Reaction Stoichiometry, Conversion, Selectivity and Yield

Use atom conservation and the extent of reaction to establish limits before evaluating conversion, selectivity and combustion products.

Core learning goals

• Explain and apply Balanced reactions and limiting reagents, including assumptions and independent verification.
• Explain and apply Conversion, yield and selectivity, including assumptions and independent verification.
• Explain and apply Elemental balances in combustion, including assumptions and independent verification.
• Explain and apply Reaction networks and atom accounting, including assumptions and independent verification.

Lessons and reading order

• [Lesson 3.1: Balanced reactions and limiting reagents](../lessons/unit-03-lesson-01.html)
• [Lesson 3.2: Conversion, yield and selectivity](../lessons/unit-03-lesson-02.html)
• [Lesson 3.3: Elemental balances in combustion](../lessons/unit-03-lesson-03.html)
• [Lesson 3.4: Reaction networks and atom accounting](../lessons/unit-03-lesson-04.html)

Unit synthesis: identify what is known

Use atom conservation and the extent of reaction to establish limits before evaluating conversion, selectivity and combustion products. A strong solution begins with a process sketch and a stream table. Write values to a stated basis, mark all missing data, and calculate degrees of freedom before attempting numerical iteration. A flow diagram is useful only if the stream symbols and assumptions can be traced into actual balance equations. If an unknown variable is introduced to close a balance, explain what physical instrument or property measurement would establish it.

Connecting the four lessons

The first lesson establishes a local quantity or concept, while the later lessons expose how its interpretation changes with additional process complexity. For example, mass fractions remain valid for a blend but reacting compositions need generation terms; heat duties may be linear in temperature under constant heat capacity but nonlinear near a phase transition. Develop a single reference stream table and compare how each analytical step changes when more units are added.

Diagnostic exercise

Assume an otherwise plausible design produces an impossible negative outlet or a reported overall recovery of 105%. Instead of clipping the number, trace which equation or boundary was omitted or whose units were inconsistent. Check whether the solver was overdetermined by a redundant balance or underdetermined by a missing composition. Document the correction and rerun your limiting-case tests.

A second diagnostic asks you to separate measured and assumed quantities. Label uncertainties if known; do not attach precision to idealized coefficients. A balance audit should preserve the original measurements and record any reconciliation separately. This habit will become important in the integrated case studies and final project.

Unit completion exercise

Draw one example flowsheet for this unit and formulate an overall balance plus two meaningful independent additional equations, if the process contains enough components. State why each equation is independent. Determine what unknowns remain and choose the cheapest credible measurement to close the problem. Explain whether the modified process is still steady, and assess one alternative operating condition without assuming unchanged performance.

Unit 3.1: Balanced reactions and limiting reagents

Book 2: Material and Energy Balances — Reaction stoichiometry and yield

What you will be able to do

Stoichiometric coefficients describe molar, not mass, ratios. Interpret n_i=n_i0+nu_i*xi; xi_max=min_i(n_i0/(-nu_i)) for consumed species and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Specialty-chemical reactor feed scheduling. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by balanced reactions and limiting reagents. Stoichiometric coefficients describe molar, not mass, ratios. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as n_i=n_i0+nu_i*xi; xi_max=min_i(n_i0/(-nu_i)) for consumed species. Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use unit consistency as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. For A+2B→C, 6 kmol A and 9 kmol B permit at most 4.5 kmol C; B limits the reaction. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. You must choose a balanced equation; a conversion percentage cannot repair an unbalanced reaction. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

Consider the industrial case: Specialty-chemical reactor feed scheduling. Before trusting a software result, identify temperature and pressure effects, instrument calibration, inventory fluctuations and unrecorded process streams. A perfectly balanced flowsheet can still be a poor representation of reality if one instrument reads systematically low. Conversely, a balance residual does not by itself prove a physical leak or chemical loss.

