10+ Year Member
i am so jealous! you get to go to lab at NIGHT?

all the fun i'm missing out on! *swoon*

10+ Year Member
lol

#### rjosh33

##### Full Member
10+ Year Member
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??

#### SaintJude

##### Full Member
10+ Year Member
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?

#### chiddler

##### Full Member
10+ Year Member
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??

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.

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?

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

##### MD
Moderator Emeritus
10+ Year Member
Amino acid pI. Zwitterionic point.
Ah, well I know absolutely nothing about that. Glad I wasn't just forgetting something...

10+ Year Member
Nm

Last edited:

#### rjosh33

##### Full Member
10+ Year Member
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.

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.

#### chiddler

##### Full Member
10+ Year Member
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.