Difficulty: Easy
Correct Answer: rate of addition - rate of removal + rate of formation = 0
Explanation:
Introduction / Context:
Material balances are foundational in chemical and biochemical engineering. For any component, the general unsteady-state balance is: accumulation = in − out + generation − consumption. At steady state, accumulation = 0, giving a simple algebraic relationship among input, output, and net formation terms.
Given Data / Assumptions:
Concept / Approach:
Set accumulation to zero and rearrange: 0 = in − out + formation → in − out + formation = 0. Sign conventions are crucial; “addition” corresponds to in, “removal” to out. This compact expression is widely used to check consistency of process calculations and reactor designs.
Step-by-Step Solution:
Verification / Alternative check:
Dimensional analysis confirms consistent units (e.g., mol/s). Plugging typical reactor data should satisfy the equality when inventories are constant.
Why Other Options Are Wrong:
Common Pitfalls:
Mixing sign conventions; forgetting that “formation” can be negative when the component is consumed net.
Final Answer:
rate of addition - rate of removal + rate of formation = 0
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