To decide whether further detail is necessary, first quantify the decision at issue. A rough balance may be sufficient to choose between two pilot runs but not to specify relief equipment, guarantee product quality, or assert environmental compliance. Explain which property or stream measurement would most reduce uncertainty, and how it could be obtained without introducing a new uncontrolled hazard.

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in n_i=n_i0+nu_i*xi; xi_max=min_i(n_i0/(-nu_i)) for consumed species scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

Prepare a second scenario in which the least certain input changes by 10% while the other stated conditions remain fixed. Estimate whether the output changes proportionally. If the result violates a conservation limit, retrace variable definitions. If it remains feasible, identify an observation that could distinguish between the original and changed scenarios.

Verification and critical-thinking questions

1. State the system boundary and draw the streams for balanced reactions and limiting reagents; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: stoichiometric coefficients describe molar, not mass, ratios?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: You must choose a balanced equation; a conversion percentage cannot repair an unbalanced reaction. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

The laboratory models in this volume can illustrate how a calculated response changes as conditions vary. Locate a related simulation in the book index, write down a prediction before operating its controls, and test whether the result is monotone, bounded or approaching an asymptotic limit. Compare at least one displayed numerical result with an independent calculation. A graphical match is not sufficient: test numerical values and units separately.

Further study

Consult the freely accessible LearnChemE Material and Energy Balances resources and the NIST Chemistry WebBook for property-data methodology. Use a suitable authoritative property model for real design rather than applying constant heat capacities or ideal-mixture assumptions indiscriminately.

Unit 3.2: Conversion, yield and selectivity

Book 2: Material and Energy Balances — Reaction stoichiometry and yield

What you will be able to do

Yield of desired product on feed differs from selectivity among reacted material. Interpret X_A=(n_Ain-n_Aout)/n_Ain; S_B/C=n_B/n_C when product stoichiometry matches and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Parallel isomerization and oxidation pathways. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by conversion, yield and selectivity. Yield of desired product on feed differs from selectivity among reacted material. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as X_A=(n_Ain-n_Aout)/n_Ain; S_B/C=n_B/n_C when product stoichiometry matches. Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use measurable stream composition as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. Of 100 kmol A fed, 70 reacts; 52 kmol desired B forms and 18 kmol unwanted C forms. Conversion is 70%, yield on feed 52%, and B/C selectivity 2.89. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. A high conversion alone does not imply a high useful-product yield. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

Consider the industrial case: Parallel isomerization and oxidation pathways. Before trusting a software result, identify temperature and pressure effects, instrument calibration, inventory fluctuations and unrecorded process streams. A perfectly balanced flowsheet can still be a poor representation of reality if one instrument reads systematically low. Conversely, a balance residual does not by itself prove a physical leak or chemical loss.

To decide whether further detail is necessary, first quantify the decision at issue. A rough balance may be sufficient to choose between two pilot runs but not to specify relief equipment, guarantee product quality, or assert environmental compliance. Explain which property or stream measurement would most reduce uncertainty, and how it could be obtained without introducing a new uncontrolled hazard.

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in X_A=(n_Ain-n_Aout)/n_Ain; S_B/C=n_B/n_C when product stoichiometry matches scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

Prepare a second scenario in which the least certain input changes by 10% while the other stated conditions remain fixed. Estimate whether the output changes proportionally. If the result violates a conservation limit, retrace variable definitions. If it remains feasible, identify an observation that could distinguish between the original and changed scenarios.

Verification and critical-thinking questions

1. State the system boundary and draw the streams for conversion, yield and selectivity; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: yield of desired product on feed differs from selectivity among reacted material?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: A high conversion alone does not imply a high useful-product yield. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

The laboratory models in this volume can illustrate how a calculated response changes as conditions vary. Locate a related simulation in the book index, write down a prediction before operating its controls, and test whether the result is monotone, bounded or approaching an asymptotic limit. Compare at least one displayed numerical result with an independent calculation. A graphical match is not sufficient: test numerical values and units separately.

