To calculate the density of carbon dioxide (CO₂) at a temperature of 97°C and a pressure of 760 mm Hg, we can use the ideal gas law equation and the relationship between density, pressure, temperature, and molecular weight.
### 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 97°C:
\[
T = 97 + 273.15 = 370.15 \, K
\]
2. **Convert Pressure to Atmospheres:**
The pressure in mm Hg needs to be converted to atmospheres. We know that:
\[
760 \, \text{mm Hg} = 1 \, \text{atm}
\]
Therefore, the pressure \( P \) is:
\[
P = 1 \, \text{atm}
\]
3. **Identify the Universal Gas Constant \( R \):**
The value of the universal gas constant \( R \) in liter atm per mole per Kelvin is:
\[
R = 0.0821 \, \text{L atm} \, \text{mol}^{-1} \, \text{K}^{-1}
\]
4. **Determine the Molecular Weight of Carbon Dioxide:**
The molecular weight of CO₂ can be calculated as follows:
- Atomic weight of Carbon (C) = 12 g/mol
- Atomic weight of Oxygen (O) = 16 g/mol
- CO₂ has one carbon atom and two oxygen atoms:
\[
\text{Molecular weight of CO₂} = 12 + (2 \times 16) = 12 + 32 = 44 \, \text{g/mol}
\]
5. **Use the Density Formula:**
The density \( D \) of a gas can be calculated using the rearranged ideal gas law:
\[
D = \frac{PM}{RT}
\]
Where:
- \( D \) = density (g/L)
- \( P \) = pressure (atm)
- \( M \) = molecular weight (g/mol)
- \( R \) = universal gas constant (L atm mol⁻¹ K⁻¹)
- \( T \) = temperature (K)
6. **Substitute the Values:**
Substitute the known values into the density formula:
\[
D = \frac{(1 \, \text{atm}) \times (44 \, \text{g/mol})}{(0.0821 \, \text{L atm} \, \text{mol}^{-1} \, \text{K}^{-1}) \times (370.15 \, K)}
\]
7. **Calculate the Density:**
Performing the calculation:
\[
D = \frac{44}{0.0821 \times 370.15} \approx \frac{44}{30.407215} \approx 1.45 \, \text{g/L}
\]
### Final Answer:
The density of carbon dioxide at 97°C and 760 mm Hg is approximately:
\[
\boxed{1.45 \, \text{g/L}}
\]
