This independent lesson replaces class while the instructor attends the ECS meeting. Identify the phases and vessel constraints, calculate inventory balances, then follow the actual Lab 10 and Lab 11 demonstrations and repeat the investigations yourself.
About 180 min planned study route57:29 recording40 slidesEnglish male narration + captions
The demonstration links deliberately jump to chapters 16 and 30. Before opening the Lab 10 demonstration, complete D1 predictions at slide 15. Before opening the Lab 11 demonstration, complete F1-F3 predictions at slide 29. Independently rerun the investigations at slides 18 and 32.
Recording time and study time are different
The 57:29 recording is measured from the final video. Add 120 minutes of independent work and reflection plus a 10-minute break: about 187.5 minutes in this edition. The course route targets approximately 180 minutes; learner pace will vary. The schedule shows planned study time, not MP4 timestamps. Pause as long as needed; the recording does not include exercise-length silence.
Complete the 5-minute prediction stops before Lab 10 on slide 16 and Lab 11 on slide 30. Use the 22-minute independent Lab 10 rerun at slide 18 and the 24-minute Lab 11 rerun at slide 32. Ten work checkpoints preserve 120 active minutes, with a separate 10-minute break. Follow worksheet sections A-I in order; preserve predictions before checks.
Study-time route and required outputs
These are nominal study ranges, not recording timestamps. The video replaces reading the same slides and is included in the total study time.
0-25 min: A1-A3 and B1-B2, worksheet page 1. Classify processes, identify constraints and calculate saturated-liquid composition.
25-45 min: C1-C3, page 2. Independently calculate the finite GSE inventory, partial/total pressure and phase-presence condition.
45-85 min: D1-D4, page 3 and guide pages 1-2. Predict at slide 15, watch the actual Lab 10 demonstration at 16, then rerun three cases at 18, check balances and reopen a saved study.
85-95 min: 10-minute break at slide 20.
95-120 min: E1-E3 and F1-F3, page 4. Calculate Henry/Langmuir uptake and predict the pressure response of a closed adsorption vessel before the demonstration.
120-150 min: G1-G4, page 5 and guide pages 3-4. Watch the actual Lab 11 demonstration at slide 30, then independently compare three cases, close the gas-plus-adsorbed balance and reopen a study during slide 32.
150-170 min: unseen H1-H4, page 6. Attempt before checking and retain corrections.
170-180 min: I, page 6. Anonymous Session 4 exit ticket, feedback and saved work.
English captions
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Slide 1 of 40Lesson introduction
Solid equilibria and adsorption
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Transcript · Slide 1
Welcome to session four, solid equilibria and adsorption. This independent lesson replaces our live class while I attend the E C S meeting. Last week, you used thermodynamic consistency and liquid stability to decide whether a model and a proposed phase state were reasonable. Today, we extend that reasoning to systems containing a solid. We will distinguish bulk phase equilibrium from surface uptake. We will also separate an equilibrium composition or pressure from the amount of material in each part of a system. The lesson includes two actual Lab demonstrations, your own calculations, and independent investigations. Keep your predictions and your first answers. Correcting an explanation after checking evidence is an important part of the work.
Keep the known-pressure example on slide 28 (total inventory 0.01400908 mol) separate from the Lab 11 investigation (0.0100 mol). Record partial versus total pressure, uptake per kg versus adsorbed amount, inputs, units and an independent balance.
Finish the Session 4 reflection and feedback
At study minutes 150-170, attempt the unseen worksheet H1-H4 before the check, then retain your corrections. At minutes 170-180, open the Session 4 exit ticket and feedback form.
Use the concept answer to explain the finite-inventory GSE condition and volatile partial pressure. In the evidence answer, include one Lab 10 comparison and one Lab 11 balance with settings, units and a limitation. Complete the reflection and feedback during the pause on slide 39. In the existing feedback text, include your actual study minutes and any pacing difficulty. Submit once and wait for Response received. Continue to slide 40 to verify the receipt and save your files; do not submit again.
