A solution of sucrose (molar mass =342) is prepared by dissolving 688.4 g in 1000 g of water. Calculate
The vapour pressure of solution at 293 K.

Options

A. `0.0229`
B. `0.4`
C. `0.5989`
D. `0.326`

Explanation

To calculate the vapor pressure of a solution of sucrose at 293 K, we will follow these steps:

### Step 1: Calculate the number of moles of sucrose.
The formula to calculate the number of moles is:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Given:
- Mass of sucrose = 688.4 g
- Molar mass of sucrose = 342 g/mol

\[ \text{Number of moles of sucrose} = \frac{688.4 \, \text{g}}{342 \, \text{g/mol}} \approx 2.01 \, \text{moles} \]

### Step 2: Calculate the number of moles of water.
Using the molar mass of water (approximately 18 g/mol):

\[ \text{Number of moles of water} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Step 3: Calculate the total number of moles in the solution.
\[ \text{Total moles} = \text{moles of sucrose} + \text{moles of water} = 2.01 + 55.56 \approx 57.57 \, \text{moles} \]

### Step 4: Calculate the mole fraction of water.
The mole fraction of water (\(X_{water}\)) is given by:

\[ X_{water} = \frac{\text{moles of water}}{\text{total moles}} = \frac{55.56}{57.57} \approx 0.965 \]

### Step 5: Calculate the vapor pressure of the solution.
Using Raoult's Law, the vapor pressure of the solution (\(P_{solution}\)) can be calculated as:

\[ P_{solution} = X_{water} \times P^0_{water} \]

Where \(P^0_{water}\) is the vapor pressure of pure water at 293 K, which is given as 23.756 mm Hg.

\[ P_{solution} = 0.965 \times 23.756 \approx 22.9 \, \text{mm Hg} \]

### Final Answer:
The vapor pressure of the sucrose solution at 293 K is approximately **22.9 mm Hg**.

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