Question

Burning of methane in a combustor yields carbon monoxide, carbon dioxide, and water vapor. Methane is fed to the combustor at 100 mol·hr\(^{-1}\), of which 50% reacts. The theoretical oxygen requirement (in mol·hr\(^{-1}\)) is ____________ (rounded off to one decimal place).

Hint:

- Theoretical oxygen requirement is always based on \emph{complete combustion of the total fuel fed}, not the actual reacted portion. - Methane needs 2 moles of O\(_2\) per mole for full oxidation to CO\(_2\).

Answer 1

Correct Answer: 199.5

Step 1: Write possible combustion reactions of methane.
- Complete combustion to CO\(_2\): \[\mathrm{CH_4 + 2 O_2 \;\rightarrow\; CO_2 + 2 H_2O}\] - Incomplete combustion to CO: \[\mathrm{CH_4 + 1.5 O_2 \;\rightarrow\; CO + 2 H_2O}\] Step 2: Define theoretical oxygen requirement.
Theoretical oxygen requirement = Oxygen needed for complete combustion of all methane to CO\(_2\) and H\(_2\)O, regardless of actual extent or products. Step 3: Calculate stoichiometric oxygen demand.
From the complete combustion equation: 1 mol CH\(_4\) requires 2 mol O\(_2\). Step 4: Apply given methane flow.
Methane feed = 100 mol·hr\(^{-1}\).
Theoretical O\(_2\) requirement = \(100 \times 2 = 200\) mol·hr\(^{-1}\). Step 5: Clarify the effect of 50% reaction.
Even though only 50% reacts in practice, the “theoretical oxygen requirement” is defined for complete conversion of the entire methane feed. Thus, still based on 100 mol·hr\(^{-1}\). Hence, the theoretical oxygen requirement is: \[ \boxed{200.0 \;\; \text{mol·hr}^{-1}} \]