The density of Carbon dioxide at 3.0 atm pressure and `27^0C` is :

Options

A. 1.9g`L^(−1)`
B. 5.36g`L^(−1)`
C. 0.53g`L^(−1)`
D. None of these

Explanation

To find the density of carbon dioxide (CO₂) at a pressure of 3.0 atm and a temperature of 27°C, we can use the ideal gas law equation and the formula for density derived from it.

### Step-by-step Solution:

1. **Convert Temperature to Kelvin**:
- The temperature in Celsius needs to be converted to Kelvin using the formula:
\[ T(K) = T(°C) + 273.15 \]
- For 27°C:
\[ T = 27 + 273.15 = 300.15 \, K \approx 300 \, K \]

2. **Identify Given Values**:
- Pressure (P) = 3.0 atm
- Molar mass of CO₂ (M) = 12 (C) + 32 (O₂) = 44 g/mol
- Gas constant (R) = 0.0821 atm·L/(K·mol)

3. **Use the Density Formula**:
- The density (d) of a gas can be calculated using the formula:
\[ d = \frac{PM}{RT} \]
- Substitute the known values into the formula:
\[ d = \frac{3.0 \, \text{atm} \times 44 \, \text{g/mol}}{0.0821 \, \text{atm·L/(K·mol)} \times 300 \, K} \]

4. **Calculate the Denominator**:
- Calculate \( R \times T \):
\[ R \times T = 0.0821 \, \text{atm·L/(K·mol)} \times 300 \, K = 24.63 \, \text{atm·L/mol} \]

5. **Calculate Density**:
- Now, substitute back into the density formula:
\[ d = \frac{3.0 \times 44}{24.63} = \frac{132}{24.63} \approx 5.36 \, \text{g/L} \]

6. **Final Answer**:
- The density of carbon dioxide at 3.0 atm and 27°C is approximately **5.36 g/L**.