Answer
Density of Carbon Monoxide Gas
🧪 Problem Statement
Calculate the density of carbon monoxide (CO) gas at the following conditions:
- Temperature: 15 °C
- Pressure: 1.00 atm
Assume ideal gas behavior. Express the result in g/L rounded to three significant digits.
📘 Theoretical Background
Ideal Gas Law:
PV = nRT
To relate the gas law to density, use the relationships:
- \( n = m/M \)
- \( d = m/V \)
Substituting into the gas law:
d = PM / RT
🔢 Known Values
| Quantity | Symbol | Value |
|---|---|---|
| Pressure | P | 1.00 atm |
| Temperature | T | 15 °C = 288 K |
| Molar mass of CO | M | 28.0 g/mol |
| Gas constant | R | 0.0821 L·atm/mol·K |
🧮 Calculation
Substitute the values into the formula:
d = (1.00 × 28.0) / (0.0821 × 288)
Calculate the denominator:
RT = 0.0821 × 288 = 23.6448
Now compute density:
d = 28.0 / 23.6448 ≈ 1.1849 g/L
✅ Final Answer
Density = 1.18 g/L (rounded to three significant digits)
📌 Conclusion
The density of carbon monoxide gas at 15 °C and 1.00 atm is:
1.18 g/L
This value is obtained using the ideal gas law and is applicable under typical laboratory conditions where CO behaves approximately as an ideal gas.