Question

25.6g of sulphur in 100g benzene shows depression in freezing point of $5.12{}^\circ \text{C}$. ${{\text{K}}_{\text{f}}}$ for benzene is $5.12{}^\circ \text{C kg mo}{{\text{l}}^{-1}}$. The molecular formula of sulphur in benzene is:
A. ${{\text{S}}_{2}}$
B. ${{\text{S}}_{6}}$
C. ${{\text{S}}_{8}}$
D. ${{\text{S}}_{12}}$

Answer 1

Hint: Depression in freezing point is a colligative property because it depends on the number of solutes and has a formula $\Delta {{\text{T}}_{\text{f}}}\text{ = }{{\text{K}}_{\text{f}}}\text{ }\times \text{ m}$. Here, $\Delta {{\text{T}}_{\text{f}}}$ is the depression in the freezing point, m is the molality which is the ratio of no. of moles of solute to the volume of solvent in kg. ${{\text{K}}_{\text{f}}}$ is a constant known as Cryoscopic constant.

Complete answer:
In the question, it is given that the depression or decrease in the freezing point is $5.12{}^\circ \text{C}$ and the value of the cryoscopic constant is $5.12{}^\circ \text{C}$ $\text{Kg mo}{{\text{l}}^{-1}}$.
The formula of molality will be:

$\text{Molality = }\dfrac{\text{Mass of the solute }\times \text{ 1000}}{\text{Molar mass of solute }\times \text{ volume of solvent(g)}}$

Here, it is given that the mass of solute is 25.6g, the molar mass is unknown, the volume of solvent is given 100g.

So, molality will be: $\text{Molality = }\dfrac{\text{25}\text{.6 }\times \text{ 1000}}{\text{M }\times \text{ 100}}\text{ }.....\text{(1)}$

Now, we know that the formula of depression in freezing point is $\Delta {{\text{T}}_{\text{f}}}\text{ = }{{\text{K}}_{\text{f}}}\text{ }\times \text{ m }....\text{(2)}$
So, by putting the value of molality from equation 1 into equation 2 we will get,

$\text{5}\text{.12 = }\dfrac{\text{5}\text{.12 }\times \text{ 25}\text{.6 }\times \text{ 1000}}{\text{M }\times \text{ 100}}$

M = 256 g/mol.
So, the molar mass of the compound is 256 but we know that the atomic mass of sulphur is 32g.
Now, let the molecular formula of sulphur is ${{\text{S}}_{8}}$. The molecular mass will be:
$32\text{ }\times \text{ x = 256}$
x = 8
So the sulphur exists as $S_8$ in benzene.

Therefore, option C is the correct answer.

Note: At freezing point, the presence of both solid and liquid state is observed at equilibrium. So, the vapour pressure of the liquid and solid is equal, which results in the decrease in the freezing point. Freezing point depends on the volume of solvent as it is inversely proportional to it and directly proportional to the molality.