pKa values, determining pH?

[orangeblossom]

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Question from examkrackers, simulated test #1H

Based on the pKa values for phosphoric acid given below, what would be the approximate pH of a 1.0 M solution of NaH2PO4?

pKa1 = 2.16
pKa2 = 7.21
pKa3 = 12.32

(a) 3.6
(b) 7.0
(c) 7.2
(d) 11.8

Answer is (a)

So, for H2PO4-, i get that as an acid, pKa is 7.21, and as a base, pKb = 11.84 (14-2.16). However how do you know that, based on those values, H2PO4- is a better acid than a base? (i'm paraphrasing the EK explanations.)

 

[Postictal Raiden]

Question from examkrackers, simulated test #1H

Based on the pKa values for phosphoric acid given below, what would be the approximate pH of a 1.0 M solution of NaH2PO4?

pKa1 = 2.16
pKa2 = 7.21
pKa3 = 12.32

(a) 3.6
(b) 7.0
(c) 7.2
(d) 11.8

Answer is (a)

So, for H2PO4-, i get that as an acid, pKa is 7.21, and as a base, pKb = 11.84 (14-2.16). However how do you know that, based on those values, H2PO4- is a better acid than a base? (i'm paraphrasing the EK explanations.)

At pKa2, [H2PO4-] = [HPO4 2-]

[HPO4 2-][H+]/[H2PO4-] = 10^-7.21

x^2/1-x = 10^-7.21, and here we assume that x<<<1, so x^2=10^-7.2

x = [H+] = 2.5x10^-4

pH = -log(2.5x10^-4) = 3.6

 

[orangeblossom]

oh, I see now. But EK says not to work out the calculation. the explanation says that, based on 7.21 and 11.84 values, you should realize that H2PO4- is a better acid than base.

Not sure how that reasoning works though.

 

[Postictal Raiden]

oh, I see now. But EK says not to work out the calculation. the explanation says that, based on 7.21 and 11.84 values, you should realize that H2PO4- is a better acid than base.

Not sure how that reasoning works though.

The only way I could reason it and get the right answer is by looking at pKa2 and noticing that it's slightly basic. Which means after loosing half of H+ from H2PO4-, the pH barely becomes basic. That indicates that the pH of H2PO4- is well below 7. The only option fits the bill is option A.

However, if, for example, 4.5 was an option, doing the calculation becomes inevitable.

 

[BB8730]

oh, I see now. But EK says not to work out the calculation. the explanation says that, based on 7.21 and 11.84 values, you should realize that H2PO4- is a better acid than base.

Not sure how that reasoning works though.

The strength of an acid is defined by how well it dissociates into H+. A higher Ka value or a lower pKa value means that it dissociates better into H+, making it a stronger acid. The same thing goes for Kb and pKb. A higher Kb or lower pKb means it acts as a stronger base. With a lower pKa than pKb, you know it acts better as an acid and the pH of the solution will be less than 7.