Answer
Density of Carbon Monoxide Gas
🔍 Problem Statement
Calculate the density of carbon monoxide (CO) gas at:
- Temperature: –10 °C
- Pressure: 1.00 atm
- Volume: 22.4 L
Assume ideal gas behavior. Express the answer in g/L, rounded to three significant digits.
📘 Known Values
| Quantity | Symbol | Value |
|---|---|---|
| Temperature | T | –10 °C = 263 K |
| Molar Mass of CO | M | 28.0 g/mol |
| Pressure | P | 1.00 atm |
| Volume | V | 22.4 L |
| Gas Constant | R | 0.08206 L·atm/mol·K |
🧠 Step-by-Step Solution
Step 1: Find Number of Moles
PV = nRT
n = PV / RT
n = (1.00 × 22.4) / (0.08206 × 263) = 22.4 / 21.58 ≈ 1.038 mol
n = PV / RT
n = (1.00 × 22.4) / (0.08206 × 263) = 22.4 / 21.58 ≈ 1.038 mol
Step 2: Calculate Mass of CO
mass = moles × molar mass
mass = 1.038 × 28.0 = 29.064 ≈ 29.06 g
mass = 1.038 × 28.0 = 29.064 ≈ 29.06 g
Step 3: Calculate Density
density = mass / volume
density = 29.06 / 22.4 = 1.2975 ≈ 1.298 g/L
density = 29.06 / 22.4 = 1.2975 ≈ 1.298 g/L
✅ Final Answer
Density of CO = 1.298 g/L
📌 Conclusion
The density of carbon monoxide gas at –10 °C and 1.00 atm is:
1.298 g/L
This was determined using the ideal gas law and standard relationships between moles, mass, and volume.