Steady-state mass balance:\nFor a system operating at steady state, when does the simple relation “inputs = outputs” hold true?

Introduction / Context:
Mass balances distinguish between total mass and component mass. At steady state, accumulation is zero. Even with reactions, total mass is conserved, though individual species balances include generation or consumption terms.

Given Data / Assumptions:

• System at steady state (d/dt of holdup = 0).
• No leaks or unaccounted losses; total mass is conserved.
• Chemical reactions may occur internally.

Concept / Approach:
Total mass balance at steady state is: total mass in = total mass out. Component balances are: in − out + generation − consumption = 0. Reactions affect components, not the conservation of total mass (assuming no nuclear reactions).

Step-by-Step Solution:

Verification / Alternative check:
Consider A → B in a CSTR at steady state. Although A decreases and B increases, the sum of mass flow rates remains constant if density changes are accounted for in volumetric terms.

Why Other Options Are Wrong:

• Without reaction only / only without reaction and without losses: Too restrictive; the total mass relation is broader.
• None of these / 100% conversion requirement: Not relevant to total mass conservation.

Common Pitfalls:
Confusing total mass balance with species balances; overlooking leaks or evaporative losses which would violate the simple equality.

Final Answer:
With chemical reaction (total mass basis, no accumulation)