Calculate to three significant digits the density of carbon monoxide gas at exactly -5 °C and exactly 1 atm. You can assume carbon monoxide gas
Answer
🧪 Density of Carbon Monoxide (CO) Gas
Problem Overview
Calculate the density of carbon monoxide gas under the following conditions:
- Temperature: −5.0 °C
- Pressure: 1.00 atm
- Assume: Ideal gas behavior
Step 1: Convert Temperature to Kelvin
T = −5.0 + 273.15 = 268.15 K
Step 2: Use the Ideal Gas Law in Terms of Density
Start with the ideal gas law:
PV = nRT
Using the identity n = m / M and ρ = m / V, derive:
ρ = (PM) / (RT)
Step 3: Known Values
- P = 1.00 atm
- T = 268.15 K
- M (CO) = 28.01 g/mol
- R = 0.0821 L·atm/(mol·K)
Step 4: Substitute and Solve
ρ = (1.00 × 28.01) / (0.0821 × 268.15)
ρ = 28.01 / 22.021215 ≈ 1.272 g/L
ρ = 28.01 / 22.021215 ≈ 1.272 g/L
✅ Final Answer:
ρ ≈ 1.27 g/L (to three significant digits)
Key Concepts:
- Density is directly proportional to pressure and molar mass.
- Density is inversely proportional to temperature.
- This equation is derived from the ideal gas law and can be applied to any ideal gas.