Phase Behavior, Pure Component PVT and Fluid Equilibria

Central engineering problem

Phase equilibrium depends on temperature, pressure and composition; simple models are instructive but are not universally accurate.

The unit develops four tightly connected ideas. A process description should become a quantitative and testable claim: an explicit boundary, evidence for values, dimensional consistency, and a way to distinguish real physical behavior from model simplifications. The relevant measurements and operating envelopes must be named before making a process decision. In introductory chemical engineering, a plausible numerical result is necessary but not sufficient; it must also obey conservation, physical feasibility and operational safety.

Learning outcomes

After studying this unit, a student should be able to explain the physical role of the four topics, construct or interpret a simple numerical representation, identify a falsifying measurement, and document how the assumptions restrict the result. Numerical work should use explicit material or energy bases and show uncertainty or sensitivity whenever decisions depend on approximate data.

Lesson sequence

• [Gases and pressure-volume-temperature relations](../lessons/unit-06-lesson-01.html)
• [Vapor pressure and phase maps](../lessons/unit-06-lesson-02.html)
• [Ideal mixture vapor-liquid equilibrium](../lessons/unit-06-lesson-03.html)
• [Flash calculations and phase fractions](../lessons/unit-06-lesson-04.html)

Interactive laboratories

• [Lab 11: Ideal gas pressure in a vessel](../labs/lab-11.html)
• [Lab 12: Ideal binary VLE and vapor enrichment](../labs/lab-12.html)
• [Lab 13: Binary flash and Rachford–Rice root](../labs/lab-13.html)

Synthesis activity

Build a one-page process evidence sheet that distinguishes four columns: directly observed quantities, derived quantities, estimated properties, and external constraints. For each lesson's primary equation, test whether a 10% change in its dominant input yields a proportionate response. Explain exceptions, including compositions bounded between zero and one and physical states requiring feasibility checks. Conclude with at least two measurements needed to confirm the result in a real laboratory or plant.

Assessment standard

Successful work must show a system boundary or process purpose, symbolic equations before values, units during substitution, an independent conservation or limiting-case check, and a concise explanation of where a more advanced treatment is required. Attach plots only when their input assumptions are documented. The purpose is transferable engineering reasoning rather than memorized formula application.

Unit 6.1: Gases and pressure-volume-temperature relations

Chemical Engineering Fundamentals · Unit 6: Phase behavior

Purpose and measurable learning outcomes

The ideal-gas law is a reference model, not a universal equation of state. State absolute pressure, absolute temperature and volume in consistent units. At high pressures or near saturation a compressibility factor may be needed. A sealed vessel with temperature change can experience pressure rise, but the vessel design must use verified properties and mechanical limits.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

To test an ideal-gas assumption, compare the temperature and pressure region with known phase boundaries and availability of real-gas data. At constant moles and volume, P2/P1=T2/T1 if temperature is in kelvin. Thus 290→350 K raises absolute pressure by a factor 350/290≈1.207. A vessel at 100 kPa absolute becomes about 120.7 kPa absolute. This ratio does not establish mechanical integrity or pressure rating; it merely translates one thermodynamic assumption to an expected pressure trend.

Governing quantitative relationship

P V = n R T; with n=2 mol, T=300 K and V=0.05 m³, P≈99.77 kPa using R=8.314 J/(mol K).

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

A rigid vessel has constant n and V while temperature increases from 290 to 350 K. Determine ideal pressure ratio, then explain where the approximation could fail.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Entering gauge pressure into an equation requiring absolute pressure.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. A rigid vessel has constant n and V while temperature increases from 290 to 350 K. Determine ideal pressure ratio, then explain where the approximation could fail. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Entering gauge pressure into an equation requiring absolute pressure. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 11](../labs/lab-11.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-06.html) · [Book contents](../index.html)

Unit 6.2: Vapor pressure and phase maps

Chemical Engineering Fundamentals · Unit 6: Phase behavior

Purpose and measurable learning outcomes

Vapor pressure depends on temperature; a liquid boils when its vapor pressure equals ambient pressure under simplified equilibrium conditions. Plotting a phase boundary requires a validated correlation and correct units. Mixtures may have different bubble and dew conditions. The Antoine equation can be convenient but has substance-specific constants and limited fit ranges; never reuse coefficients outside their ranges.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

Pressure changes the equilibrium boiling condition because evaporation and condensation equilibrate at a pressure-dependent saturation state. A qualitative vapor-pressure graph should have a clear temperature axis and use credible fitted data. Avoid conflating a metastable superheated liquid, nucleation behavior and equilibrium boiling. For real mixtures, phase boundaries may span a temperature interval and evolve with composition. A process designer should obtain validated vapor pressures for each component and check whether the proposed operating point approaches two-phase flow that could disrupt pumping or heat transfer.