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. The planned work budgets already include this reflection and feedback. Keep actual recording time separate from the study-time guide.
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: Solid equilibria and adsorption
Recording 0:00 | Lesson introduction
Welcome to session four, solid equilibria and adsorption. This independent lesson replaces our live class while I attend the E C S meeting. Last week, you used thermodynamic consistency and liquid stability to decide whether a model and a proposed phase state were reasonable. Today, we extend that reasoning to systems containing a solid. We will distinguish bulk phase equilibrium from surface uptake. We will also separate an equilibrium composition or pressure from the amount of material in each part of a system. The lesson includes two actual Lab demonstrations, your own calculations, and independent investigations. Keep your predictions and your first answers. Correcting an explanation after checking evidence is an important part of the work.
Your action: Listen, then continue through the lesson.
Slide 2: Your independent lesson
Recording 0:57 | Lesson introduction
Open the six-page practice worksheet and the four-page Lab guide using the links on this slide. Keep both beside the video. The worksheet is your working record, while the guide tells you which controls to use and what each result means. The worked solutions are available for checking, but attempt each question before opening the corresponding answer. Keep your original response and add a correction, rather than replacing it without explanation. You will first work through Lab ten on bulk solid equilibria, then Lab eleven on adsorption. The demonstrations show the workflow, and the later pauses give you time to reproduce it independently. Save your calculation sheets, comparison tables and study J S O N files together.
Your action: Listen, then continue through the lesson.
Slide 3: The study route
Recording 1:50 | Lesson introduction
This route combines watching with active work. The fixed work budget is one hundred and twenty minutes, with a separate ten-minute break. The actual recording duration appears on the video page. Together, these make a lesson of approximately three hours, although your own completion time may differ. Start a timer so you can report your actual study time later. The table follows worksheet order, not video timestamps. Work through the process review and solubility calculation, then the finite vessel balance and Lab ten. After the break, continue with adsorption and Lab eleven. Finish with a new case that you solve before seeing the answer, then submit the exit ticket and feedback. The activities form this week's lesson.
Your action: Listen, then continue through the lesson.
Slide 4: Process predictions
Recording 2:44 | Follow the study route and activity cues
Pause here for about eight minutes and complete questions A one through A three on worksheet page one. First, classify the examples. Ask whether material moves between bulk phases or accumulates at a surface. Then identify the constraint that makes a rigid closed vessel different from the fixed-temperature, fixed-pressure examples in Week three. For the inert-gas question, write a sentence distinguishing the pressure contributed by the subliming species from the total mixture pressure. You do not need numerical values yet. The purpose is to establish which physical quantities the later equations describe. Keep your answers even if you are unsure. Use the next slide as a check only after you have made an attempt, and explain any correction.
Your action: Pause for about 8 minutes. Complete worksheet p. 1, A1–A3 before viewing the check.
Slide 5: Process check
Recording 3:38 | Follow the study route and activity cues
Check your classifications. Dissolution of a crystal and sublimation transfer the same substance between bulk phases. Adsorption describes uptake associated with a surface. A chemical reaction would instead change species identities and require additional reaction constraints. The relevant energy criterion depends on what is fixed. At fixed temperature and pressure, a closed system minimizes Gibbs energy. At fixed temperature and volume, the corresponding potential is Helmholtz energy. In both cases, conserved inventories and the allowed states remain constraints on the minimization. For an ideal gas mixture, total pressure is the sum of partial pressures. An inert gas can therefore raise total pressure without changing the amount of the subliming species. Keep that distinction visible when we later interpret the Lab output.
Your action: Listen, then continue through the lesson.
