The vapour pressure of a solution can be determined using Raoult’s Law. This law posits that the vapour pressure of the solvent within a solution is directly proportional to its mole fraction. The formula is given by:
\[
P = P_0 \times X_{\text{solvent}}
\]
Where:
- \( P_0 = 32.8 \, \text{mm Hg} \) represents the vapour pressure of pure water.
- \( X_{\text{solvent}} \) denotes the mole fraction of water in the solution.
To calculate the vapour pressure of the solution, follow these steps:
Step 1: Determine the moles of glucose.
\[
\text{Moles of glucose} = \frac{2}{180} = 0.0111 \, \text{mol}
\]
Step 2: Calculate the moles of water.
\[
\text{Moles of water} = \frac{100}{18} = 5.56 \, \text{mol}
\]
Step 3: Compute the mole fraction of water.
\[
X_{\text{water}} = \frac{\text{moles of water}}{\text{moles of water} + \text{moles of glucose}} = \frac{5.56}{5.56 + 0.0111} = 0.998
\]
Step 4: Calculate the vapour pressure of the solution.
\[
P = 32.8 \times 0.998 = 32.734 \, \text{mm Hg}
\]
Consequently, the vapour pressure of the solution is 32.734 mm Hg.