Question

Which solution has the lowest freezing point?

(1) 10. g of KI dissolved in 100. g of water
(2) 20. g of KI dissolved in 200. g of water
(3) 30. g of KI dissolved in 100. g of water
(4) 40. g of KI dissolved in 200. g of water

Answer 1

Answer: (3) 30 g of KI dissolved in 100 g of water

Explanation: Formula used for lowering in freezing point is,

`\Delta T_f=k_f* m`

or,

`\Delta T_f=k_f* \frac{w_(solute)}{M_(solute)* M_(solvent)\text{ (in kg)}}`

where,

`T_f` = change in freezing point

`k_f` = freezing point constant

m = molality

1) 10 g of KI dissolved in 100 g of water:

`\Delta T_f=1.86* (10)/(166* 0.1)=1.16^0C`

2) 20 g of KI dissolved in 200 g of water

`\Delta T_f=1.86* (20)/(166* 0.2)=1.12^0C`

3) 30 g of KI dissolved in 100 g of water

`\Delta T_f=1.86* (30)/(166* 0.1)=3.36^0C`

As the depression is maximum, the solution will have lowest freezing point.

4) 40 g of KI dissolved in 200 g of water

`\Delta T_f=1.86* (40)/(166* 0.2)=2.24^0C`

Answer 2

Correct Answer: Option 3 i.e. 30 g of KI dissolved in 100 g of water.

Reason:
Depression in freezing point is a colligative property and it is directly proportional to molality of solution.

Molality of solution is mathematically expressed as,
Molality =
`\frac{\text{Number of moles}}{\text{Weight of solvent (Kg)}}`

In case of option 1 and 2, molality of solution is 0.602 m. For option 3, molality of solution is 1.807 m, while in case of option 4, molality of solution is 1.205 m.

Thus, second solution (option 2) has highest concentration (in terms of molality). Hence, it will have lowest freezing point