Stoichiometric combustion of methane with pure oxygen to complete conversion is specified. How many additional independent specifications are required to determine both product composition and total product flow rate?

Introduction / Context:
Degrees-of-freedom accounting helps determine how many independent specifications are needed to fully define material balances. For a single-reaction combustion with complete conversion and stoichiometric mixing, the system becomes fully determined without extra inputs beyond the stoichiometric relation itself and a chosen basis.

Given Data / Assumptions:

• Reaction: CH4 + 2 O2 → CO2 + 2 H2O.
• Stoichiometric proportion of O2 to CH4 is enforced.
• Complete combustion (no CO, no unburned CH4, no O2 in products).
• No inerts are present; pressure–temperature not needed for composition.

Concept / Approach:
Under these constraints, product composition is fixed: the only species present are CO2 and H2O in a 1:2 molar ratio. For any chosen feed basis (e.g., 1 mol CH4), the total product flow follows directly from stoichiometry. In degrees-of-freedom terms, the number of unknown outlet component flow rates equals the number of independent equations provided by stoichiometry and completeness, leaving zero additional specifications required to compute both composition and flow on a per-basis scale.

Step-by-Step Solution:

Verification / Alternative check:
Choosing any feed basis (e.g., F mol CH4) scales products proportionally; composition remains constant and total flow scales with basis.

Why Other Options Are Wrong:

• (b)–(e) imply missing information; however, stoichiometry and completeness already close the problem for composition and relative/absolute flow on a chosen basis.

Common Pitfalls:
Confusing the need for a numerical feed rate (basis) with an additional independent specification; degrees-of-freedom analysis counts equations and unknowns per basis selection.

Final Answer:
0