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Material/Energy Balances practice questions

10 free Material/Energy Balances questions for the FE Chemical Exam (FE) exam, each with the correct answer and an explanation for every option.

Start the questionsFree 10-question FE quiz

What this domain covers

The largest FE Chemical domain: mass and energy balances on processes with and without reaction, including recycle, bypass and purge.

Exam weight
10%
On a real exam
≈ 11 questions
In our bank
60 questions

Topics that come up most

  • Degrees of freedom and basis selection
  • Balances on reacting systems with extent of reaction
  • Recycle, bypass and purge streams
  • Energy balances with heats of reaction and combustion
  • Ideal gas behaviour and humidity in balances

How to study it

Solve every balance problem the same way: sketch the flowsheet, label all streams, choose a basis and count unknowns before you write an equation.

Sample Material/Energy Balances questions

Try each one before opening the answer. Original questions written to the official exam objectives.

  1. Question 1

    100 mol of A is fed to a reactor where A → B with 70% conversion. The outlet contains:

    • A0 mol A and 100 mol B
    • B70 mol A and 30 mol B
    • C30 mol A and 70 mol B
    • D30 mol A and 30 mol B
    Show answer and explanation

    Answer: C) 30 mol A and 70 mol B

    • AIncorrect. Conversion is only 70%.
    • BIncorrect. Conversion is the fraction reacted.
    • CCorrect. 70 mol react to form 70 mol B.
    • DIncorrect. 70 mol of B form.

  2. Question 2

    Methane is burned with 20% excess air (CH₄ + 2O₂ → CO₂ + 2H₂O). The O₂ supplied per mole of CH₄ is:

    • A2.4 mol
    • B2.0 mol
    • C1.2 mol
    • D11.4 mol
    Show answer and explanation

    Answer: A) 2.4 mol

    • ACorrect. 1.2 × the 2 mol stoichiometric O₂.
    • BIncorrect. Add the 20% excess.
    • CIncorrect. Stoichiometric O₂ is 2 mol.
    • DIncorrect. That's moles of air, not O₂.

  3. Question 3

    A stream containing 40 mol% A enters a stream splitter and leaves as two outlet streams. What is the composition of each outlet stream?

    • A40 mol% A in each outlet
    • B20 mol% A in each outlet
    • C80 mol% A in one outlet, 0 mol% A in the other
    • DDepends on the split ratio between the outlets
    Show answer and explanation

    Answer: A) 40 mol% A in each outlet

    A splitter divides one stream into several streams that all have the feed composition. Only the flow rates change, so each outlet is 40 mol% A.

    • ACorrect. A splitter only divides the flow. Both outlets have the same composition as the feed; only their flow rates differ.
    • BIncorrect. Splitting the flow divides the molar flow rates, not the mole fractions. Halving the stream does not halve the concentration.
    • CIncorrect. Different outlet compositions would take a separation unit such as a distillation column or membrane. A splitter has no separating action.
    • DIncorrect. The split ratio sets how much flow goes to each outlet. The composition of each outlet equals the feed composition no matter what the ratio is.

  4. Question 4

    50 kg/h of pure water is added to 100 kg/h of a 30 wt% solution. The resulting concentration is:

    • A15 wt%
    • B20 wt%
    • C30 wt%
    • D10 wt%
    Show answer and explanation

    Answer: B) 20 wt%

    • AIncorrect. Recheck: 30/150.
    • BCorrect. 30 kg solute in 150 kg.
    • CIncorrect. Water dilutes it.
    • DIncorrect. Recheck: 30/150.

  5. Question 5

    An ideal gas stream flows at 10 mol/s, 300 K and 100 kPa. Using R = 8.314 J/(mol·K), what is its volumetric flow rate, approximately?

    • A249 m³/s
    • B0.249 m³/s
    • C0.0249 m³/s
    • D2.49 m³/s
    Show answer and explanation

    Answer: B) 0.249 m³/s

    Use V = nRT/P with pressure in pascals: (10)(8.314)(300)/100,000 ≈ 0.249 m³/s.

