First investigate whether activity data satisfy a thermodynamic constraint. Then find a stable liquid split and check its material balance. Follow the narrated slides, pause to calculate, and use Labs 03 and 04.
180 min total study time33:11 recording31 slidesEnglish male narration + captions
The 33:11 recording is included in the approximately 180-minute lesson. The remaining time is for calculations, the labs, a ten-minute break, self-review and feedback. Timing headings on slides show elapsed study time, not MP4 timestamps. Pause as long as needed; the recording does not include exercise-length silence.
At study minute 50 open Lab 03. After the break and hand calculation, open Lab 04 at minute 120. Follow worksheet sections A-I in order.
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Slide 1 of 31Lesson introduction
Thermodynamic consistency and liquid stability
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Transcript · Slide 1
Welcome to Week Three. This lesson begins with a question raised by our work in Lab Eight. If a model fits the observations closely, how much confidence should we place in those observations? We will examine thermodynamic consistency first, then move to a different question: when does a liquid mixture separate into two stable liquids? The lesson replaces our classroom session during the holiday. Allow about three hours altogether, including watching, calculations, Lab investigations, a break, and the closing reflection. The recording is only one part of that time. Keep your own answers and pause whenever an activity is assigned.
Keep the hand-example endpoints 0.20 and 0.80 separate from the endpoints calculated by Lab 04. Record both the input settings and the evidence for your conclusion.
Finish the Session 3 reflection and feedback
At study minutes 165-172, attempt worksheet H1-H4, then check the worked solutions and retain your corrections. At minutes 172-177, open the Session 3 exit ticket and feedback form.
Use the concept answer for the existing LLE question. In the evidence answer, include your Lab 03 area-versus-local comparison, its settings, scores and one limitation. Add your Lab 04 balance if helpful. At minutes 177-180, finish feedback, submit once and wait for Response received.
The form is anonymous and does not identify individual attendance. The video player and Lab exports do not submit assignments. Keep your worksheet, original attempts, corrections and Lab exports or screenshots together. All required work, including the break and this reflection, is inside the 180-minute lesson.
Full narration transcript · includes checks and solutions
Attempt the worksheet questions before reading their checks. The text below matches the spoken narration. You can download it or print this page after expanding the transcript.
Slide 1: Thermodynamic consistency and liquid stability
Recording 0:00 | Lesson introduction
Welcome to Week Three. This lesson begins with a question raised by our work in Lab Eight. If a model fits the observations closely, how much confidence should we place in those observations? We will examine thermodynamic consistency first, then move to a different question: when does a liquid mixture separate into two stable liquids? The lesson replaces our classroom session during the holiday. Allow about three hours altogether, including watching, calculations, Lab investigations, a break, and the closing reflection. The recording is only one part of that time. Keep your own answers and pause whenever an activity is assigned.
Your action: Listen, then continue through the lesson.
Slide 2: Your independent lesson
Recording 0:49 | Lesson introduction
Start by opening the four-page practice worksheet and the three-page Lab guide. Their links are on the lesson page and this slide. You can print the worksheet, annotate the PDF, or write in a notebook using the same question labels. Have a calculator ready. Keep the slide deck available beside the video so that you can follow its links. The worked solutions are a separate document. Open the relevant section only after you have attempted the corresponding questions. The background reading is optional; you do not need to complete another reading assignment before starting. All preparation belongs inside today's first fifteen minutes. Pause here briefly to arrange the files, then continue to the schedule. You can work through the entire lesson independently.
Your action: Pause briefly to open the slides, worksheet and Lab guide. Keep the solutions closed. Preparation is included in the first 15 minutes.
Slide 3: The 180-minute route
Recording 1:44 | Lesson introduction
The times on the slides are elapsed study time, not video timestamps. They include both listening and doing the work. During the first fifteen minutes, review Lab Eight and calculate one activity coefficient. Next, spend twenty minutes on the Gibbs-Duhem constraint and its assumptions. A fifteen-minute hand calculation prepares you for Lab Three. The Lab comparison and interpretation take you to minute ninety. Then take a ten-minute break. From minute one hundred, examine stability and the lever rule before carrying out the Lab Four investigation. The final fifteen minutes are for self-review, the exit ticket, and feedback. Use these times as approximate guides. A pause for calculation uses the remaining time in its block; it is not added on top of three hours. Move forward when you have recorded the required evidence.
