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Assuming very dilute aqueous solution of...

Assuming very dilute aqueous solution of urea, calculate the vapour pressure of solution ( in mm of Hg ) of 0.1 moles of urea in 180 grams of water at `25^(@)C` in ( The vapour pressure of water at `25^(@)C` is 24 mm Hg )

A

2.376

B

20.76

C

23.76

D

24.76

Text Solution

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The correct Answer is:
To calculate the vapor pressure of a dilute aqueous solution of urea, we can follow these steps: ### Step 1: Identify the given data - Moles of urea (solute) = 0.1 moles - Mass of water (solvent) = 180 grams - Vapor pressure of pure water at 25°C (P₀) = 24 mm Hg ### Step 2: Calculate the number of moles of water To find the number of moles of water, we use the formula: \[ \text{Number of moles of water} = \frac{\text{mass of water (g)}}{\text{molar mass of water (g/mol)}} \] The molar mass of water (H₂O) is approximately 18 g/mol. \[ \text{Number of moles of water} = \frac{180 \text{ g}}{18 \text{ g/mol}} = 10 \text{ moles} \] ### Step 3: Calculate the mole fraction of urea The mole fraction (X) of urea can be calculated using the formula: \[ X_{\text{urea}} = \frac{\text{moles of urea}}{\text{moles of urea} + \text{moles of water}} \] Substituting the values we have: \[ X_{\text{urea}} = \frac{0.1}{0.1 + 10} = \frac{0.1}{10.1} \approx 0.0099 \] ### Step 4: Apply Raoult's Law According to Raoult's Law, the relative lowering of vapor pressure is given by: \[ \frac{P₀ - P_s}{P₀} = X_{\text{solute}} \] Where: - \( P_s \) = vapor pressure of the solution - \( P₀ \) = vapor pressure of the pure solvent (water) Substituting the known values: \[ \frac{24 - P_s}{24} = 0.0099 \] ### Step 5: Solve for \( P_s \) Now, we can rearrange the equation to find \( P_s \): \[ 24 - P_s = 0.0099 \times 24 \] Calculating \( 0.0099 \times 24 \): \[ 0.0099 \times 24 \approx 0.2376 \] So, we have: \[ 24 - P_s = 0.2376 \] Now, solving for \( P_s \): \[ P_s = 24 - 0.2376 = 23.7624 \text{ mm Hg} \] ### Step 6: Round the answer Rounding to two decimal places, we get: \[ P_s \approx 23.76 \text{ mm Hg} \] ### Final Answer The vapor pressure of the solution is approximately **23.76 mm Hg**. ---
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