Question

The solution with lowest freezing point temperature:
A. $0.1\text{ }M\text{ MgC}{{\text{l}}_{2}}$
B. $0.1\text{ }M\text{ HCl}{{\text{O}}_{4}}$
C. $0.1\text{ }M\text{ N}{{\text{H}}_{4}}OH$
D. $0.1\text{ }M\text{ KOH}$
E. $0.1\text{ }M\text{ LiN}{{\text{O}}_{3}}$

Answer 1

Hint: By taking the Van't hoff factor as a reference we can find the solution for the above question. The relation between the Van't hoff factor and freezing point is inversely proportional. Using the above relation and the value of the Van't hoff factor choose the correct option from the above.

Complete step by step solution:
Van't hoff factor I is the number of particles formed in a solution from one formula unit of solute. This I is the property of the solute. If the solution is non-isolate that means it does not separate into ions in solution. For those the value of I is equal to 1.
For example sucrose solid can convert into sucrose liquid but the ions cannot separate in the solution.
If the solute is the strong electrolyte then the value of Van't hoff factor is more than 1 and for a weak electrolyte it may be less than one or can be equal to 1.
 We know that Van't hoff factor is inversely proportional to the freezing point. It means that the compound which is having the highest Van't hoff factor is having the lowest freezing point.
 From the above given options only magnesium chloride is having the highest Van't hoff factor which is equal to 3 and the rest of the compounds are having Van't hoff factor less than 3. Since the highest value of the Van't hoff factor is held by magnesium chloride, it is only having the lowest freezing point compared to the other given compounds.

Hence option (A) is the correct answer.

Note: The Van't hoff factor is the measure of the effect of the solute on the colligative properties like freezing point, boiling point elevation, relative lowering in vapor pressure and osmotic pressure etc. it is generally denoted by i. As the concentration of the solute increases the Van't hoff factor decreases. Since the concentration of all the compounds in the above options are the same and hence we didn’t consider the concentration in the above solution.