Question

Which aqueous solution has a minimum freezing point?
A. $0.01M\text{ }NaCl.$
B. \[0.005\text{ }M\text{ }{{C}_{2}}{{H}_{5}}OH.\]
C. \[0.005\text{ }M\text{ }MgC{{l}_{2}}.\]
D. \[0.005\text{ }M\text{ }MgS{{O}_{4}}.\]

Answer 1

Hint: We know that the Van’t Hoff factor is defined as the ratio of moles of particles formed when a substance is dissolved to the moles of the substance by mass. The more the number of moles of solute the more will be the Van’t Hoff factor and more will be the value of the depression in the freezing point of the solvent.

Complete answer:
By recalling the Van’t Hoff factor $\left( i \right),$ which is the number of discrete ions formed in a solution from one formula unit of solute. The Van't Hoff factor also accounts for the effect of a solute on colligative properties such as, freezing point depression, boiling point elevation etc. The compound for which is maximum, will have the maximum depression in freezing point. Depression in freezing point is a colligative property of a solution i.e., it depends on the moles of solute irrespective of the nature of particles present in the solution. We need to calculate the value of the van't Hoff factor of the given compounds to check which has the maximum freezing point.
Whenever we add a solute to the solution, it lowers the original freezing point of the solution and this depression in freezing point can be calculated with the help pf below formula; \[\Delta {{T}_{f}}=i\times {{K}_{f}}\times m.\] Where $\Delta {{T}_{f}}$ is the freezing point depression, i is the Van’t Hoff factor, is the freezing constant and m is the molality. Van’t Hoff factor, it depends on the degree of association/dissociation of solute in the solution and the number of ions produced in the solution.
van’t Hoff factor, \[i=2\] for \[NaCl,\] so concentration \[=\text{ }0.02\] , which is maximum in the present case. Hence, $\Delta {{T}_{f}}$ is maximum or freezing point is minimum in \[0.01\text{ }M\text{ }NaCl.\]The aqueous solution of \[0.01M\text{ }NaCl\] has a minimum freezing point.

So, the correct answer is “Option A”.

Note:
 Remember that the colligative properties are the properties of a solution which solely depends on the number of particles of the solute and not on the type or nature of the solute. Freezing point of a solution is one such colligative property.