Question

Which of the following aqueous solution have the highest freezing point:
(A) 0.1 m sucrose
(B) 0.01 m NaCl
(C) 0.1 m NaCl
(D) 0.01 m \[N{{a}_{2}}S{{O}_{4}}\]

Answer 1

Hint: Freezing point is the temperature at which the liquid state of a substance turns into a solid state when it is cooled. The freezing point of the solution depends on the van't hoff factor of the solution. The freezing point of the solution also depends on the depression in freezing point. The formula for depression in freezing point is \[mRT\times i\]

Complete step by step solution:
The freezing point of the solution depends on the depression in freezing point and van't hoff factor. Higher the freezing point of the solution lower is the depression in freezing point. So in case of sucrose the van't hoff factor is 1 so its depression in freezing point will be 0.1. So in case of NaCl the ions will get dissociate by following equation
\[N{{a}_{2}}S{{O}_{4}}2N{{a}^{+}}+S{{O}_{4}}^{2-}\]
The ions in them is 2. So the depression in freezing point is 0.02. So in case of option c the ions will get dissociate by following equation
\[NaClN{{a}^{+}}+C{{l}^{-}}\]. The ions in them is 2. So the depression in freezing point is 0.2. so in case of option d the ions will get dissociate by following equation
\[N{{a}_{2}}S{{O}_{4}}2N{{a}^{+}}+S{{O}_{4}}^{2-}\]
Here the total number of ions is 3. So the depression in freezing point is 0.003.
So here the lowest depression in freezing point has sucrose, hence it will have the highest freezing point.

So the correct option for this question is option A.

Note: Students should remember the concept of van't hoff factor. They should show the dissociation equations. The definition of depression in freezing point should be learnt. The freezing point of the solution is always less than the freezing point of the pure solvent. The depression in freezing point will always be negative because the temperature of the solution is lower than that of the pure solvent.