Further study

Consult the freely accessible LearnChemE Material and Energy Balances resources and the NIST Chemistry WebBook for property-data methodology. Use a suitable authoritative property model for real design rather than applying constant heat capacities or ideal-mixture assumptions indiscriminately.

Unit 3.3: Elemental balances in combustion

Book 2: Material and Energy Balances — Reaction stoichiometry and yield

What you will be able to do

Oxygen needs and air nitrogen must be handled before wet or dry gas reporting. Interpret CH4+2O2→CO2+2H2O; n_N2=3.76*n_O2,in under dry-air approximation and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Boiler-stack oxygen analyzer with an excess-air calculation. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by elemental balances in combustion. Oxygen needs and air nitrogen must be handled before wet or dry gas reporting. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as CH4+2O2→CO2+2H2O; n_N2=3.76*n_O2,in under dry-air approximation. Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use physical limit cases as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. For 1 kmol methane at 25% excess air, O2 supplied is 2.5 kmol and N2 is 9.4 kmol. Wet exhaust has CO2 1, H2O 2, O2 0.5 and N2 9.4 kmol. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. Dry gas fractions exclude condensed water; wet gas fractions do not. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

Consider the industrial case: Boiler-stack oxygen analyzer with an excess-air calculation. Before trusting a software result, identify temperature and pressure effects, instrument calibration, inventory fluctuations and unrecorded process streams. A perfectly balanced flowsheet can still be a poor representation of reality if one instrument reads systematically low. Conversely, a balance residual does not by itself prove a physical leak or chemical loss.

To decide whether further detail is necessary, first quantify the decision at issue. A rough balance may be sufficient to choose between two pilot runs but not to specify relief equipment, guarantee product quality, or assert environmental compliance. Explain which property or stream measurement would most reduce uncertainty, and how it could be obtained without introducing a new uncontrolled hazard.

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in CH4+2O2→CO2+2H2O; n_N2=3.76*n_O2,in under dry-air approximation scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

Prepare a second scenario in which the least certain input changes by 10% while the other stated conditions remain fixed. Estimate whether the output changes proportionally. If the result violates a conservation limit, retrace variable definitions. If it remains feasible, identify an observation that could distinguish between the original and changed scenarios.

Verification and critical-thinking questions

1. State the system boundary and draw the streams for elemental balances in combustion; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: oxygen needs and air nitrogen must be handled before wet or dry gas reporting?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: Dry gas fractions exclude condensed water; wet gas fractions do not. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

The laboratory models in this volume can illustrate how a calculated response changes as conditions vary. Locate a related simulation in the book index, write down a prediction before operating its controls, and test whether the result is monotone, bounded or approaching an asymptotic limit. Compare at least one displayed numerical result with an independent calculation. A graphical match is not sufficient: test numerical values and units separately.

Further study

Consult the freely accessible LearnChemE Material and Energy Balances resources and the NIST Chemistry WebBook for property-data methodology. Use a suitable authoritative property model for real design rather than applying constant heat capacities or ideal-mixture assumptions indiscriminately.

Unit 3.4: Reaction networks and atom accounting

Book 2: Material and Energy Balances — Reaction stoichiometry and yield

What you will be able to do

Multiple reactions require a separate extent for each independent reaction. Interpret n_out=n_in+N*xi where N is the species-by-reaction stoichiometric matrix and demonstrate how it follows from an appropriate boundary. Identify whether the equation describes an overall, species, elemental, or energy balance; discuss what is actually measured and the conditions under which the balance is valid.

Essential physical insight

Reaction-pathway analysis with intermediate B losses. The critical objective is not to memorize a plug-in formula but to recognize conserved quantities and define the physical process correctly. Break the problem into stream variables, known specifications, unknowns, and constitutive or property relationships. A numerical estimate is an engineering claim only if its basis and limitations are reproducible.

