Gas density at standard conditions – carbon dioxide Express the density of CO2 at normal conditions as kg per normal cubic meter (kg/Nm^3). Choose the correct expression.

Difficulty: Easy

Correct Answer: 44/22.4

Explanation:


Introduction / Context:
Normal cubic meter (Nm^3) refers to gas volume at standard temperature and pressure. Converting molar properties to mass per unit standard volume is a frequent step in gas metering, emissions reporting, and process calculations.


Given Data / Assumptions:

  • Molar mass of CO2 = 44 kg/kmol.
  • Molar volume at STP (approximately) = 22.4 m^3/kmol (for ideal gas at 0°C, 1 atm).
  • Seeking density in kg per Nm^3.


Concept / Approach:
Density at STP is mass per mole divided by molar volume. For any gas, ρ = M / V_m, where M is molar mass and V_m is molar volume at the stated standard conditions. For CO2: ρ ≈ 44 kg/kmol / 22.4 m^3/kmol.


Step-by-Step Solution:

Write density formula: ρ = M / V_m.Insert CO2 values: M = 44 kg/kmol; V_m = 22.4 m^3/kmol.Compute expression: ρ = 44/22.4 kg/m^3 ≈ 1.964 kg/Nm^3.Select the expression matching this computation.


Verification / Alternative check:
Comparing to air (≈28.97/22.4 ≈ 1.29 kg/Nm^3), CO2's higher density is consistent with its higher molar mass.


Why Other Options Are Wrong:

  • 44/22400: Uses liters in the denominator but keeps kg units, giving kg per liter-scale denominator numerically wrong for kg/Nm^3.
  • 22.4/44: Inverts the correct ratio, yielding m^3/kg rather than kg/m^3.
  • None of these: Incorrect because 44/22.4 is correct.


Common Pitfalls:
Mixing L/mol with m^3/mol without consistent unit conversions; forgetting that 1 Nm^3 corresponds to 1 m^3 at standard conditions.


Final Answer:
44/22.4

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