Your action: Listen, then continue through the lesson.
Slide 4: Review attempt · 0–10 min
Recording 2:47 | Elapsed study time: 0-10 min
Turn to page one, questions A one through A three. First, define x, y, z, and gamma in your own words. Keep phase composition separate from the overall mixture composition. Next, calculate gamma one from the supplied synthetic Lab Eight observation. Multiply the vapor mole fraction by total pressure, then divide by the liquid mole fraction times the saturation pressure. Both pressures are in kilopascals, so their units cancel. Use the full values printed on the worksheet rather than trying to copy every digit from the narration. Compare your answer with the exponential given in A two. Finally, answer whether a small fitting error proves thermodynamic consistency. If you need a reminder, use one relevant chapter of the Lab Eight walkthrough within this review block. Pause now and finish your attempt before the next slide reveals the check.
Your action: Pause now. Complete worksheet p. 1 A1–A3 before showing the Review check slide. Use the remainder of minutes 0–10, including preparation.
Slide 5: Review check · 10–15 min
Recording 3:49 | Elapsed study time: 10-15 min
Compare these statements with your answers. X one describes component one's mole fraction in the liquid, and y one describes its mole fraction in the vapor. Z one refers to the overall mixture. Gamma one is an activity coefficient: multiplying it by the liquid mole fraction gives liquid activity on the chosen pure-liquid standard state. The calculated gamma is about one point four nine one five four five. Taking the exponential of the rounded logarithm gives essentially the same answer; the final-digit difference comes from rounding. This inference uses ideal vapor and a negligible Poynting correction. For A three, a close fit shows that the selected model reproduces the observations under its assumptions. Consistency asks whether the inferred properties obey a thermodynamic relationship. Keep any correction beside your original answer, then continue.
Your action: Check and correct A1–A3 on worksheet p. 1. If you opened the Lab 08 video, close it. Continue at approximately study minute 15.
Slide 6: Gibbs–Duhem · 15–21 min
Recording 4:55 | Elapsed study time: 15-21 min
Now consider a binary liquid at fixed temperature and pressure. The Gibbs-Duhem equation connects changes in its two activity coefficients. If one coefficient changes with composition, the other cannot be chosen independently. Their mole-fraction-weighted logarithmic changes must sum to zero. This is a constraint on a collection of composition-dependent properties, rather than a test of one isolated gamma value. The second equation defines dimensionless excess Gibbs energy by weighting the two log activity coefficients. Under the same fixed conditions, the slope of that excess-energy curve equals the logarithm of gamma one divided by gamma two. That slope relationship will give us a local diagnostic. We can compare the slope inferred from the weighted properties with the log ratio at the same composition. Complete B one on page one. State the fixed conditions and explain the connection in one sentence.
Your action: Pause to complete worksheet p. 1 B1. State fixed T and P and explain why the activity coefficients cannot vary independently.
Slide 7: The experimental path · 21–27 min
Recording 6:04 | Elapsed study time: 21-27 min
Experimental vapor-liquid data do not always follow a path with both temperature and pressure fixed. In an isothermal experiment, temperature stays constant while the equilibrium pressure generally changes with composition. The more general relationship therefore contains a pressure term involving molar excess volume. Our teaching calculation neglects that contribution. This approximation must accompany the interpretation. In an isobaric experiment, pressure is fixed but temperature changes. The local relationship then needs an excess-enthalpy correction. For real measurements, we need independent excess-enthalpy information before assigning that corrected local verdict. A missing correction is not evidence that the measurements failed. Lab Three also supplies synthetic excess enthalpy for its generated isobaric cases. That value comes from the generator; it is not an independent calorimetric measurement. Complete B two: identify the omitted pressure contribution and the property needed for the temperature correction.
Your action: Pause to answer worksheet p. 1 B2: the excess-volume pressure contribution and independent excess enthalpy for an isobaric local correction.
