19.5 g of fluoro acetic acid (molar mass = 78 g mol^ -1 ) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was 1°C. What is K_a of fluoro acetic acid? (For water, K_f = 1.86 K kg mol^ -1 ). Assume molarity and molality to have same values.
D. 3 10^ -3
The molality of the solution is given by: m = Mass of solute Molar mass of solute Mass of solvent in kg m = 19.5 78 0.5 = 0.5 mol kg ^ -1 The depression in freezing point is given by: T_f = i K_f m Substituting the given values: 1 = i 1.86 0.5 1 = i 0.93 i = 1 0.93 = 100 93 For the dissociation of a weak acid HA H^+ + A^-, the van 't Hoff factor is i = 1 + , where is the degree of dissociation. 1 + = 100 93 = 100 93 - 1 = 7 93 The acid dissociation constant K_a is given by: K_a = C ^2 1 - Since molarity and molality have the same values, C = 0.5 M . K_a = 0.5 ( 7 93 )^2 1 - 7 93 K_a = 0.5 49 93^2 86 93 = 0.5 49 93 86 K_a = 24.5 7998 3.06 10^ -3 The closest value is 3 10^ -3 . Answer: 3 10^ -3
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