The density of Carbon dioxide at 2.0 atm pressure and `27^0C` is :

Options

A. 1.9g`L^(−1)`
B. 3.57g`L^(−1)`
C. both
D. none

Explanation

To find the density of carbon dioxide (CO₂) at a pressure of 2.0 atm and a temperature of 27°C, we can use the ideal gas equation and the formula for density derived from it.

### Step-by-Step Solution:

1. **Convert Temperature to Kelvin**:
- The temperature given is 27°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
- So,
\[ T = 27 + 273 = 300 \, K \]

2. **Identify the Given Values**:
- Pressure (P) = 2.0 atm
- Molar mass of CO₂ (M) = 44 g/mol
- Gas constant (R) = 0.0821 atm·L/(K·mol)

3. **Use the Density Formula**:
- The formula for density (D) derived from the ideal gas law is:
\[ D = \frac{PM}{RT} \]
- Where:
- D = density
- P = pressure
- M = molar mass
- R = gas constant
- T = temperature in Kelvin

4. **Substitute the Values into the Formula**:
- Now we substitute the values we have into the density formula:
\[ D = \frac{(2.0 \, \text{atm}) \times (44 \, \text{g/mol})}{(0.0821 \, \text{atm·L/(K·mol)}) \times (300 \, K)} \]

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

6. **Calculate the Density**:
- Now substitute back into the density equation:
\[ D = \frac{(2.0) \times (44)}{24.63} \]
- Calculate the numerator:
\[ 2.0 \times 44 = 88 \]
- Now divide:
\[ D = \frac{88}{24.63} \approx 3.57 \, \text{g/L} \]

7. **Final Result**:
- Therefore, the density of carbon dioxide at 2.0 atm and 27°C is approximately:
\[ D \approx 3.57 \, \text{g/L} \]

### Summary:
The density of carbon dioxide at 2.0 atm pressure and 27°C is approximately **3.57 g/L**.