Chemical engineering mass balance: at strict steady state, which algebraic statement correctly represents the material balance for any component in a system?

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:

  • We consider a control volume with defined inlets and outlets.
  • “Formation” here denotes net production (generation − consumption) from reactions for the component of interest.
  • Strict steady state implies time-invariant inventories (accumulation term is zero).


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:

1) Start from the general balance: accumulation = in − out + formation.2) At steady state, accumulation = 0.3) Therefore, in − out + formation = 0.4) Translate to the phrasing in the options: rate of addition − rate of removal + rate of formation = 0.


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:

  • Addition + removal − formation = 0: sign error on removal and formation.
  • All plus signs: violates conservation unless trivial zeros.
  • None of the above: a correct statement exists.
  • Accumulation = addition + removal + formation: incorrect general form.


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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