Calculate to three significant digits the density of carbon monoxide gas at exactly 15∘C and exactly 1 atm. You can assume carbon monoxide gas
Answer
🧪 Density of Carbon Monoxide (CO) Gas
Problem:
Calculate the density of CO gas at the following conditions:
- Temperature: 15.0 °C
- Pressure: 1.00 atm
- Assume: CO behaves as an ideal gas
Step 1: Convert Temperature to Kelvin
T = 15.0 + 273.15 = 288.15 K
Step 2: Use the Ideal Gas Law for Density
Start from the ideal gas law:
PV = nRT
Substitute n = m / M and ρ = m / V to get:
ρ = (PM) / (RT)
Step 3: Known Values
- P = 1.00 atm
- T = 288.15 K
- M (CO) = 28.01 g/mol
- R = 0.08206 L·atm/mol·K
Step 4: Calculate
ρ = (1.00 × 28.01) / (0.08206 × 288.15)
ρ = 28.01 / 23.6467 ≈ 1.1847 g/L
ρ = 28.01 / 23.6467 ≈ 1.1847 g/L
✅ Final Answer:
ρ ≈ 1.18 g/L (rounded to three significant digits)
Key Takeaways:
- Density is directly proportional to pressure and molar mass.
- Density is inversely proportional to temperature.
- This method uses the ideal gas law to estimate gas density accurately under standard conditions.