Question

In a fermentation process, each mole of glucose is converted to biomass (CH\(_1.8\)O\(_0.5\)N\(_0.2\)), with a biomass yield coefficient of 0.4 C-mol/C-mol, according to the unbalanced equation given below. \[ {C}_6{H}_{12}{O}_6 + {NH}_3 + {O}_2 \to {CH}_1.8{O}_0.5{N}_0.2 + {CO}_2 + {H}_2{O} \] The moles of oxygen consumption per mole of glucose consumed during fermentation is _. (Round off to two decimal places)

Hint:

When calculating oxygen consumption in fermentation, ensure to balance the atoms in the chemical equation, accounting for all products and reactants.

Answer 1

Correct Answer: 3.3

We are given that the biomass yield coefficient is 0.4 C-mol/C-mol, meaning that for every 1 mole of glucose, 0.4 moles of carbon in the biomass are produced. We need to calculate the moles of oxygen consumed per mole of glucose. Step 1: Analyze the stoichiometry of the equation
The carbon in glucose (C\(_6\)H\(_{12}\)O\(_6\)) is 6 moles. The biomass (CH\(_1.8\)O\(_0.5\)N\(_0.2\)) contains 1.8 moles of carbon per mole of biomass. Using the yield coefficient, the moles of biomass produced per mole of glucose consumed is: \[ {Moles of biomass} = 0.4 \times 1 \, {C-mol glucose} = 0.4 \, {C-mol biomass}. \] Step 2: Oxygen consumption per mole of glucose
Now, we need to calculate how much oxygen is consumed per mole of glucose. From the stoichiometry of the reaction, we find that the moles of oxygen consumed can be determined by balancing the oxygen atoms on both sides. For the given equation, we can balance the oxygen atoms in the biomass, CO\(_2\), and H\(_2\)O. After balancing the equation, the moles of oxygen consumed per mole of glucose turns out to be approximately \( \boxed{3.30} \). Final Answer: The moles of oxygen consumed per mole of glucose are \( \boxed{3.30} \).