Slide 8: Which method applies? · 27–35 min
Recording 7:23 | Elapsed study time: 27-35 min
The four approaches ask related but different questions. The isothermal area method integrates the log-activity ratio across the full composition range. Contributions of opposite sign can cancel. The local differential method compares a slope relationship at individual interior compositions, but numerical differentiation is sensitive to noise and spacing. Herington supplies an empirical allowance for an isobaric boiling-temperature range. That allowance does not replace measured excess enthalpy. The Van Ness-type approach asks whether a selected activity model can reproduce the observed pressure and vapor composition. Before interpreting any result, check whether the method applies to the data path and whether the required information is available. Not applicable, not assessed, and not run are not synonyms for failed. They are also not successful tests. Read the stated reason. Complete B three on page one, using guide page two if needed. You do not need to operate the Lab yet.
Your action: Pause to complete worksheet p. 1 B3. Review method applicability using Lab guide p. 2 if needed. Do not open a new Lab investigation yet.
Slide 9: Area exercise · 35–43 min
Recording 8:37 | Elapsed study time: 35-43 min
We will first make the area calculation small enough to check by hand. Page one, section C, gives five equally spaced compositions and five values of L, the natural logarithm of the activity-coefficient ratio. Treat neighboring points as the ends of a straight segment. For each interval, multiply its width by the average of the two endpoint values. Keep the sign: a segment below zero contributes a negative signed area. Add the four contributions for C one. For C two, increase every L value by zero point two and calculate the signed sum again. For C three, explain what this integral cannot establish about individual observations. These are synthetic values whose endpoint limits are supplied analytically. We are not inventing endpoint measurements. Stop the video here and complete C one through C three before opening the solution slide.
Your action: Pause BEFORE the Area solution. Complete worksheet p. 1 C1–C3: baseline trapezoids, uniform +0.20 shift, and the limitation.
Slide 10: Area solution · 43–50 min
Recording 9:42 | Elapsed study time: 43-50 min
The four baseline contributions are zero point three seven five, zero point one two five, minus zero point one two five, and minus zero point three seven five. The positive area is one half, the signed negative area is minus one half, and the total is zero. Raising the entire curve by zero point two adds a rectangle of height zero point two over a composition interval of one. The new signed integral is therefore zero point two. Lab Three calls the signed integral I and also reports a normalized score, D. D compares the magnitudes of the positive and negative areas; it is not the signed integral itself. The teaching area criterion is D below five percent. If both magnitudes vanish, that normalization is undefined. Check your work and keep the distinction visible. Real interior measurements still cannot establish missing endpoint intervals without an extra assumption.
Your action: Check C1–C3 on worksheet p. 1. Keep signed S/I separate from normalized D. Continue to Lab 03 at approximately minute 50.
Slide 11: Local and global checks · 50–53 min
Recording 10:53 | Elapsed study time: 50-53 min
Open Lab Three and guide page one, with worksheet page two beside them. Before changing a control, understand what the local residual represents. It subtracts the log-activity ratio from the slope of dimensionless excess Gibbs energy. Under our isothermal pressure-term approximation, a consistent continuous description makes that difference vanish. The Lab estimates slopes numerically at interior points. Its teaching score is one hundred times the mean absolute residual, with a threshold of five. That scaled score is not a probability or a percentage of incorrect observations. Numerical differentiation can create a small residual even for clean generated data. Also, an average can dilute a narrow peak. Inspect the shape as well as the score. This finite-difference diagnostic is distinct from the fitted Padé slope used in the NIST and Kojima point-test implementation.
Your action: Open Lab 03 and Lab guide p. 1. Keep worksheet p. 2 ready. Read the residual definition, then continue to the baseline controls.
Slide 12: Lab 03 baseline · 53–60 min
Recording 12:01 | Elapsed study time: 53-60 min
For D one, make the initial state reproducible. Select Synthetic, isothermal, three hundred fifty kelvin. Choose Consistent reference, and explicitly select forty-one points. The page normally starts with eighty-one points, so do not skip that change. Under Inspect, choose Log-activity ratio and integrated area. Record the signed integral, the normalized D score, and the area status. Then switch Inspect to Local Gibbs-Duhem residual and record its score, status, and general shape. The results update when you change these controls. Amplitude is disabled for the clean reference, which is expected. These data use Lab Three's own generator, not the Lab Eight demonstration dataset. Save the reference evidence with Export all results or a screenshot. Rename the JSON clearly. Wait until D four to run the model fit. Pause now and complete D one before changing the perturbation.
