Determine the fraction of each of the 3 forms of malonic acid, H2M, HM-, and M2-, that exists in aqueous solutions of the following pH values. a) 2.000 b) 2.847 c) 4.000 d) 5.696 e) 6.000
a) pH = 2
[H+] = 0.01
Ka1 = [HM-][H+]/[H2M]
1.51 x 10^-3 = (0.01)^2/[H2M]
[H2M] = 0.066 M
Ka2 = [M^2-][H+]/[HM-]
2 x 10^-6 = x^2/(0.01)
[M^2-] = 1.41 x 10^-4 M
[HM-] = 0.01 M
b) pH = 2.847
[H+] = 1.42 x 10^-3 M
Ka1 = [HM-][H+]/[H2M]
1.51 x 10^-3 = (1.42 x 10^-3)^2/[H2M]
[H2M] = 1.33 x 10^-3 M
Ka2 = [M^2-][H+]/[HM-]
2 x 10^-6 = x^2/(1.42 x 10^-3)
[M^2-] = 5.33 x 10^-5 M
[HM-] = 1.47 x 10^-3 M
c) pH = 4
[H+] = 1 x 10^-4 M
Ka1 = [HM-][H+]/[H2M]
1.51 x 10^-3 = (1.0 x 10^-4)^2/[H2M]
[H2M] = 6.62 x 10^-6 M
Ka2 = [M^2-][H+]/[HM-]
2 x 10^-6 = x^2/(1 x 10^-4
[M^2-] = 1.41 x 10^-5 M
[HM-] = 1.14 x 10^-4 M
d) pH = 5.696
[H+] = 2.01 x 10^-6 M
Ka1 = [HM-][H+]/[H2M]
1.51 x 10^-3 = (2.01 x 10^-6)^2/[H2M]
[H2M] = 2.68 x 10^-9 M
Ka2 = [M^2-][H+]/[HM-]
2 x 10^-6 = x^2/(2.01 x 10^-6)
[M^2-] = 2.00 x 10^-6 M
[HM-] = 4.01 x 10^-6 M
e) pH = 6
[H+] = 1 x 10^-6 M
Ka1 = [HM-][H+]/[H2M]
1.51 x 10^-3 = (1 x 10^-6)^2/[H2M]
[H2M] = 6.62 x 10^-10 M
Ka2 = [M^2-][H+]/[HM-]
2 x 10^-6 = x^2/(1 x 10^-6)
[M^2-] = 1.41 x 10^-6 M
[HM-] = 2.41 x 10^-6 M
Determine the fraction of each of the 3 forms of malonic acid, H2M, HM-, and M2-,...
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