The relative lowering of vapour pressure produced by dissolving 71.5 g of a substance in 1000 g of water is 0.00713. The molecular mass of the substance will be:

Options

A. 18.0 g/mol
B. 342 g/mol
C. 60 g/mol
D. 180 g/mol

Answer

To find the molecular mass of the substance, we can use the information given in the problem along with Raoult's law. Here’s a step-by-step solution:

### Step 1: Understand the Concept
According to Raoult's law, the relative lowering of vapor pressure (ΔP/P0) is equal to the mole fraction of the solute (X_solute).

### Step 2: Set Up the Equation
We are given the relative lowering of vapor pressure:
\[ \Delta P/P_0 = 0.00713 \]
This means:
\[ X_{solute} = 0.00713 \]

### Step 3: Calculate the Mole Fraction of the Solvent
The mole fraction of the solvent (X_solvent) can be calculated as:
\[ X_{solvent} = 1 - X_{solute} = 1 - 0.00713 = 0.99287 \]

### Step 4: Relate Mole Fraction to Moles
The mole fraction of the solvent is also defined as:
\[ X_{solvent} = \frac{n_{solvent}}{n_{solvent} + n_{solute}} \]
Where:
- \(n_{solvent}\) is the number of moles of the solvent (water).
- \(n_{solute}\) is the number of moles of the solute.

### Step 5: Calculate Moles of Solvent
The number of moles of water can be calculated using its mass and molecular weight:
\[ n_{solvent} = \frac{mass_{water}}{molar\ mass_{water}} = \frac{1000\ g}{18\ g/mol} = 55.56\ mol \]

### Step 6: Set Up the Equation with Moles
Now substituting the values into the mole fraction equation:
\[ 0.99287 = \frac{55.56}{55.56 + n_{solute}} \]

### Step 7: Rearranging the Equation
Cross-multiplying gives:
\[ 0.99287(55.56 + n_{solute}) = 55.56 \]
Expanding this:
\[ 55.56 \times 0.99287 + 0.99287 \times n_{solute} = 55.56 \]
Calculating \(55.56 \times 0.99287\):
\[ 55.06 + 0.99287 \times n_{solute} = 55.56 \]
Now, isolate \(n_{solute}\):
\[ 0.99287 \times n_{solute} = 55.56 - 55.06 = 0.50 \]
\[ n_{solute} = \frac{0.50}{0.99287} \approx 0.504\ mol \]

### Step 8: Calculate the Molecular Mass of the Solute
Now we can find the molecular mass (M) of the solute using the formula:
\[ M = \frac{mass_{solute}}{n_{solute}} = \frac{71.5\ g}{0.504\ mol} \approx 141.67\ g/mol \]

### Step 9: Conclusion
The molecular mass of the substance is approximately 141.67 g/mol.