Answer
Density of Carbon Dioxide (CO₂) at 15 °C
🧪 Problem Statement
Calculate the density of carbon dioxide gas (CO₂) at:
- Temperature: 15 °C
- Pressure: 1.00 atm
Assume ideal gas behavior and report the result in g/L, rounded to three significant digits.
📘 Theoretical Basis
We start with the ideal gas law:
PV = nRT
We derive 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 = Ideal gas constant = 0.08206 L·atm/mol·K
- T = Temperature in Kelvin = 288.15 K
📋 Given Values
| Quantity | Symbol | Value |
|---|---|---|
| Pressure | P | 1.00 atm |
| Temperature | T | 15 °C = 288.15 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 values into the formula
d = (1.00 × 44.01) / (0.08206 × 288.15)
Step 2: Calculate the denominator
RT = 0.08206 × 288.15 = 23.6511
Step 3: Calculate the density
d = 44.01 / 23.6511 ≈ 1.8607 g/L
✅ Final Answer
Density of CO₂ = 1.86 g/L (to three significant digits)
📌 Conclusion
At a temperature of 15 °C and pressure of 1 atm, the density of carbon dioxide gas is:
1.86 g/L
This result assumes ideal gas behavior, which is valid for CO₂ under typical laboratory conditions.