Governing quantitative relationship

For an illustrative Clausius–Clapeyron approximation, ln(P2/P1)= -(ΔHvap/R)(1/T2−1/T1), with T in kelvin.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

Compare a boiling process at sea-level pressure with reduced pressure. Explain qualitatively why vacuum can reduce boiling temperature.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Assuming phase equilibrium and boiling temperatures are unchanged when pressure changes.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. Compare a boiling process at sea-level pressure with reduced pressure. Explain qualitatively why vacuum can reduce boiling temperature. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Assuming phase equilibrium and boiling temperatures are unchanged when pressure changes. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 12](../labs/lab-12.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-06.html) · [Book contents](../index.html)

Unit 6.3: Ideal mixture vapor-liquid equilibrium

Chemical Engineering Fundamentals · Unit 6: Phase behavior

Purpose and measurable learning outcomes

Raoult’s law for an ideal liquid with an ideal vapor gives y_i P = x_i P_i^sat at a fixed temperature. Summing vapor partial pressures gives the bubble pressure. Systems with strong nonideality or azeotropes require activity-coefficient or other appropriate models; ideal results are a baseline only. An x-y diagram helps visualize enrichment but cannot determine stage count alone.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

At fixed temperature with illustrative ideal vapor pressures 80 kPa and 20 kPa, a liquid composition x_A=0.4 gives bubble pressure P=0.4×80+0.6×20=44 kPa and vapor composition y_A=(0.4×80)/44≈0.727. This enrichment occurs because A is more volatile in the model. If its vapor pressure were equal to B's, then y_A=x_A, and simple equilibrium contact would not separate them. Real systems may show nonideality or azeotropes, so the calculation is explanatory rather than predictive for an unspecified chemical pair.

Governing quantitative relationship

For x_A=0.4, P_A^sat=80 kPa and P_B^sat=20 kPa: P=44 kPa; y_A=32/44≈0.7273.

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

At fixed T, increase liquid mole fraction of the more volatile species. Plot vapor mole fraction and explain why the diagonal marks equal phase compositions.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Claiming that Raoult’s law holds for electrolytes and strongly nonideal mixtures.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. At fixed T, increase liquid mole fraction of the more volatile species. Plot vapor mole fraction and explain why the diagonal marks equal phase compositions. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Claiming that Raoult’s law holds for electrolytes and strongly nonideal mixtures. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 13](../labs/lab-13.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-06.html) · [Book contents](../index.html)

Unit 6.4: Flash calculations and phase fractions

Chemical Engineering Fundamentals · Unit 6: Phase behavior

Purpose and measurable learning outcomes

An isothermal flash separates one feed into equilibrium vapor and liquid when K-values and overall composition permit two phases. Solve component balances and y_i=K_i x_i simultaneously. The Rachford–Rice equation gives vapor fraction with known K-values; if both K-values lie on the same side of unity, there may be no two-phase solution. Check compositions sum to unity and fractions lie between zero and one.

After completing this lesson, distinguish the principal measured variables from dependent calculations, explain the role of the selected boundary or material system, and defend the operating range in which the simplified model is credible. Use the lesson's worked calculation, then change one assumption and describe how the governing equation or interpretation changes. Do not assume that matching a single numerical result validates the entire physical process.

Technical development

For the binary case z_A=0.5, K_A=2 and K_B=0.5, the Rachford–Rice expression at vapor fraction β is 0.5/(1+β)−0.25/(1−0.5β). Setting it to zero yields β=0.5. Therefore x_A=0.5/1.5=1/3 and y_A=2/3. Composition of B follows by complement and the feed is exactly the weighted sum of vapor and liquid products. A robust numerical solver must first evaluate function signs at β=0 and β=1 and decline to invent a two-phase root when both signs agree.

Governing quantitative relationship

Flash balance: z_i=(1−β)x_i+β y_i; x_i=z_i/[1+β(K_i−1)].

A physically interpretable engineering calculation is written first using named quantities and units. Compute at a stated operating condition, check that every term has compatible dimensions, and then compare the answer with conservation and expected practical bounds. Record whether a quantity was measured, calculated from another measurement, specified by a manufacturer, or merely assumed for illustration.