    • AIncorrect. This comes from putting P = 100 (kPa) into the formula with R in J/(mol·K). The units don't match, so the answer is 1,000 times too large.
    • BCorrect. V = nRT/P = (10)(8.314)(300)/(100,000 Pa) ≈ 0.249 m³/s.
    • CIncorrect. This comes from converting 100 kPa to 1,000,000 Pa instead of 100,000 Pa, which makes the volume 10 times too small.
    • DIncorrect. This comes from converting 100 kPa to 10,000 Pa instead of 100,000 Pa, which makes the volume 10 times too large.

  6. Question 6

    An evaporator concentrates 1,000 kg/h of a 10 wt% solution to 50 wt%. The water evaporated is:

    • A900 kg/h
    • B500 kg/h
    • C200 kg/h
    • D800 kg/h
    Show answer and explanation

    Answer: D) 800 kg/h

    • AIncorrect. That's all the water in the feed.
    • BIncorrect. Use a solute balance.
    • CIncorrect. That's the product rate.
    • DCorrect. Solute 100 kg/h ends in 200 kg/h of product.

  7. Question 7

    A reactor carries out the reaction A + B → C. It is fed 10 mol of A and 8 mol of B, and 5 mol of C forms. How many moles of A remain unreacted?

    • A10 mol
    • B5 mol
    • C3 mol
    • D0 mol
    Show answer and explanation

    Answer: B) 5 mol

    Under 1:1 stoichiometry, each mole of C formed uses one mole of A. So 10 − 5 = 5 mol of A remain.

    • AIncorrect. This ignores the A used up by the reaction. Forming C consumes A.
    • BCorrect. The reaction is 1:1, so forming 5 mol of C uses 5 mol of A, leaving 10 − 5 = 5 mol.
    • CIncorrect. This is the B left over (8 − 5). The question asks about A.
    • DIncorrect. A is not the limiting reactant, and only 5 of the 10 mol of A react.

  8. Question 8

    A gas stream of 10 mol/s with cp = 30 J/(mol·K) is heated by 100 K. The heater duty is:

    • A30 kW
    • B3 kW
    • C300 kW
    • D0.3 kW
    Show answer and explanation

    Answer: A) 30 kW

    • ACorrect. Q = ṅcpΔT = 10(30)(100) W.
    • BIncorrect. Recheck the arithmetic.
    • CIncorrect. Recheck the arithmetic.
    • DIncorrect. Recheck the arithmetic.

  9. Question 9

    100 kg/h of feed approaches a unit, and 20 kg/h bypasses it. How much feed passes through the unit?

    • A100 kg/h
    • B120 kg/h
    • C20 kg/h
    • D80 kg/h
    Show answer and explanation

    Answer: D) 80 kg/h

    • AIncorrect. Part of the feed bypasses.
    • BIncorrect. The bypass is subtracted.
    • CIncorrect. That's the bypass.
    • DCorrect. Split-point balance: 100 − 20.

  10. Question 10

    A process has 100 mol/h of fresh feed and a 200-mol/h recycle stream. The recycle ratio (recycle/fresh feed) is:

    • A2
    • B0.5
    • C3
    • D300
    Show answer and explanation

    Answer: A) 2

    • ACorrect. 200 mol/h recycle ÷ 100 mol/h fresh feed.
    • BIncorrect. That's inverted.
    • CIncorrect. That's reactor feed over fresh feed.
    • DIncorrect. That's the reactor feed rate.

Material/Energy Balances: FAQs

How much of the FE exam is Material/Energy Balances?

Material/Energy Balances is 10% of the FE exam by the official exam guide's weighting, which on a 110-question form works out to roughly 11 questions. The real exam's exact split varies by form.

What does the Material/Energy Balances domain cover?

The largest FE Chemical domain: mass and energy balances on processes with and without reaction, including recycle, bypass and purge.

How should I study Material/Energy Balances for FE?

Solve every balance problem the same way: sketch the flowsheet, label all streams, choose a basis and count unknowns before you write an equation.

Where can I practise more Material/Energy Balances questions?

This page has 10 free Material/Energy Balances questions with answers. The ExamWize FE question bank has 60 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Other FE topics

Also: 15 free questions across all topics, the FE cheat sheet and the study guide.

Get Material/Energy Balances exam-ready

The full FE bank has 60 Material/Energy Balances questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

See the full FE practice examsTake the free diagnostic

Not affiliated with NCEES; questions are original, written from the official exam outline, and never copied from the real exam.