Question

Blood is a buffered solution with pH values ranging from 7.35-7.45. The important components of blood that contribute to its buffering capacity are species derived from carbonic acid and phosphoric acid. This problem emphasizes the phosphoric acid component. ( there will be three species = H2PO4- , HPO4^2- , PO4^3-

Ka1 = 7.25 * 10^-3

Ka2 = 6.31 * 10^-8

Ka3 = 3.98 * 10^-13

1) Write the three equilibria that relate phosphoric acid with each of these species listed. (You should write three chemical equilibria, using chemical symbols, that all resemble the following.)

2)For a pH value of 7.40, calculate the following ratios (you may use relevant Ka values that are tabulated for 25C in Appendix D of your textbook):

[Species #1]/[Phosphoric Acid]

[Species #2] / [Phosphoric Acid]

[Species #3]/ [Phosphoric Acid]

3) Which forms of phosphoric acid are the most abundant and the least abundant in water at a pH of 7.40?

For question# 2 I got

a) 182161

b) 288803

c) 2.888

Answer 1

a.

H₃PO₄ = H₂PO₄^- + H⁺

H₂PO₄^- = HPO₄^2- + H⁺

HPO₄^2- = PO₄^3- + H⁺

b.

Ka1 = 7.25 * 10^-3     pKa1 = 2.14

Ka2 = 6.31 * 10^-8     pKa2 = 7.20

Ka3 = 3.98 * 10^-13    pKa3 = 12.40

From the buffer formula :

log([base]/[acid]) = pH – pKa

   log ([H₂PO₄^-]/[ H₃PO₄]) = pH – pKa1 = 7.40-2.14 = 5.26

   log ([HPO₄^2-]/[ H₂PO₄^-]) = pH – pKa2 = 7.40-7.20 = 0.20

   log ([PO₄^3-]/[ HPO₄^2-]) = pH – pKa3 = 7.40-12.40 = - 5.00

[H₂PO₄^-]/[ H₃PO₄] = 10^5.26 = 182 000 : 1

[HPO₄^2-]/[ H₂PO₄^-] = 10^0.20 = 1.58 : 1

[PO₄^3-]/[ HPO₄^2-] = 10^-5.00 = 1: 100 000

Thus

[HPO₄^2-]/[ H₃PO₄] = 182 000 x 1.58 = 284 000 : 1

[PO₄^3-] / [ H₃PO₄] = 182 000 x 1.58 /100 000 = 2.84

Your results are correct but keep only 3 significant figures. (as in Ka)

c. see the previous results:

HPO₄^2- is the most abundant

H₃PO₄ is the least abundant