The density of methane at 4.0 atm pressure and `27^0C` is :

Options

A. 1.30g`L^(−1)`
B. 0.13g`L^(−1)`
C. 2.6g`L^(−1)`
D. 0.26g`L^(−1)`

Explanation

To find the density of methane (CH₄) at a pressure of 4.0 atm and a temperature of 27°C, we can use the ideal gas equation in the form that relates density to pressure, molar mass, and temperature.

### Step-by-Step Solution:

1. **Convert Temperature to Kelvin**:
- The temperature in Celsius is given as 27°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
- Therefore,
\[ T = 27 + 273.15 = 300.15 \, K \approx 300 \, K \, (\text{for simplicity}) \]

2. **Identify Molar Mass of Methane**:
- The molecular formula for methane is CH₄. The molar mass can be calculated as:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol × 4 = 4 g/mol
- Thus, the molar mass of methane (CH₄) is:
\[ M = 12 + 4 = 16 \, g/mol \]

3. **Use the Ideal Gas Density Formula**:
- The density (D) of a gas can be calculated using the formula:
\[ D = \frac{PM}{RT} \]
- Where:
- \( P \) = pressure in atm (4.0 atm)
- \( M \) = molar mass (16 g/mol)
- \( R \) = ideal gas constant (0.0821 atm·L/(K·mol))
- \( T \) = temperature in Kelvin (300 K)

4. **Substitute Values into the Density Formula**:
- Plugging in the values we have:
\[ D = \frac{(4.0 \, \text{atm}) \times (16 \, g/mol)}{(0.0821 \, atm·L/(K·mol)) \times (300 \, K)} \]

5. **Calculate the Denominator**:
- First, calculate \( R \times T \):
\[ R \times T = 0.0821 \times 300 = 24.63 \, atm·L/mol \]

6. **Calculate the Density**:
- Now, substituting back into the density equation:
\[ D = \frac{(4.0 \times 16)}{24.63} = \frac{64}{24.63} \approx 2.60 \, g/L \]

7. **Final Result**:
- The density of methane at 4.0 atm and 27°C is approximately:
\[ D \approx 2.60 \, g/L \]