If the vapour pressure of pure water at `25^@C` is 23.8 mmHg , then calculate the vapour pressure lowering caused by the addition of 100 g of sucrose (molecular mass = 342 g/mol) to 100 g of water

Options

A. 00.12 mmHg
B. 0.125 mmHg
C. 1.15 mmHg
D. 1.25 mmHg

Answer

To solve the problem of calculating the vapor pressure lowering caused by the addition of 100 g of sucrose to 100 g of water, we can follow these steps:

### Step 1: Calculate the moles of sucrose
The molecular mass of sucrose is given as 342 g/mol. We can calculate the number of moles of sucrose using the formula:

\[ \text{Moles of sucrose} = \frac{\text{mass of sucrose}}{\text{molar mass of sucrose}} = \frac{100 \, \text{g}}{342 \, \text{g/mol}} \approx 0.292 \, \text{mol} \]

### Step 2: Calculate the moles of water
The molar mass of water is approximately 18 g/mol. We can calculate the number of moles of water:

\[ \text{Moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}} = \frac{100 \, \text{g}}{18 \, \text{g/mol}} \approx 5.556 \, \text{mol} \]

### Step 3: Calculate the total moles in the solution
Now, we find the total number of moles in the solution:

\[ \text{Total moles} = \text{Moles of sucrose} + \text{Moles of water} = 0.292 \, \text{mol} + 5.556 \, \text{mol} \approx 5.848 \, \text{mol} \]

### Step 4: Calculate the mole fraction of sucrose
The mole fraction of sucrose (\(X_{sucrose}\)) can be calculated as follows:

\[ X_{sucrose} = \frac{\text{Moles of sucrose}}{\text{Total moles}} = \frac{0.292 \, \text{mol}}{5.848 \, \text{mol}} \approx 0.050 \]

### Step 5: Calculate the vapor pressure lowering
According to Raoult's Law, the vapor pressure lowering (\(\Delta P\)) can be calculated using the formula:

\[ \Delta P = P_0 \times X_{sucrose} \]

Where \(P_0\) is the vapor pressure of pure water at 25°C, which is given as 23.8 mmHg.

Substituting the values:

\[ \Delta P = 23.8 \, \text{mmHg} \times 0.050 \approx 1.19 \, \text{mmHg} \]

### Conclusion
The vapor pressure lowering caused by the addition of 100 g of sucrose to 100 g of water is approximately **1.19 mmHg**.

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