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 = 2.3x105AH(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?

Explanation / Answer

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

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

Over all reaction,

AH2(aq) + 2 H2O(l) A2(aq) + 2 H3O+(aq), K = ?

0.500 M                       0.000            0.000                    initial

0.500 - x                        x                   2x                      equilibrium

K = Kc1 * Kc2 = 2.3 * 10-5 * 1.2*10-6 = 2.76 * 10-11

And K = [A2-][H3O+]2/[AH2]

2.76 * 10-11 = (x)(2x)2 / (0.500 - x)

SInce, K is too small, 0.500 - x is approximately equal to 0.500

SO,

2.76 * 10-11 = 4x3 / 0.500

4x3 = 1.38 * 10-11

x3 = 3.45 * 10-12

x = 1.51 * 10-4 M

Therefore, concentration of A2- = 1.51 * 10-4M and [H3O+] = 2 * 1.51 * 10-4 = 3.02 * 10-4 M

Now, [H2A] = 0.500 - 0.000151 = 0.49985 M

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