Calculate to three significant digits the density of carbon dioxide gas at exactly -15 C and exactly 1 atm, You can assume carbon dioxide gas behaves
Answer
Density of Carbon Dioxide Gas at –15 °C
🧪 Problem Statement
Calculate the density of carbon dioxide (CO₂) gas at:
- Temperature: –15 °C
- Pressure: 1.00 atm
Assume ideal gas behavior and express the result in g/L, rounded to three significant digits.
📘 Theoretical Framework
We use the density form of the ideal gas law:
d = (PM) / (RT)
Where:
- P = pressure (atm)
- M = molar mass of CO₂ = 44.01 g/mol
- R = 0.08206 L·atm/mol·K
- T = temperature in Kelvin
🔢 Known Values
| Quantity | Symbol | Value |
|---|---|---|
| Pressure | P | 1.00 atm |
| Temperature | T | –15 °C = 258.15 K |
| Molar Mass of CO₂ | M | 44.01 g/mol |
| Gas Constant | R | 0.08206 L·atm/mol·K |
🧮 Step-by-Step Calculation
Step 1: Plug into the density formula
d = (1.00 × 44.01) / (0.08206 × 258.15)
Step 2: Compute the denominator
RT = 0.08206 × 258.15 = 21.179
Step 3: Calculate the density
d = 44.01 / 21.179 ≈ 2.077 g/L
✅ Final Answer
Density of CO₂ = 2.08 g/L (to three significant digits)
📌 Conclusion
At –15 °C and 1 atm pressure, the density of carbon dioxide gas is:
2.08 g/L
This value is calculated using the ideal gas law and is valid under standard assumptions where CO₂ is treated as an ideal gas.