Dry air was passed successively through a solution of 5 g of a solutte in 80 g of water and then through pure water. The loss in mass of solution was 2.5 g and that of pure solvent was 0.04 g The molecular mass of the solute is :

Options

A. 70.31
B. 3.125
C. 312.5
D. none of these

Answer

To solve the problem, we need to find the molecular mass of the solute based on the given data. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Given Data
- Mass of solute (W_solute) = 5 g
- Mass of solvent (W_solvent) = 80 g
- Loss in mass of solution (ΔW_solution) = 2.5 g
- Loss in mass of pure solvent (ΔW_solvent) = 0.04 g

### Step 2: Understand the Concept of Vapor Pressure Lowering
The vapor pressure lowering can be described by the formula:
\[ \frac{P_0 - P_s}{P_0} = x_{\text{solute}} \]
Where:
- \(P_0\) = vapor pressure of pure solvent
- \(P_s\) = vapor pressure of the solution
- \(x_{\text{solute}}\) = mole fraction of the solute

### Step 3: Relate Loss of Mass to Mole Fraction
The loss in mass of the solution is proportional to the vapor pressure lowering, and the loss in mass of pure solvent is proportional to the vapor pressure of the solvent.

From the problem:
\[ \frac{P_0 - P_s}{P_s} = \frac{\Delta W_{\text{solvent}}}{\Delta W_{\text{solution}}} \]
Substituting the values:
\[ \frac{0.04}{2.5} \]

### Step 4: Calculate the Ratio
Calculating the ratio:
\[ \frac{0.04}{2.5} = 0.016 \]

### Step 5: Set Up the Mole Fraction Equation
Using the mole fraction definition:
\[ \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}} = 0.016 \]
Where:
- \(n_{\text{solute}} = \frac{W_{\text{solute}}}{M_{\text{solute}}}\)
- \(n_{\text{solvent}} = \frac{W_{\text{solvent}}}{M_{\text{solvent}}}\)

Given that the molar mass of water (solvent) is 18 g/mol, we can express \(n_{\text{solvent}}\):
\[ n_{\text{solvent}} = \frac{80}{18} \]

### Step 6: Substitute into the Mole Fraction Equation
Substituting \(n_{\text{solute}}\) and \(n_{\text{solvent}}\) into the equation:
\[ \frac{\frac{5}{M_{\text{solute}}}}{\frac{5}{M_{\text{solute}}} + \frac{80}{18}} = 0.016 \]

### Step 7: Cross Multiply and Solve for M_solute
Cross multiplying gives:
\[ \frac{5}{M_{\text{solute}}} = 0.016 \left(\frac{5}{M_{\text{solute}}} + \frac{80}{18}\right) \]
Expanding and simplifying:
\[ 5 = 0.016 \cdot 5 + 0.016 \cdot \frac{80}{18} M_{\text{solute}} \]
\[ 5 = 0.08 + \frac{1.28}{M_{\text{solute}}} \]
Rearranging gives:
\[ 5 - 0.08 = \frac{1.28}{M_{\text{solute}}} \]
\[ 4.92 = \frac{1.28}{M_{\text{solute}}} \]
Thus:
\[ M_{\text{solute}} = \frac{1.28}{4.92} \]
Calculating gives:
\[ M_{\text{solute}} \approx 0.260 g/mol \]

### Final Answer
The molecular mass of the solute is approximately **0.260 g/mol**.