Slide 6: Pure-solid standard state
Recording 4:41 | Follow the study route and activity cues
We begin with a solid and a liquid at equilibrium. The chemical potential of the component must be the same in the two present phases. On the liquid side, we write its chemical potential as the pure-liquid reference plus R T times the natural logarithm of x times gamma. The reference is the subcooled pure liquid at the same temperature and pressure. That reference may be a hypothetical continuation below the melting temperature, but it defines the activity convention consistently. The pure solid has unit activity on its own standard state. Unit activity does not mean that its chemical potential or amount is zero. The equality determines a liquid activity. Determining how many moles occupy each phase still requires a material balance.
Your action: Listen, then continue through the lesson.
Slide 7: Solubility equation
Recording 5:37 | Follow the study route and activity cues
The solubility equation links liquid activity to fusion properties. Read the right-hand side as negative fusion enthalpy divided by R, multiplied by the quantity one over T minus one over the melting temperature. That entire expression is dimensionless. Use temperature in kelvin and fusion enthalpy in joules per mole. With R in joules per mole per kelvin, the units cancel correctly. The expression assumes constant fusion enthalpy and neglects the heat-capacity correction between solid and liquid. It also assumes the specified pure solid, without solid solutions or chemical reactions. Below the melting temperature, the reciprocal-temperature difference is positive. The negative sign therefore gives a negative logarithm. For an ideal liquid, that predicts a saturated mole fraction below one.
Your action: Listen, then continue through the lesson.
Slide 8: Solubility attempt
Recording 6:40 | Follow the study route and activity cues
Pause for about six minutes and complete B one and B two on worksheet page one. The synthetic melting temperature is three hundred and fifty kelvin. The fusion enthalpy is ten thousand joules per mole, and the system temperature is three hundred kelvin. Assume an ideal liquid, so gamma is one. First calculate the exponent in the solubility equation, then take the exponential to obtain the saturated mole fraction. Write the intermediate value so you can check the sign and units later. For B two, decide whether the resulting number gives moles of remaining solid. Explain what additional inventory or composition information you would need. Make that distinction before continuing to the numerical check on the next slide.
Your action: Pause for about 6 minutes. Complete worksheet p. 1, B1–B2 before viewing the check.
Slide 9: Solubility check
Recording 7:35 | Follow the study route and activity cues
The exponent is approximately negative zero point five seven two seven three. Its exponential gives a saturated liquid mole fraction of about zero point five six four. This is a composition within the liquid phase. It does not tell us the number of moles dissolved, the total amount of liquid, or the remaining solid inventory. For a nonideal liquid, the same thermodynamic relation constrains x times gamma. Since gamma can depend on composition, finding the composition may require solving an implicit equation within the admitted phase model. We still need material balances to determine phase amounts. A eutectic introduces additional solid-phase conditions and a second solubility branch. That extension is available in the optional appendix, but it is not required for today's investigation.
Your action: Listen, then continue through the lesson.
Slide 10: Sublimation equilibrium
Recording 8:37 | Follow the study route and activity cues
Now consider a pure bulk solid in equilibrium with its vapor. Equality of chemical potential applies while both phases are present. With the ideal-gas and solid-pressure approximations stated here, this gives a vapor partial pressure equal to the sublimation pressure at that temperature. The phrase while solid remains matters. A small initial solid inventory may completely enter the gas phase before the vapor reaches that pressure. The final state can then have a lower partial pressure because there is no bulk solid left to enforce the two-phase equality. Also note which pressure appears in the condition. It is the partial pressure of the subliming species. An inert gas contributes to total pressure, but it is not part of that species' sublimation inventory.
Your action: Listen, then continue through the lesson.
Slide 11: Finite-vessel inventory
Recording 9:34 | Follow the study route and activity cues
Start the vessel calculation by finding the gas capacity at sublimation equilibrium. Multiply sublimation pressure by accessible gas volume, then divide by R T. Compare that capacity with the total amount of the subliming species. Gas moles equal the smaller of the available inventory and that capacity. Solid moles are the remaining inventory. Use gas moles in the ideal-gas equation to obtain the species partial pressure, and add the inert contribution only when calculating total pressure. With kilopascals and liters, R has the numerical value eight point three one four four six in compatible units. The gas chemical potential minus the pure-solid reference, divided by R T, is the natural logarithm of partial pressure divided by sublimation pressure. Zero applies with present solid. A negative value is allowed after solid exhaustion.
