Polyprotic acids contain more than one dissociable proton. Each dissociation ste

Question

Polyprotic acids contain more than one dissociable proton. Each dissociation step has its own acid dissociation constant, K_a1, K_a2, etc. For example, a diprotic acd H_2 A reacts as follows: H_2A(aq) + H_2O(1) H_3O^+(aq) + HA^-(aq) K_a1 = [H_3O^+][HA^-]/[H_2A] HA^-(aq) + H_2O(1) H_3O^+(aq) + A^2-(aq) K_a2 = [H_3O^+][A^2-]/[HA^-] Calculate the equilibrium concentration of H_3O+ in a 0.40 M solution of carbonic acid. Express your answer to two significant figures and include the appropriate units. Calculate the equilibrium concentration of CO_3^2- in a 0.40 M solution of carbonic acid. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

we first find [HCO3-] using Ka1

H2CO3 (aq) + H2O (l) <--> H3O+ (aq) + HCO3- (aq)

Ka1 = [H3O+] [HCO3-] / [ H2CO3]

4.3 x 10^ -7 = X^2 / ( 0.4-X)

X = 4.145 x 10^ -4 = [HCO3-]

now we have 2nd dissociation eq

HCO3- (aq) + H2O (l) <---> CO3^2- (aq) + H3O + (aq)

at equilibrium [HCO3-] = 0.0004145-x   , [CO3^2--] = [H3O+] = X

Ka2 = [CO3^2-] [H3O+] /[ HCO3-]

4.8 x 10^-11 = X^2 / ( 0.0004145 - X)

X = 1.4 x 10^-7 M = [CO3^2-]

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