A set of solutions is prepared using 180 g of water as a solvent and 10 g of different non-electrolyte and non-volatile solutes A,B and C. What is the correct order of relative lowering of vapour pressure? (Given: molar mass of A = 100 g/mol, B = 200 g/mol, C = 10000 g/mol respectively)

A>B>C

The correct answer is option 1. A>B>C.

The relative lowering of vapor pressure (\( \pi \)) for a dilute solution is given by:

\(\pi = \frac{{\Delta P}}{{P_0}} = \frac{{n_1}}{{n_1 + n_2}} \)

Where:

\( \Delta P \) is the lowering of vapor pressure,

\( P_0 \) is the vapor pressure of the pure solvent,

\( n_1 \) and \( n_2 \) are the number of moles of solvent and solute respectively.

The number of moles of solute can be calculated using the given mass and molar mass of each solute:

\(n_2 = \frac{{\text{Mass of solute}}}{{\text{Molar mass of solute}}} \)

Given:

Mass of water (solvent) = 180 g

Mass of solute:

For solute A = 10 g

For solute B = 10 g

For solute C = 10 g

Molar mass of solute:

For solute A = 100 g/mol

For solute B = 200 g/mol

For solute C = 10000 g/mol

Let is calculate the number of moles of solute for each case:

For solute A:

\( n_2^A = \frac{{10 \, \text{g}}}{{100 \, \text{g/mol}}} = 0.1 \, \text{mol} \)

For solute B:

\( n_2^B = \frac{{10 \, \text{g}}}{{200 \, \text{g/mol}}} = 0.05 \, \text{mol} \)

For solute C:

\(n_2^C = \frac{{10 \, \text{g}}}{{10000 \, \text{g/mol}}} = 0.001 \, \text{mol} \)

Now, let's calculate the relative lowering of vapor pressure for each case:

For solute A:

\( \pi^A = \frac{{n_2^A}}{{n_1 + n_2^A}} = \frac{{0.1}}{{0.1 + 180}} \)

For solute B:

\(\pi^B = \frac{{n_2^B}}{{n_1 + n_2^B}} = \frac{{0.05}}{{0.05 + 180}} \)

For solute C:

\(\pi^C = \frac{{n_2^C}}{{n_1 + n_2^C}} = \frac{{0.001}}{{0.001 + 180}} \)

Comparing the values of \( \pi \) for solutes A, B, and C, we can determine the correct order of relative lowering of vapor pressure. The solute with the highest value of \( \pi \) will have the highest relative lowering of vapor pressure.

By comparing the values, we find: \(\pi^A > \pi^B > \pi^C \)

So, the correct order of relative lowering of vapor pressure is: A > B > C