Deriving the balance from the process boundary

Start from the observations implied by reaction networks and atom accounting. Multiple reactions require a separate extent for each independent reaction. Represent each material crossing the boundary with a signed rate and state its measurement basis. If the equipment retains material, include an accumulation term. A balance written per second cannot be directly combined with a plant log written per shift without converting the interval; similarly, mass fractions and molar compositions cannot be used in the same species account without a molecular-weight transformation. Before any algebra, list feed states, outlet states, any generation or consumption, and the measured inventory change.

Write the central relationship as n_out=n_in+N*xi where N is the species-by-reaction stoichiometric matrix. Read every variable aloud with its units, explaining which terms are independent measurements and which are derived. For a process with reaction, the component generation term is not optional. For a nonreactive mixer, a nonzero computed generation indicates a modeling or measurement mistake. Use independent balance closure as the first diagnostic check, and then compare the predicted result against simple physical limits.

A worked calculation and its interpretation

Illustrative case. For A→B and B→C, extents 4 and 1 kmol from 10 kmol A yield A=6, B=3 and C=1 kmol. This numerical calculation is a worked illustration and not a measurement from an operating facility. Write the stream table with at least one named component, a physical total rate, and a units column. Substitute numbers into the governing equation and solve the unknown before rounding. Keep at least one more significant figure in intermediate calculations than will be reported to the operator.

The numerical result has value only within the stated assumptions. Identical observed overall conversion can hide different intermediate-product inventory. Confirm that any calculated component fraction is between zero and one, that recoveries never exceed their admissible range and that energy duties obey the stated sign convention. A unit conversion error can shift a prediction by factors of 1,000 or 3,600 even when the arithmetic appears internally consistent.

Why the answer changes in a real plant

Consider the industrial case: Reaction-pathway analysis with intermediate B losses. Before trusting a software result, identify temperature and pressure effects, instrument calibration, inventory fluctuations and unrecorded process streams. A perfectly balanced flowsheet can still be a poor representation of reality if one instrument reads systematically low. Conversely, a balance residual does not by itself prove a physical leak or chemical loss.

To decide whether further detail is necessary, first quantify the decision at issue. A rough balance may be sufficient to choose between two pilot runs but not to specify relief equipment, guarantee product quality, or assert environmental compliance. Explain which property or stream measurement would most reduce uncertainty, and how it could be obtained without introducing a new uncontrolled hazard.

Guided redesign exercise

Imagine a proposed 20% increase in the process feed or load. Identify which terms in n_out=n_in+N*xi where N is the species-by-reaction stoichiometric matrix scale linearly and which could change because of capacity limits, residence time, equilibrium, or heat transfer. Recompute the balance on a consistent time basis and explain why unchanged efficiency or composition may be an unreasonable assumption. Do not silently extrapolate a laboratory coefficient outside the range where it was measured.

Prepare a second scenario in which the least certain input changes by 10% while the other stated conditions remain fixed. Estimate whether the output changes proportionally. If the result violates a conservation limit, retrace variable definitions. If it remains feasible, identify an observation that could distinguish between the original and changed scenarios.

Verification and critical-thinking questions

1. State the system boundary and draw the streams for reaction networks and atom accounting; label every unknown rather than assigning guessed values.
2. Explain the difference between an identity enforced by conservation and an empirical correlation that may fail at changed conditions.
3. What measurement would most directly test the assumption: multiple reactions require a separate extent for each independent reaction?
4. Recompute the illustrative case using a different but consistent calculation basis. Which outputs must remain invariant?
5. Construct a limiting-case test and explain precisely what would constitute a physically impossible result.

Practical check: Identical observed overall conversion can hide different intermediate-product inventory. A satisfactory answer should separate the equation, numerical result, process interpretation, and limitations rather than ending with a number alone.

Practical laboratory connection

The laboratory models in this volume can illustrate how a calculated response changes as conditions vary. Locate a related simulation in the book index, write down a prediction before operating its controls, and test whether the result is monotone, bounded or approaching an asymptotic limit. Compare at least one displayed numerical result with an independent calculation. A graphical match is not sufficient: test numerical values and units separately.

