Question

Choose the aqueous solution below with the highest freezing point. These are all solutions of nonvolatile solutes and you should assume ideal van't Hoff factors where applicable.

0.25 m (NH4)3PO4

0.35 m K2CO3

0.45 m KCN

Answer 1

The depression in freezing point of the solution with the addition of compound X is calculated by the following formula: AT, = iK, xm .... (1) Here, K, is the molal freezing-point depression constant, i is Van't Hoff factor and m is the molality. The change in temperature, AT, is given by the following expression: AT, = T: -T; Here, T, is the freezing point of solution and T is the freezing point of pure water. The equation corresponding to the dissociation of (NH4), PO, is: (NH4), PO4(s) +3NH, (aq) +PO. (aq) The number of ions formed are two. In case of complete dissociation, Van't Hoff factor is equal to the number of ions formed. Substitute the values of K. Van't Hoff factor, and molality in equation (1) as shown below: AT, = iK, Xm = 4xK; x0.25 =1.00K, ΙΙ. The equation corresponding to the dissociation of K,CO, is: K,CO2 (s) +2K+ (aq) +0,- (aq) The number of ions formed are three. In case of complete dissociation, Van't Hoff factor is equal to the number of ions formed.

Substitute the values of K., Van't Hoff factor, and molality in equation (1) as shown below: AT; = iK, Xm = 4xK, 0.25 =1.00K, The equation corresponding to the dissociation of K,CO, is: K,CO2 (s) +2K+ (aq) + CO2?- (aq) The number of ions formed are three. In case of complete dissociation, Van't Hoff factor is equal to the number of ions formed. Substitute the values of K. Van't Hoff factor, and molality in equation (1) as shown below: AT, = iK, Xm = 3xK; 0.35 =1.05K, III. The equation corresponding to the dissociation of KCN is: KCNS) →K+ (aq) + CN- (aq) The number of ions formed are three. In case of complete dissociation, Van't Hoff factor is equal to the number of ions formed. Substitute the values of K;. Van't Hoff factor, and molality in equation (1) as shown below: AT, =1K, xm = 2 x K x0.45 =0.9K,

Lower the value of AT,, higher would be the freezing point of the solution. The freezing point is highest for KCN. Therefore, the correct option is (3).