Which of the following aqueous solutions has a higher vapour pressure if the density of water is `1g//"cc"` ?
(a) Solution having mole fraction of cane sugar `=0.1`
(b) Solution having molal concentration `=1m`

Answer

To determine which aqueous solution has a higher vapor pressure, we need to analyze the two given solutions based on their mole fractions and molal concentrations.

### Step 1: Understand the Concept of Vapor Pressure
The vapor pressure of a solution is affected by the presence of solute particles. According to Raoult's Law, the vapor pressure of a solvent in a solution is directly related to the mole fraction of the solvent. The more solute particles present, the lower the vapor pressure of the solution.

### Step 2: Analyze the First Solution
**Solution (a)** has a mole fraction of cane sugar = 0.1.

- The mole fraction of water (solvent) can be calculated as:
\[ \text{Mole fraction of water} = 1 - \text{Mole fraction of solute} = 1 - 0.1 = 0.9 \]

### Step 3: Analyze the Second Solution
**Solution (b)** has a molal concentration of 1m (1 molal).

- To convert molality to mole fraction, we need to know the mass of the solvent (water). Assuming we have 1 kg (1000 g) of water:
- Moles of water = \( \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \)
- Moles of solute (1m solution) = 1 mole (since it's 1 molal)
- Total moles in the solution = 55.56 + 1 = 56.56
- Mole fraction of solute = \( \frac{1}{56.56} \approx 0.0177 \)
- Mole fraction of water = \( 1 - 0.0177 \approx 0.9823 \)

### Step 4: Compare the Vapor Pressures
- For Solution (a):
- Mole fraction of water = 0.9
- Higher mole fraction of water means higher vapor pressure.

- For Solution (b):
- Mole fraction of water = 0.9823
- Higher mole fraction of water means higher vapor pressure.

### Step 5: Conclusion
Since Solution (b) has a higher mole fraction of water (0.9823) compared to Solution (a) (0.9), Solution (b) will have a higher vapor pressure.

**Final Answer: Solution (b) has a higher vapor pressure.**

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