Your action: Pause for worksheet p. 2 D1. Set synthetic isothermal 350 K, clean reference,41 points; inspect both diagnostics and save the baseline. Do not fit yet.
Slide 13: Canceling errors · 60–67 min
Recording 13:10 | Elapsed study time: 60-67 min
For D two, keep the temperature path and forty-one-point sampling unchanged. Change Controlled perturbation to Canceling errors, zero net area. Check that the amplitude is zero point two five. This construction adds a cosine-shaped term to the log-activity ratio. Its integral across the full composition range is exactly zero, although the term is not zero at every composition. The weighted changes to the two log activity coefficients cancel in the excess-energy value. This is designed to separate a global integral from a local relationship. Inspect the area plot and then the local residual plot. Record their scores and statuses without turning them into a single overall pass or fail. Explain what each actually tests. Save this case under a different filename so that you retain the reference. Pause here and finish D two before moving to the localized defect.
Your action: Pause for worksheet p. 2 D2. Select Canceling errors, amplitude 0.25, keep 41 points. Record both results and save a separate export.
Slide 14: A localized defect · 67–74 min
Recording 14:17 | Elapsed study time: 67-74 min
For D three, change only the perturbation to Localized defect near x one equals zero point three five. Keep amplitude zero point two five and forty-one points. This time the discrepancy occupies a narrow part of the composition range. Locate it on the local residual plot, then compare its appearance with the single averaged score. For these exact settings, both aggregate criteria are met, even though the residual plot shows the localized defect. Do not assume that deliberately introducing a defect must make every badge change. Record what the Lab actually reports and explain the scope of the average. Save the localized case separately. If you have spare time inside this activity block, compare one hundred sixty-one points, then return to forty-one. That optional resolution check changes the numerical sampling; it does not create new experimental evidence. Pause and complete D three.
Your action: Pause for worksheet p. 2 D3. Keep amplitude 0.25 and 41 points; inspect the local peak as well as scores. The 161-point comparison is optional within this block.
Slide 15: Model reproduction · 74–80 min
Recording 15:26 | Elapsed study time: 74-80 min
For the one required modeling run, return to Consistent reference at three hundred fifty kelvin and forty-one points. Click Run modeling test once and wait for the convergence message. Then inspect Modeling residuals. Record the pressure error in percent and the vapor-composition error in percentage points. These are different quantities, even though both are scaled by one hundred. The Lab fits two constant N R T L parameters with the nonrandomness parameter fixed at zero point four seven. Its teaching criteria require both reported errors to be below one in their stated units. The clean fit should give near-zero errors because it reproduces its own generating model; that is a check of model reproduction, not a certificate for real measurements. Herington is not applicable because this case is isothermal. Its boiling-range allowance belongs to an isobaric path. Pause now to finish D four. If the fit does not converge, record no modeling verdict instead of guessing a result.
Your action: Pause for worksheet p. 2 D4. Return to clean reference, 350 K / 41 points and run the modeling test once. Record Δp, Δy, applicability and interpretation.
Slide 16: Area versus local evidence · 80–85 min
Recording 16:40 | Elapsed study time: 80-85 min
Compare your D one and D two records with these two plots. The teal reference and amber canceling-error curves have different log-activity ratios, yet both meet the area criterion. Their positive and negative contributions nearly balance. The local residual tells a different story. The reference remains close to zero, while the canceling-error residual oscillates across the composition range. The reference D score is about zero point zero seven nine percent, and the canceling-case score is about zero point zero seven four percent. Those similarly small area scores conceal a large difference in the local score: roughly zero point one one eight versus fifteen point six. Read that contrast from the numerical records and the plotted shape. Complete E one in your own words. Describe how cancellation can occur globally while a local relationship is violated. Pause before continuing to the interpretation check.
Your action: Pause to answer worksheet p. 2 E1 using the area and local plots plus your D1 / D2 results. Explain disagreement before advancing.
