Calculate to three significant digits the density of carbon monoxide gas at exactly 30 “C and exactly I atm. You can assume carbon monoxide
Answer
🧪 Density of Carbon Monoxide (CO) Gas
Problem Statement
Calculate the density of carbon monoxide gas under the following conditions:
- Temperature: 30.0 °C
- Pressure: 1.00 atm
- Assumption: Ideal gas behavior
Step 1: Convert Temperature to Kelvin
T = 30.0 + 273.15 = 303.15 K
Step 2: Use the Ideal Gas Law in Terms of Density
Starting from the ideal gas law:
PV = nRT
Substitute n = m / M and ρ = m / V to derive:
ρ = (PM) / (RT)
Step 3: Known Values
- P = 1.00 atm
- T = 303.15 K
- M (CO) = 28.01 g/mol
- R = 0.0821 L·atm/mol·K
Step 4: Substitute and Calculate
ρ = (1.00 × 28.01) / (0.0821 × 303.15)
ρ = 28.01 / 24.884415 ≈ 1.1257 g/L
ρ = 28.01 / 24.884415 ≈ 1.1257 g/L
✅ Final Answer:
ρ ≈ 1.13 g/L (rounded to three significant digits)
Key Concepts:
- Density is directly proportional to pressure and molar mass.
- Density is inversely proportional to temperature.
- This relationship is derived from the ideal gas law and applies to any ideal gas.