Vapour pressure of a solvent is `17.5` mmHg while that of itsdilute solution is `17.45`. The mole fraction of the solvent is

Options

A. `0.997`
B. `0.075`
C. `17.48`
D. `1.05`

Answer

To find the mole fraction of the solvent in a dilute solution, we can use the formula for the decrease in vapor pressure. Here’s a step-by-step solution:

### Step 1: Understand the Given Values
We are given:
- Vapor pressure of the pure solvent, \( P_0 = 17.5 \, \text{mmHg} \)
- Vapor pressure of the dilute solution, \( P = 17.45 \, \text{mmHg} \)

### Step 2: Calculate the Decrease in Vapor Pressure
The decrease in vapor pressure (\( \Delta P \)) can be calculated as:
\[ \Delta P = P_0 - P \]
Substituting the values:
\[ \Delta P = 17.5 \, \text{mmHg} - 17.45 \, \text{mmHg} = 0.05 \, \text{mmHg} \]

### Step 3: Use Raoult's Law
According to Raoult's Law, the decrease in vapor pressure is related to the mole fraction of the solute (\( x_2 \)):
\[ \frac{\Delta P}{P_0} = x_2 \]
Substituting the values we found:
\[ \frac{0.05 \, \text{mmHg}}{17.5 \, \text{mmHg}} = x_2 \]

### Step 4: Calculate the Mole Fraction of the Solute
Now we calculate \( x_2 \):
\[ x_2 = \frac{0.05}{17.5} \approx 0.002857 \]

### Step 5: Calculate the Mole Fraction of the Solvent
The mole fraction of the solvent (\( x_1 \)) can be calculated using the relationship:
\[ x_1 = 1 - x_2 \]
Substituting the value of \( x_2 \):
\[ x_1 = 1 - 0.002857 \approx 0.997143 \]

### Final Answer
Thus, the mole fraction of the solvent is approximately:
\[ \boxed{0.997} \]