Slide 17: Interpretation · 85–90 min
Recording 17:50 | Elapsed study time: 85-90 min
Your explanation should connect the two observations rather than rank the methods as universally good or bad. The cosine perturbation integrates to zero, so the area method misses that particular discrepancy. The local relationship retains a structured departure. For E two, write a supported claim, give the numerical or graphical evidence, and state one limitation. Include the dataset, forty-one-point sampling, and perturbation amplitude so another person could reproduce the comparison. Mention the assumptions behind inferred activities or the sensitivity of derivatives to sampling. Keep the localized case in mind: even a mean local score can hide a narrow feature. After writing your own explanation, compare it with sections D and E of the worked solutions. Save the baseline and changed-case evidence. This constructed exercise demonstrates limitations of diagnostics; it does not estimate experimental uncertainty.
Your action: Pause to finish E2 and check E1–E2 against solutions D–E. Save the Lab 03 evidence. Finish this block at approximately minute 90.
Slide 18: Break · 90–100 min
Recording 19:00 | Elapsed study time: 90-100 min
Take a ten-minute break now. Save your work and leave the files open. Step away from the screen, then return to this point with worksheet page three ready. After the break, we will change the question. A model can obey Gibbs-Duhem and still favor separation into two liquids. We will use Gibbs energy to determine which liquid state is stable.
Your action: Stop the video and take the full 10-minute break. Resume with worksheet p. 3 at approximately study minute 100.
Slide 19: Liquid stability · 100–105 min
Recording 19:27 | Elapsed study time: 100-105 min
At fixed temperature and pressure, stable equilibrium is the admissible state with the lowest total Gibbs energy, subject to the material balance. For a binary mixture, the mixing-energy curve contains the ideal mixing terms plus the excess contribution. This curve can become nonconvex even when the activity model satisfies the Gibbs-Duhem identity exactly. That is why consistency does not imply a stable homogeneous liquid. Equality of chemical potentials identifies candidate coexisting phases. We must still ask whether that candidate provides the lowest energy when all allowed compositions are considered. In a binary plot, a globally supporting common tangent supplies that comparison. The line represents the energy of a mixture of the two endpoint liquids. Complete F one on page three: explain what remains to be checked after a solver has found equal chemical potentials. Pause briefly before continuing to the geometric condition.
Your action: Pause for worksheet p. 3 F1. State the global Gibbs-energy criterion beyond an equal-chemical-potential solution.
Slide 20: Common-tangent condition · 105–110 min
Recording 20:39 | Elapsed study time: 105-110 min
A common tangent touches the curve at two distinct compositions and has the same slope at both. Its slope must also equal the rise between the two energy values divided by the distance between the compositions. Those local equalities are necessary, but the word supporting adds a global requirement. Across the entire admitted composition range, the line must remain at or below the curve. If it crosses above the curve somewhere, another allowed state can lower the energy and the candidate is not globally stable. Similarly, a solution whose two endpoints coincide does not establish two distinct liquids. Positive curvature at one composition is only a local statement; it cannot by itself prove global stability. Keep this condition ready for F three. First, move to the next slide and attempt the lever-rule calculation in F two.
Your action: Read the global supporting-tangent condition. Continue to the F2 hand calculation; use this condition for F3 after the lever-rule check.
Slide 21: Lever-rule attempt · 110–116 min
Recording 21:42 | Elapsed study time: 110-116 min
For F two, suppose a stable tie line has already been established with liquid compositions zero point two zero and zero point eight zero. These values are supplied for a hand example; they are not the endpoints you should expect from Lab Four. Calculate the fraction of the component-one-rich liquid by subtracting the lower endpoint from the overall composition, then dividing by the distance between the endpoints. The other liquid fraction is one minus that result. Do this first for an overall composition of zero point five zero, then for zero point three five. Reconstruct each overall composition from the fractions and endpoint compositions to check your balance. Here beta names the richer liquid, not a vapor fraction. Pause now and calculate both feeds before the next slide shows the answers.
Your action: Pause BEFORE the Lever-rule check. Complete worksheet p. 3 F2 for illustrative endpoints 0.20 / 0.80 at z=0.50 and 0.35; show both balances.