Further study

Consult the freely accessible LearnChemE Material and Energy Balances resources and the NIST Chemistry WebBook for property-data methodology. Use a suitable authoritative property model for real design rather than applying constant heat capacities or ideal-mixture assumptions indiscriminately.

Applied project 3: Recycled solvent wash with purge and emission accounting

Scenario and process objective

A purification system reuses an organic wash solvent. Fresh solvent enters to replace losses, a recovery condenser returns most vaporized solvent, and a small bleed prevents accumulation of contaminants. A naive calculation claims that nearly all solvent is recovered because recycle flow is large, even though the plant has no validated vent composition measurement.

The project must be documented as a sequence of claims: identify what conservation enforces, which property data are assumed, which quantities are operator observations, and which decisions remain uncertain. Prepare a separate stream table for every external feed or outlet. Do not insert convenient values for missing streams and then present the case as uniquely solved. A correctly identified underdetermined model is more valuable than an unjustified numerical answer.

Calculation and reference result

Treat total flow and each significant species separately. If fresh contaminant ingress is 1.5 kg/h and its mass fraction in the sole purge stream is 0.075, steady contaminant balance requires purge of 20 kg/h. The contaminant mass out equals 1.5 kg/h irrespective of total internal circulation. Recovery efficiency must be calculated from solvent component flows, not from the mass of the recycled mixture.

The figures above are idealized training values; they are not operational measurements. Repeat the calculation independently using base SI units and show at least one back-substitution into the original overall or species balance. Keep dimensional conversions visible, especially if a heat rate passes between kJ/h and kW or a composition passes between percent and fraction.

Model criticism and operating context

The simple result fails when contaminants react, separate into another product stream, accumulate in tanks or escape through unmeasured vents. A reliable mass-balance audit compares meters at a matched time basis and inventories at interval endpoints. Do not assume the condenser can handle arbitrary recycle throughput without energy and hydraulic consequences.

A design report needs a statement of operating range and expected effects that the simplified equations leave out. For example, thermodynamic equilibrium may be inappropriate during a rapid transient; a nominal heat-transfer coefficient may depend on fouling or regime; a flow meter may give an average that is misaligned with an inventory sampling time. Identify which omitted effect could reverse the preferred operating decision.

Required investigation

Vary the purge contaminant mass fraction from 3% to 15%; calculate required purge and discuss the tradeoff between solvent loss and contamination. Outline a measurement campaign to distinguish a false mass closure from a real emission.

Provide a graphical sensitivity study with clearly labeled axes and units. Use at least two independent checks on the reported values. One check must be a conservation identity and the other a dimensional, physical-bounds, or alternative-method check. If the case is not fully determined, specify the least expensive measurement that would make the next calculation defensible, and quantify how measurement uncertainty could influence the decision.

Extension: implementation and quality assurance

Design a two-stage implementation plan: first, a low-cost experiment or audit, and second, a revised model calibrated with those observations. Decide how you would document instrumentation, calibration, sampling and data provenance. Provide a concise statement of operational risks that would prevent deployment of the model without expert supervision.

Decision memo template

• What is known: state the measured feed and product values, date range, units and calculation basis.
• What is calculated: identify conserved totals, composition conversions and any heat duty.
• What is assumed: list ideal-gas behavior, perfect mixing, constant heat capacity, reaction completion or transfer efficiency only if used.
• What remains uncertain: name unmeasured streams, material properties or error correlations.
• What to do next: propose a specific measurement and the change in decision it could permit.

Questions for viva or peer discussion

1. Which equation would become invalid if inventory changed over the measurement window?
2. Can a numerically closed overall mass balance conceal a large component imbalance? Construct an example.
3. What is the most dangerous units mistake for this case, and what magnitude would it introduce?
4. Explain the effect of a 10% feed increase on both production and utility rates, including capacity limits.
5. What evidence would allow a simplified teaching model to support a plant engineering decision?