Reasoning about model scope

The equation is deliberately narrower than a full industrial design. It can illuminate a conserved quantity, a thermodynamic trend, an equipment response or a measurement inconsistency, but omitted behaviors may dominate near phase change, rapid transients, strong chemical nonideality, severe fouling or abnormal operations. When results depend heavily on a single assumed coefficient, an engineer should gather better evidence for that coefficient instead of adding more significant digits to the output.

A useful independent test asks whether the model behaves sensibly when an input approaches a limiting case. A zero feed should not generate positive material output. A concentration from two conserved mixed streams should remain in the interval bounded by those inlet concentrations. A heat-transfer model should not imply an impossible cold-to-hot flow without external work. If such a check fails, re-examine the boundary, equation and units before inspecting the software.

Worked investigation

For a binary mixture with z_A=0.5, K_A=2 and K_B=0.5, solve for β; verify vapor and liquid compositions.

Suggested solution method. Identify known and unknown quantities explicitly. Choose a consistent basis (for example kg/h, kmol/h or kW) and write a separate balance for every conserved component or for energy. Substitute values only after solving the symbolic relationship. Evaluate any feasibility constraint such as nonnegative inventories, a physically possible composition or a positive temperature driving force. Reconcile the answer against another observation wherever possible, and state what additional measurements would distinguish competing explanations.

Diagnostic misconception

Incorrect shortcut: Forcing a two-phase solution when the feed equilibrium state is actually one phase.

To correct this, state precisely which simplifying assumption would be required for the shortcut to work and test that assumption against real material, property or operating data. Small spreadsheet residuals do not independently establish physical correctness. Never silently hide an unaccounted side stream, unknown phase transition or unavailable safety limit.

Practice questions with answer guidance

1. Quantitative reconstruction. Starting from the relationship above, write the governing equation symbolically, label every variable with units, and reproduce its stated numerical example. Answer guidance: Every substituted term must retain its units until cancellation; report the final result on the same basis as the described process. Check the arithmetic using a second calculation, ideally a component or energy balance.

2. Case diagnosis. For a binary mixture with z_A=0.5, K_A=2 and K_B=0.5, solve for β; verify vapor and liquid compositions. Answer guidance: Distinguish what can be calculated from the supplied data from what remains unknown. List missing properties or measurements before declaring a real operating decision justified.

3. Sensitivity and skepticism. Change the most influential input by 10% while keeping other assumptions fixed. Predict whether the output increases, decreases or remains unchanged, and explain the mechanism. Answer guidance: Differentiate the relationship qualitatively or numerically; an output that becomes physically impossible indicates a model-limit failure, not a valid prediction.

4. Professional communication. Forcing a two-phase solution when the feed equilibrium state is actually one phase. Answer guidance: Replace this shortcut with a version-controlled note containing correct variable definitions, relevant uncertainty, one numerical counterexample and a plan for validation.

Simulation-led learning

Open [interactive laboratory 11](../labs/lab-11.html), which exercises a related quantitative process model. Check the initial output by hand; use the exported curve to identify its dominant sensitivity. In the accompanying lab notes, distinguish which model inputs correspond to directly measurable quantities and which would require property correlations or empirical fitting. Record a falsifiable observation rather than describing the curve as simply realistic.

Further study

Compare this introductory method with material-and-energy balances, chemical engineering thermodynamics or process systems analysis, as applicable. For an industrial application, consult substance-specific property measurements, current engineering standards and the site's written safety procedures. The laboratory model is for learning, not for commissioning or regulatory evidence.

[← Unit overview](../units/unit-06.html) · [Book contents](../index.html)

Unit 6 applied engineering project — A low-pressure vapor–liquid demonstration vessel

Setting and purpose

An educational binary mixture has supplied ideal vapor-pressure and K-value assumptions. This is a synthetic teaching case, not a recommendation to operate a real process. Students must select reasonable illustrative numbers, label every invented number as an assumption, and keep all units, reference conditions and composition bases visible. The purpose is to assemble the unit's concepts into a consistent model that a reviewer can challenge.

Engineering question

Compute bubble pressure and vapor enrichment, test the flash solution and identify conditions where ideal models should not be trusted. State a single primary decision being supported, such as selecting a material-balance boundary, accepting a measurement, identifying a missing outlet or prioritizing an additional experiment. Do not use an unsupported plant-wide profit number or an unverified regulatory threshold to justify the decision.

