A gas occupies 300 ml at `27^(@)C` and 740 mm Hg pressure. Calculate its volume at S.T.P. ? 

Options

A. 0.3650 L
B. 0.2658 L
C. 200 L
D. 365 L

Explanation

To solve the problem of finding the volume of a gas at Standard Temperature and Pressure (STP), we will use the combined gas law, which is given by:

\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

### Step 1: Identify the given values
- Initial volume \( V_1 = 300 \, \text{ml} = 0.300 \, \text{L} \) (since \( 1 \, \text{L} = 1000 \, \text{ml} \))
- Initial temperature \( T_1 = 27 \, ^\circ C = 27 + 273 = 300 \, \text{K} \) (convert Celsius to Kelvin)
- Initial pressure \( P_1 = 740 \, \text{mm Hg} \)
- Standard pressure \( P_2 = 1 \, \text{atm} = 760 \, \text{mm Hg} \)
- Standard temperature \( T_2 = 0 \, ^\circ C = 273 \, \text{K} \)

### Step 2: Convert the initial pressure to atm
\[ P_1 = \frac{740 \, \text{mm Hg}}{760 \, \text{mm Hg/atm}} = 0.974 \, \text{atm} \]

### Step 3: Rearrange the combined gas law to solve for \( V_2 \)
\[ V_2 = \frac{P_1 V_1 T_2}{P_2 T_1} \]

### Step 4: Substitute the known values into the equation
\[ V_2 = \frac{(0.974 \, \text{atm}) (0.300 \, \text{L}) (273 \, \text{K})}{(1 \, \text{atm}) (300 \, \text{K})} \]

### Step 5: Calculate \( V_2 \)
1. Calculate the numerator:
\[ 0.974 \times 0.300 \times 273 = 79.869 \, \text{L K} \]
2. Calculate the denominator:
\[ 1 \times 300 = 300 \, \text{atm K} \]
3. Now divide the numerator by the denominator:
\[ V_2 = \frac{79.869}{300} = 0.2659 \, \text{L} \]

### Final Answer
The volume of the gas at STP is approximately \( 0.2658 \, \text{L} \).