Tartaric acid is a weak organic acid that occurs naturally in many plants (parti

Question

Tartaric acid is a weak organic acid that occurs naturally in many plants (particularly grapes). It is diprotic, which means that it has two ionizable hydrogen atoms. The two hydrogen atoms ionize according to the scheme:

AH2(aq) + H2O(l) -> AH(aq) + H3O+(aq)           Kc = 2.3x105

AH(aq) + H2O(l) -> A2(aq) + H3O+(aq)             Kc = 1.2x106

Where AH2 is the unionized acid, AH has lost one ionizable proton, and A2 has lost both ionizable protons. If 1 mole of tartaric acid is dissolved in 2 L of water, what will be the concentration of the fully ionized acid when equilibrium has been established?

            a)         2.9x105 M

*          b)         1.9x104 M ( the correct answer, but i don't know why)

            c)         8.9x104 M

            d)         5.8x105 M

            e)         2.6x103 M

Explanation / Answer

Molarity of AH2 = 1mol/2L = 0.5 M

AH2 <==> AH+ + H+

Ka1 = [AH+][H+]/[AH2]

or, 2.3 *10^-5 = x*x/0.5-x

as tartaric acid is weak acid , only a small amount will be ionized x is small. So, 0.5-x~0.5

x = 3.39*10^-3 M

[AH+] = 3.39*10^-3 M

Now consider the ionization of AH+

AH+ <==> A^2+ + H+

Kc = [A^2-][H+]/[AH+]

or, 1.2*10^-6 = x^2/3.39*10^-3 -x

or, 4.07*10^-9 -1.2x*10^-6 -x^2 = 0

or, x = 6.38*10^-5 M

[A^2-] = 6.38*10^-5 M

or, x =

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