Required evidence and calculation plan

1. Write a process statement that defines input materials, expected outputs and the relevant boundaries. Distinguish a batch inventory from a flow and give the measurement time basis.
2. Build an input data table with dimensions, source type, uncertainty estimate and acceptable bounds. Separate readings from engineering assumptions.
3. Derive at least three equations rather than relying only on a calculator. For each, show a dimensional check and a feasible limiting case. Include a separate component balance when a concentration or reaction is involved.
4. Carry out two contrasting cases: a nominal baseline and a plausible changed operating condition. If the changed condition violates the simplified model, stop and write that result as an important finding.
5. Use the unit laboratories as computational demonstrations; export plots, retain input settings, and compare with a direct hand calculation. Plots are evidence about a mathematical model, not proof about an operating plant.
6. Describe data or safety limitations. Include possible missing streams, property correlations, instrument bias, parameter dependence and common-cause uncertainty where they matter.
7. Communicate the result as a reproducible engineering note with an executive statement, flow diagram, equations, tables, a source list and an open list of unresolved questions.

Review checkpoints

• Conservation: material and energy accounting closure must be explicit; an unresolved residual is named, not silently forced to zero.
• Feasibility: compositions must be physically bounded and equipment temperatures and pressures checked against the model's assumptions.
• Traceability: a competent reader can identify exactly which values are assumed, measured or derived, and can reproduce the major quantities.
• Safety and ethics: no classroom calculation is presented as industrial relief sizing, pharmaceutical validation, field authorization or environmental compliance proof.

Deliverables

Submit one concise process diagram, one independently checkable calculation sheet, two simulation exports, a one-page uncertainty/sensitivity commentary and a 250-word statement on what evidence would change your conclusion. Defend the chosen model scope and openly identify a more advanced analysis needed before industrial deployment.

Unit 6 assessment: Phase behavior

These 12 problems combine quantitative reproduction, model validity, and audit methodology. Answers below are intended as diagnostic reasoning, not fabricated plant data.

Question 1: analysis of gases and pressure-volume-temperature relations

A rigid vessel has constant n and V while temperature increases from 290 to 350 K. Determine ideal pressure ratio, then explain where the approximation could fail.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 6.1. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 2: model validity

Entering gauge pressure into an equation requiring absolute pressure. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 3: quantitative audit

Use the lesson's worked equation: P V = n R T; with n=2 mol, T=300 K and V=0.05 m³, P≈99.77 kPa using R=8.314 J/(mol K). Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 5: analysis of vapor pressure and phase maps

Compare a boiling process at sea-level pressure with reduced pressure. Explain qualitatively why vacuum can reduce boiling temperature.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 6.2. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 6: model validity

Assuming phase equilibrium and boiling temperatures are unchanged when pressure changes. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 7: quantitative audit

Use the lesson's worked equation: For an illustrative Clausius–Clapeyron approximation, ln(P2/P1)= -(ΔHvap/R)(1/T2−1/T1), with T in kelvin. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 9: analysis of ideal mixture vapor-liquid equilibrium

At fixed T, increase liquid mole fraction of the more volatile species. Plot vapor mole fraction and explain why the diagonal marks equal phase compositions.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 6.3. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 10: model validity

Claiming that Raoult’s law holds for electrolytes and strongly nonideal mixtures. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 11: quantitative audit

Use the lesson's worked equation: For x_A=0.4, P_A^sat=80 kPa and P_B^sat=20 kPa: P=44 kPa; y_A=32/44≈0.7273. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.

Question 13: analysis of flash calculations and phase fractions

For a binary mixture with z_A=0.5, K_A=2 and K_B=0.5, solve for β; verify vapor and liquid compositions.

Answer guidance: State the material or energy basis, identify which unknown can be inferred and which requires additional data, and use the equation derived in lesson 6.4. If the case is numerical, retain units during substitution and check conservation. If qualitative, give a testable comparison, not an unsupported claim of safety or feasibility.

Question 14: model validity

Forcing a two-phase solution when the feed equilibrium state is actually one phase. Identify the assumption violated by this shortcut and supply one physically plausible counterexample. Explain whether the shortcut creates a systematic overestimate or underestimate under the conditions you chose.

Answer guidance: Begin with the definition of the reported quantity and its denominator; compare alternative physical bases. Where the bias direction depends on process conditions, state that dependence explicitly rather than forcing a single numerical answer.

Question 15: quantitative audit

Use the lesson's worked equation: Flash balance: z_i=(1−β)x_i+β y_i; x_i=z_i/[1+β(K_i−1)]. Perform an independent dimensional and limiting-case check. Explain what data would change the precision of the inferred result.

Answer guidance: Check dimensions and conservation first. A good audit records measurement range, calibration status, uncertainties and separate estimates for unmodeled phenomena.