Aerobic biomass yield on glucose is .4 g/g. Glucose has molecular weight 180 g/mol and biomass is $C_5H_7O_2N$ with molecular weight 113 g/mol. With no endogenous metabolism, find percentage of carbon going to CO₂ from 1 mol/L glucose, to two decimals.
One mole glucose supplies 180 g substrate and $6(12)=72$ g carbon. Biomass formed is $.4(180)=72$ g. Biomass carbon fraction is $5(12)/113=60/113$,so biomass retains $72(60/113)=38.23009$ g carbon. Remaining carbon becomes CO₂: $(72-38.23009)/72\times100=\mathbf{46.90\%}$. This uses a mass-based yield, not a molar yield.
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