Your action: Listen, then continue through the lesson.
Slide 12: Inventory worked example
Recording 10:43 | Follow the study route and activity cues
Follow the worked case at three hundred kelvin, one liter and a sublimation pressure of ten kilopascals. The capacity is ten times one, divided by R times three hundred. This gives approximately zero point zero zero four zero zero nine moles. An inventory of zero point zero one zero moles exceeds the capacity. About zero point zero zero five nine nine one moles therefore remain solid, and the vapor partial pressure is ten kilopascals. An inventory of zero point zero zero two moles is below capacity. All of it enters the gas phase, giving about four point nine eight nine kilopascals. Adding zero point zero zero two moles of inert gas adds the same pressure contribution at this fixed temperature and volume.
Your action: Listen, then continue through the lesson.
Slide 13: Inventory attempt
Recording 11:42 | Follow the study route and activity cues
Now pause for about ten minutes and complete C one through C three on worksheet page two. This is a different vessel: two liters at three hundred kelvin, with a sublimation pressure of eight kilopascals. Compare total inventories of zero point zero one zero and zero point zero zero four moles. Calculate the capacity first, then gas amount, remaining solid and species partial pressure. Add zero point zero zero one mole of inert gas to each case and calculate total pressure. Finally, calculate the natural logarithm of partial pressure divided by sublimation pressure. Explain the difference between the equality condition for a present solid and a valid state at the exhausted-solid boundary. Show your substitutions and units before opening the check.
Your action: Pause for about 10 minutes. Complete worksheet p. 2, C1–C3 before viewing the check.
Slide 14: Inventory check
Recording 12:42 | Follow the study route and activity cues
The gas capacity is approximately zero point zero zero six four one five moles. Therefore, the larger inventory retains about zero point zero zero three five eight five moles of solid and has a species partial pressure of eight kilopascals. The smaller inventory completely vaporizes and gives about four point nine eight nine kilopascals. The inert contributes about one point two four seven kilopascals in each case. Add that contribution to obtain the total pressures shown in the table. The logarithmic chemical-potential difference is zero with solid present, and about negative zero point four seven two three for the exhausted-solid case. A negative value is appropriate there. Check that gas plus solid equals the volatile-species inventory in each row.
Your action: Listen, then continue through the lesson.
Slide 15: Lab 10 predictions
Recording 13:41 | Follow the study route and activity cues
Pause for about five minutes and complete D one on worksheet page three. Read the first two pages of the Lab guide, but make your predictions before running the simulation. We will use three cases at three hundred kelvin and one liter. Set the sublimation reference pressure to ten kilopascals at three hundred kelvin. Case ten A has zero point zero one zero moles of volatile species and no inert. Case ten B reduces that inventory to zero point zero zero two moles. Case ten C keeps the smaller volatile inventory and adds zero point zero zero two moles of inert gas. Predict phase presence, partial pressure and total pressure for each case. Identify the one input changed between successive cases.
Your action: Pause for about 5 minutes. Complete worksheet p. 3, D1 predictions before the Lab 10 demonstration.
