The vapour pressure of a dilute aqueous solution of glucose is 750 mm of mercury at 373 K . The mole fraction of solute is :

Options

A. `(1)/(10)`
B. `(1)/(7.6)`
C. `(1)/(35)`
D. `(1)/(76)`

Answer

To find the mole fraction of the solute (glucose) in a dilute aqueous solution given the vapor pressure, we can follow these steps:

### Step 1: Understand the given data
- The vapor pressure of the solution (P) = 750 mmHg
- The vapor pressure of pure water (P₀) at 373 K = 760 mmHg

### Step 2: Use Raoult's Law
According to Raoult's Law, the relationship between the vapor pressures and the mole fractions is given by:

\[ \frac{P_0 - P}{P_0} = X_{solute} \]

where:
- \( P_0 \) = vapor pressure of the pure solvent (water)
- \( P \) = vapor pressure of the solution
- \( X_{solute} \) = mole fraction of the solute

### Step 3: Substitute the values into the equation
Substituting the values we have:

\[ \frac{760 \, \text{mmHg} - 750 \, \text{mmHg}}{760 \, \text{mmHg}} = X_{solute} \]

### Step 4: Calculate the difference in vapor pressures
Calculate \( P_0 - P \):

\[ 760 \, \text{mmHg} - 750 \, \text{mmHg} = 10 \, \text{mmHg} \]

### Step 5: Substitute back into the equation
Now, substitute this back into the equation:

\[ \frac{10 \, \text{mmHg}}{760 \, \text{mmHg}} = X_{solute} \]

### Step 6: Simplify the fraction
Now simplify the fraction:

\[ X_{solute} = \frac{10}{760} \]

### Step 7: Further simplify the fraction
This can be simplified further:

\[ X_{solute} = \frac{1}{76} \]

### Final Answer
Thus, the mole fraction of the solute (glucose) is:

\[ X_{solute} = \frac{1}{76} \]