Flue-gas averaging: A flue gas contains 0.15 kmol CO2, 0.05 kmol O2, and 0.80 kmol N2 per kmol of mixture. What is the average molecular weight of the gas mixture?

Introduction / Context:
Determining a gas mixture’s average molecular weight is a routine step in combustion calculations, gas density estimates, and compressor sizing. The average is a mole-fraction-weighted sum of component molecular weights.

Given Data / Assumptions:

• Mole fractions: yCO2 = 0.15, yO2 = 0.05, yN2 = 0.80 (sum = 1.00).
• Molecular weights: MCO2 = 44, MO2 = 32, MN2 = 28 kg/kmol.
• Ideal mixing assumed.

Concept / Approach:
The average molecular weight Mmix is given by Mmix = Σ yi * Mi. This uses mole fractions as weights because each kmol of mixture contains yi kmol of species i.

Step-by-Step Solution:

Verification / Alternative check:
As a reasonableness check, the mixture is mostly N2, so the result should be close to 28 but pulled upward by CO2 (44) and slightly by O2 (32). A value around 30 is sensible; 30.6 matches the calculation.

Why Other Options Are Wrong:

• 28.6: Too low; underweights CO2 contribution.
• 30.0: Rounded down; not the precise weighted sum.
• 32.6: Too high; would require more CO2/O2 than present.

Common Pitfalls:
Using mass fractions by mistake; the correct weighting for Mmix is mole fraction. Also, forgetting to ensure that fractions sum to unity before applying the formula.

Final Answer:
30.6