Material balances for a reacting system:\nFor the reactor carrying out A + B → C (single reaction), how many independent material balance equations can be written around the reactor?

Introduction / Context:
Writing and counting independent material balances is fundamental to setting up process calculations. For reacting systems, balances can be written on each molecular species and, optionally, on total mass. However, linear dependence must be considered to avoid overcounting equations.

Given Data / Assumptions:

• Single reaction: A + B → C.
• Species present: A, B, C (three distinct components).
• Steady-state or unsteady does not change the count of independent component balances, only their forms.
• No side reactions and no additional inert species mentioned.

Concept / Approach:
Independent component balances can be written for each species: A, B, and C. An overall mass balance can also be written, but for single-reaction systems it is a linear combination of the component balances (hence dependent). The number of independent material balance equations equals the number of chemically independent species present (here, three).

Step-by-Step Solution:

Verification / Alternative check:
Rank analysis: For one reaction among three species, the stoichiometric matrix has rank 1. The number of independent species balances remains 3; including extent of reaction handles coupling, but independence among species balances persists.

Why Other Options Are Wrong:

• 1 or 2: Underestimates; you can and should balance all three species separately.
• 4: Overestimates; the fourth equation (overall mass) is dependent on the three component balances.

Common Pitfalls:
Confusing “number of degrees of freedom” with “number of balance equations”; assuming overall mass balance adds independence in a single-reaction, single-phase system.

Final Answer:
3