A mixture of nitrogen and water vapours is admitted to a flask at 760 torr which contains a sufficient solid drying agent. After long time the pressure attained a steady value of 722 torr.
If the experiment is done at `27^(@)C` and drying agent increase in mass by 0.9 gm, what is the volume of the flask? Neglect any possible vapour pressure of drying agent and volume occupied by drying agent.

Options

A. 443.34 L
B. 246.3 L
C. 12.315 L
D. 24.63 L

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We have a mixture of nitrogen (N₂) and water vapor (H₂O) in a flask. The initial pressure is 760 torr, and after using a drying agent, the pressure drops to 722 torr. The drying agent absorbs water vapor, and its mass increases by 0.9 g. We need to find the volume of the flask at a temperature of 27°C.

### Step 2: Calculate the Partial Pressure of Water Vapor
The partial pressure of the water vapor can be found by subtracting the final pressure from the initial pressure:
\[ P_{H_2O} = P_{\text{initial}} - P_{\text{final}} = 760 \, \text{torr} - 722 \, \text{torr} = 38 \, \text{torr} \]

### Step 3: Convert Partial Pressure to Atmospheres
To use the ideal gas law, we need to convert the pressure from torr to atmospheres:
\[ P_{H_2O} = \frac{38 \, \text{torr}}{760 \, \text{torr/atm}} = 0.05 \, \text{atm} \]

### Step 4: Calculate the Moles of Water Vapor
The mass of the water vapor absorbed by the drying agent is 0.9 g. We can calculate the number of moles of water vapor using its molar mass (18 g/mol):
\[ n_{H_2O} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.9 \, \text{g}}{18 \, \text{g/mol}} = 0.05 \, \text{mol} \]

### Step 5: Convert Temperature to Kelvin
The temperature is given as 27°C. We need to convert this to Kelvin:
\[ T = 27 + 273 = 300 \, \text{K} \]

### Step 6: Use the Ideal Gas Law to Find Volume
The ideal gas law is given by the equation:
\[ PV = nRT \]
Rearranging for volume (V):
\[ V = \frac{nRT}{P} \]
Substituting the values:
- \(n = 0.05 \, \text{mol}\)
- \(R = 0.0821 \, \text{L atm/(mol K)}\)
- \(T = 300 \, \text{K}\)
- \(P = 0.05 \, \text{atm}\)

\[ V = \frac{0.05 \, \text{mol} \times 0.0821 \, \text{L atm/(mol K)} \times 300 \, \text{K}}{0.05 \, \text{atm}} \]

### Step 7: Calculate the Volume
Now, calculating the volume:
\[ V = \frac{0.05 \times 0.0821 \times 300}{0.05} = 24.63 \, \text{L} \]

### Final Answer
The volume of the flask is approximately **24.63 liters**.

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