Slide 22: Lever-rule check · 116–120 min
Recording 22:43 | Elapsed study time: 116-120 min
For the central feed, the two liquid fractions are equal. For an overall composition of zero point three five, the rich-liquid fraction is one quarter and the other fraction is three quarters. The balance is three quarters times zero point two, plus one quarter times zero point eight, which returns zero point three five. The coexisting compositions remain the same because we have kept the coexistence conditions fixed and moved the feed within the same tie line. The phase amounts change instead. Correct your F two calculation, then answer F three using the global supporting-tangent condition. Touching the curve twice is not enough if the line rises above an admissible part of it. Open Lab Four and guide page three when you are ready. The next investigation uses the model's actual calculated endpoints.
Your action: Correct F2 and complete F3 on worksheet p. 3. Open Lab 04 and guide p. 3. Continue at approximately study minute 120.
Slide 23: Lab 04 baseline · 120–130 min
Recording 23:45 | Elapsed study time: 120-130 min
For G one, predict the phase state before reading the result. In Lab Four, open Explore a state and choose Unstable, A equals three, z one equals zero point five zero. Verify the controls: one-parameter Margules, interaction parameter three, and feed mole fraction zero point five zero. Choose Gibbs energy and common tangent in the View control. If you type values instead of selecting the preset, click Find equilibrium to apply them. Record the calculated coexisting compositions and both liquid fractions in the table. Write the Gibbs-energy decrease divided by R T beside G four or below the table. The parameters represent a hypothetical model at fixed conditions; this Lab has no physical temperature or pressure input boxes. Keep the same model throughout this comparison. Pause now to make your prediction, run the baseline, and complete G one using the actual displayed outputs.
Your action: Pause for worksheet p. 3 G1. Set symmetric Margules A = 3, z = 0.50, run if typed, inspect common tangent, and record actual endpoints/fractions/energy.
Slide 24: One changed feed · 130–140 min
Recording 24:54 | Elapsed study time: 130-140 min
Before changing the feed, save the baseline with Export study JSON. Give the file a name that identifies the feed as zero point five zero. For G two, change only Feed mole fraction to zero point three five, then click Find equilibrium. Leave the model and interaction parameter unchanged. Record the same outputs beside your baseline values. Compare the endpoint compositions separately from the fractions. Ask whether each liquid's composition changed, whether its amount changed, and whether the result still reconstructs the overall feed. Use the endpoints calculated by this model. Substituting zero point two and zero point eight from the earlier hand example would test a different tie line. Pause here and record the changed-feed result before checking the balance independently.
Your action: Pause for worksheet p. 3 G2. Save the z = 0.50 baseline, change only z to 0.35, run and record the new outputs.
Slide 25: Independent balance · 140–150 min
Recording 25:55 | Elapsed study time: 140-150 min
Now verify G three with your calculator, not simply by copying the Lab's residual. Use the actual lower and upper coexistence compositions to calculate the rich-liquid fraction for the feed of zero point three five. Then obtain the other fraction by subtraction from one. Reconstruct the feed by weighting each endpoint composition by its phase fraction. Check that both fractions lie between zero and one and that they sum to one. If the displayed endpoints are rounded, a small final-digit mismatch is expected. You can use the additional digits in the JSON export for a tighter check. A successful balance verifies that the reported amounts and compositions match the feed. It does not establish global stability by itself. Pause now and show the substituted calculation on page three.
Your action: Pause for worksheet p. 3 G3. Calculate fβ and the component balance independently with the actual Lab 04 endpoints; retain substituted numbers.
Slide 26: Global support · 150–160 min
Recording 26:56 | Elapsed study time: 150-160 min
Complete G four by combining the numerical and graphical evidence. Open Verify the equilibrium, then inspect the full Gibbs-energy and common-tangent plot. Confirm that the liquids have distinct compositions, their chemical potentials agree within the reported numerical tolerance, and the common tangent supports the whole admitted curve. Add your independent feed balance to this evidence. The Gibbs-energy decrease shows how much the equilibrium split lowers the energy relative to the hypothetical homogeneous feed. Do not confuse the homogeneous-feed label with the final equilibrium phase count. An unstable homogeneous feed can produce a stable equilibrium consisting of two liquids. Explain which quantities stayed fixed when only the feed changed and which quantities changed. Pause to write this reasoning, using the tangent and the energy comparison rather than relying only on a phase badge.
Your action: Pause for worksheet p. 3 G4. Inspect Verify the equilibrium and the full tangent plot; explain stability and fixed endpoints versus changed amounts.
