The overall stoichiometry for an aerobic cell growth is3C6H12O6 + 2.5NH3 + O2 1.5CaHbOcNd + 3CO2 + 5H2OWhat is the elemental composition formula of the biomass?(A) C9H18.2O5N1.667(B) C9H22.33O6N1.667(C) C10H18.2O5N1.667(D) C10H22.33O6N1.667
Question
The overall stoichiometry for an aerobic cell growth is3C6H12O6 + 2.5NH3 + O2 1.5CaHbOcNd + 3CO2 + 5H2OWhat is the elemental composition formula of the biomass?(A) C9H18.2O5N1.667(B) C9H22.33O6N1.667(C) C10H18.2O5N1.667(D) C10H22.33O6N1.667
Solution
The stoichiometry of the reaction is given as:
3C6H12O6 + 2.5NH3 + O2 → 1.5CaHbOcNd + 3CO2 + 5H2O
We can balance the elements on both sides of the reaction to find the formula for the biomass (CaHbOcNd).
Carbon (C): On the left side, we have 36 = 18 carbons from glucose and 3 carbons from CO2, giving a total of 21 carbons. On the right side, we have 1.5a carbons in the biomass. Therefore, a = 21 / 1.5 = 14.
Hydrogen (H): On the left side, we have 312 = 36 hydrogens from glucose, 2.53 = 7.5 hydrogens from ammonia, and 52 = 10 hydrogens from water, giving a total of 53.5 hydrogens. On the right side, we have 1.5b hydrogens in the biomass. Therefore, b = 53.5 / 1.5 = 35.67.
Oxygen (O): On the left side, we have 36 = 18 oxygens from glucose and 32 = 6 oxygens from CO2, giving a total of 24 oxygens. On the right side, we have 1.5c oxygens in the biomass and 5 oxygens from water, giving a total of 1.5c + 5 oxygens. Therefore, c = (24 - 5) / 1.5 = 12.67.
Nitrogen (N): On the left side, we have 2.5 nitrogens from ammonia. On the right side, we have 1.5*d nitrogens in the biomass. Therefore, d = 2.5 / 1.5 = 1.67.
So, the elemental composition formula of the biomass is C14H35.67O12.67N1.67. None of the given options (A, B, C, D) match this formula.
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