Assessment — Unit 3: Reaction stoichiometry and yield

These questions demand a calculation or a defended explanation. State units and assumptions for every numerical answer.

Topic 3.1: Balanced reactions and limiting reagents

1. Derivation. Build a balance for: Specialty-chemical reactor feed scheduling. Derive the expression `n_i=n_i0+nu_i*xi; xi_max=min_i(n_i0/(-nu_i)) for consumed species` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: For A+2B→C, 6 kmol A and 9 kmol B permit at most 4.5 kmol C; B limits the reaction. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: You must choose a balanced equation; a conversion percentage cannot repair an unbalanced reaction. Identify the failed assumption and describe a corrective measurement.

4. Sensitivity. Change the most influential given input by +10%, leaving other inputs fixed. Determine the new result where the data suffice; otherwise explicitly name the missing information.

5. Boundary test. Present a physically meaningful limit and show how the predicted result behaves. State whether a thermodynamic property correlation remains valid in that limit.

Topic 3.2: Conversion, yield and selectivity

1. Derivation. Build a balance for: Parallel isomerization and oxidation pathways. Derive the expression `X_A=(n_Ain-n_Aout)/n_Ain; S_B/C=n_B/n_C when product stoichiometry matches` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: Of 100 kmol A fed, 70 reacts; 52 kmol desired B forms and 18 kmol unwanted C forms. Conversion is 70%, yield on feed 52%, and B/C selectivity 2.89. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: A high conversion alone does not imply a high useful-product yield. Identify the failed assumption and describe a corrective measurement.

4. Sensitivity. Change the most influential given input by +10%, leaving other inputs fixed. Determine the new result where the data suffice; otherwise explicitly name the missing information.

5. Boundary test. Present a physically meaningful limit and show how the predicted result behaves. State whether a thermodynamic property correlation remains valid in that limit.

Topic 3.3: Elemental balances in combustion

1. Derivation. Build a balance for: Boiler-stack oxygen analyzer with an excess-air calculation. Derive the expression `CH4+2O2→CO2+2H2O; n_N2=3.76*n_O2,in under dry-air approximation` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: For 1 kmol methane at 25% excess air, O2 supplied is 2.5 kmol and N2 is 9.4 kmol. Wet exhaust has CO2 1, H2O 2, O2 0.5 and N2 9.4 kmol. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: Dry gas fractions exclude condensed water; wet gas fractions do not. Identify the failed assumption and describe a corrective measurement.

4. Sensitivity. Change the most influential given input by +10%, leaving other inputs fixed. Determine the new result where the data suffice; otherwise explicitly name the missing information.

5. Boundary test. Present a physically meaningful limit and show how the predicted result behaves. State whether a thermodynamic property correlation remains valid in that limit.

Topic 3.4: Reaction networks and atom accounting

1. Derivation. Build a balance for: Reaction-pathway analysis with intermediate B losses. Derive the expression `n_out=n_in+N*xi where N is the species-by-reaction stoichiometric matrix` or explain why an additional relationship is necessary.

2. Quantitative check. Recalculate this illustrative scenario without quoting the reported result: For A→B and B→C, extents 4 and 1 kmol from 10 kmol A yield A=6, B=3 and C=1 kmol. Record a self-check based on conservation.

3. Error diagnosis. A colleague proposes an answer that contradicts this principle: Identical observed overall conversion can hide different intermediate-product inventory. Identify the failed assumption and describe a corrective measurement.

4. Sensitivity. Change the most influential given input by +10%, leaving other inputs fixed. Determine the new result where the data suffice; otherwise explicitly name the missing information.

5. Boundary test. Present a physically meaningful limit and show how the predicted result behaves. State whether a thermodynamic property correlation remains valid in that limit.

Grading rubric

Award credit for a correctly defined boundary and flow basis (25%), an equation with independent unknowns (25%), numerical units and magnitude checks (20%), critical assumptions and uncertainty (20%), and readable presentation (10%). More digits are not a substitute for property data.