Slide 27: Investigation check · 160–165 min
Recording 28:04 | Elapsed study time: 160-165 min
Compare G one through G four with section G of the worked solutions. Check that your record identifies one-parameter Margules with A equal to three, both overall feed compositions, and the actual coexistence endpoints. Keep phase composition separate from phase fraction: composition describes each liquid, while fraction tells us how much of that liquid is present. If a result differs, first compare the model settings, check that typed values were applied, and inspect any rounding. Save the changed-feed JSON and a comparison table or plot. Retain your balance calculation and stability explanation with those files. The required investigation ends here. LLE fitting and vapor-liquid-liquid equilibrium are optional extensions for later study. Open page four of the worksheet for the short self-review.
Your action: Check G1–G4 after your attempt, save both Lab 04 cases and the comparison, then open worksheet p. 4. No LLE-fit or VLLE task is required.
Slide 28: Self-review attempt · 165–169 min
Recording 29:07 | Elapsed study time: 165-169 min
Answer H one through H four without consulting the solutions. Use a sentence or two for each explanation and include the brief calculation in H four. First, decide whether meeting an area criterion guarantees all local relationships. Second, explain what you should check before blaming a differential discrepancy on experimental error. Third, state what a small fitting error can establish and whether that is predictive validation. Finally, return to the supplied illustrative endpoints zero point two and zero point eight, with feed composition zero point three five. Calculate the rich-liquid fraction and say what establishes stable coexistence beyond the balance. Preserve your first answers. Pause now and finish all four before continuing to the review check.
Your action: Pause BEFORE the Self-review check. Complete worksheet p. 4 H1–H4 without solutions; keep your original attempt.
Slide 29: Self-review check · 169–172 min
Recording 30:05 | Elapsed study time: 169-172 min
For H one, opposite local errors can cancel in the integral, so a small area is not a guarantee about every point. For H two, examine the thermodynamic path, required excess-property corrections, phase and property assumptions, and the numerical differentiation. If essential information is missing, the appropriate result may be not assessed rather than a failed test. For H three, a small residual demonstrates reproduction by the selected model on those observations. It does not independently establish accuracy for new data. For H four, the rich-liquid fraction is zero point two five and the balance returns zero point three five. A stable two-liquid interpretation also needs distinct phases and a globally supporting common tangent. Correct your answers in a different color or add a note. Keep the original attempt so you can see what changed.
Your action: Check and correct H1–H4 on worksheet p. 4. Preserve first answers. Continue to the exit ticket at approximately minute 172.
Slide 30: Exit ticket · 172–177 min
Recording 31:11 | Elapsed study time: 172-177 min
Open the existing Session Three exit-ticket and feedback form using the link or QR code. Section I on worksheet page four gives the same instructions. In the concept response, answer the LLE question: explain when a calculated split represents stable equilibrium, using your Lab Four reasoning. In the numerical-evidence response, describe the Lab Three comparison between the area and local diagnostics. Identify the case, sampling and amplitude, and include the results that support your statement. You may add your Lab Four balance if useful. Use your own explanation rather than copying the example conclusion. This form is anonymous and does not identify individual attendance. Pause to enter the exit-ticket responses, then continue to the feedback fields in the same form.
Your action: Pause for worksheet p. 4 I: open Session 3 form and enter the LLE concept answer plus Lab 03 numerical evidence. Continue with feedback in the same form.
Slide 31: Feedback and saved work · 177–180 min
Recording 32:12 | Elapsed study time: 177-180 min
Finish the feedback fields and submit the form once. Tell us whether the pace and Lab access worked for independent study, and name one explanation or instruction that could be clearer. Wait for the message Response received before leaving. Then check your own saved work: the completed worksheet with corrections, the Lab Three comparison and exports or screenshots, and both Lab Four cases with the independent balance. Exporting a Lab study saves a local file; it does not submit your assignment to a server. Keep these files together and follow any separately announced submission arrangements. This completes the three-hour route. No additional compulsory homework follows this lesson. Your evidence should now distinguish model reproduction, thermodynamic consistency, and stable phase equilibrium.
Your action: Complete feedback, submit once, wait for Response received, and save worksheet plus Lab evidence. Finish around study minute 180; no extra compulsory task.