For a solution containing non-volatile solute, the relative lowering of vapour pressure is 0.2. If the solution contains 5 moles in all, which of the following are true ?
I. Mole fraction of solute in the solution is 0.2
II. No. of moles of solute in the solution is 0.2
III. No. of moles of solvent in the solution is 4
IV. Mole fraction of solvent is 0.2 -

Options

A. I, IV
B. II, III
C. I, III
D. II, IV

Answer

To solve the problem, we need to analyze the information given about the solution containing a non-volatile solute and the relative lowering of vapor pressure.

### Step 1: Understand the Concept of Relative Lowering of Vapor Pressure
The relative lowering of vapor pressure (RLVP) for a solution containing a non-volatile solute is given by:
\[ \text{RLVP} = \frac{P_0 - P}{P_0} = x_B \]
where \( P_0 \) is the vapor pressure of the pure solvent, \( P \) is the vapor pressure of the solution, and \( x_B \) is the mole fraction of the solute.

Given that RLVP = 0.2, we have:
\[ x_B = 0.2 \]

### Step 2: Calculate the Mole Fraction of Solvent
Since the sum of the mole fractions of solute and solvent must equal 1, we can find the mole fraction of the solvent \( x_A \):
\[ x_A = 1 - x_B = 1 - 0.2 = 0.8 \]

### Step 3: Determine the Total Moles in the Solution
We know that the total number of moles in the solution is given as 5 moles:
\[ n_A + n_B = 5 \]
where \( n_A \) is the number of moles of solvent and \( n_B \) is the number of moles of solute.

### Step 4: Calculate the Number of Moles of Solute
Using the mole fraction of the solute, we can express it in terms of the total moles:
\[ x_B = \frac{n_B}{n_A + n_B} = \frac{n_B}{5} \]
Substituting \( x_B = 0.2 \):
\[ 0.2 = \frac{n_B}{5} \]
Multiplying both sides by 5:
\[ n_B = 0.2 \times 5 = 1 \]

### Step 5: Calculate the Number of Moles of Solvent
Now, we can find the number of moles of solvent \( n_A \):
\[ n_A = 5 - n_B = 5 - 1 = 4 \]

### Step 6: Verify the Mole Fraction of Solvent
We can calculate the mole fraction of the solvent to verify:
\[ x_A = \frac{n_A}{n_A + n_B} = \frac{4}{5} = 0.8 \]

### Conclusion
From our calculations, we have:
- Mole fraction of solute \( x_B = 0.2 \) (True)
- Number of moles of solute \( n_B = 1 \) (False)
- Number of moles of solvent \( n_A = 4 \) (True)
- Mole fraction of solvent \( x_A = 0.8 \) (False)

Thus, the true statements are:
- I. Mole fraction of solute in the solution is 0.2 (True)
- II. No. of moles of solute in the solution is 0.2 (False)
- III. No. of moles of solvent in the solution is 4 (True)
- IV. Mole fraction of solvent is 0.2 (False)

### Final Answer
The correct options are I and III.