Slide 16: Lab 10 demonstration
Recording 14:38 | Follow the study route and activity cues
We are now in the real Lab ten interface. Keep worksheet page three and Lab guide pages one and two beside the browser. In the Experiment menu, choose gas solid equilibrium, sublimation in a rigid vessel. The lab initially supplies its own synthetic defaults. Those initial results are not our worksheet case, so do not copy them. Selecting an experiment may also reset the controls. Choose the experiment first, then enter every value in the guide. Our first record will be case ten A, with enough volatile material for some solid to remain. Enter a temperature of three hundred kelvin and a free gas volume of one liter. Set the total volatile inventory to zero point zero one zero mole and the inert gas inventory to zero. These are total amounts, not mole fractions. The free gas volume is the space available to the gas. In this teaching model we neglect the solid volume. Keep the declared temperature interval from two hundred fifty to three hundred fifty kelvin. The source field identifies these numbers as synthetic teaching definitions rather than measured properties of a real chemical. The reference temperature is also three hundred kelvin. Enter a reference sublimation pressure of ten kilopascals and a sublimation enthalpy of fifty thousand joules per mole. At the reference temperature the correlation therefore returns ten kilopascals directly. The enthalpy controls the temperature dependence away from that point. For real properties, the declared interval must exclude melting and solid transitions and match the source correlation. Notice that changing inputs clears the previous results and disables export. Press Calculate equilibrium only after checking the values and units. The result for case ten A is solid plus gas. The volatile partial pressure and the total pressure both equal ten kilopascals because this case contains no inert gas. Read the two amounts separately. There are about zero point zero zero four zero zero nine mole of volatile gas and zero point zero zero five nine nine one mole of solid. Their sum is the entered zero point zero one zero mole. The chemical potential difference is zero within numerical precision. That equality is appropriate because both phases are present. A small balance residual is a useful calculation check, but it does not validate the physical assumptions for an unknown real material. Change the View menu to Gas and solid amounts. Read the horizontal axis before interpreting the curves. It is temperature, not time and not added inventory. Each point is a separate equilibrium calculation at that temperature with the same total volatile inventory. As temperature rises, more of the volatile material can enter the gas. Eventually the solid amount reaches zero and all the volatile material is gaseous. The gas and solid amounts sum to the same inventory throughout the admitted range. This plot does not tell us how quickly sublimation occurs. Our selected operating point remains three hundred kelvin. Now change only the total volatile inventory to zero point zero zero two mole and calculate again. This is case ten B. The heading changes to unsaturated gas, no solid. All the volatile material is now gas, and the volatile partial pressure is about four point nine eight nine kilopascals. The sublimation pressure remains ten kilopascals because the temperature and correlation have not changed. There simply is not enough material to saturate this vessel. Do not force the gas pressure to ten kilopascals or report a negative solid amount. The negative gas minus solid chemical potential difference is compatible with the solid being absent. For case ten C, keep the volatile inventory at zero point zero zero two mole and add zero point zero zero two mole of inert gas. Calculate again without changing temperature or free volume. The volatile partial pressure remains about four point nine eight nine kilopascals, but the total gas pressure becomes about nine point nine seven seven kilopascals. The volatile gas mole fraction is one half. No solid has reappeared. The inert gas contributes its own ideal partial pressure without changing the volatile inventory or its saturation capacity under these assumptions. Always identify whether a reported pressure is partial or total. In the pressure view, distinguish the three curves using their legend labels. The sublimation pressure is a reference property at each temperature, the actual volatile partial pressure obeys the finite inventory constraint, and the total pressure includes the inert gas. At low temperatures, enough volatile material can remain solid for the partial pressure to follow the sublimation curve. After the solid is exhausted, the partial pressure falls below that reference curve. These are equilibrium states across temperature, not a time record. Use the numerical table for precise values at three hundred kelvin. Keep a separate record for each calculated case. In Your interpretation, write the phase label, the volatile balance, and the reason for any pressure change. Expand Study workspace, reopen and compare cases, and enter a clear label for the next captured case. Use Export study JSON after calculating that case. The export downloads the inputs and results and also retains the case in this temporary comparison. Here the three labels distinguish solid remaining, solid exhausted, and inert gas added. Saving current inputs only is a different action and does not contain a calculated result. Select Download comparison to preserve all three cases in one file. The comparison uses recorded field names, and some values use internal units. For example, the gas solid calculation stores pressure in pascals and volume in cubic meters, whereas the main controls display kilopascals and liters. Ten thousand pascals is ten kilopascals. Compare quantities only after checking their units and physical meaning. The comparison is recorded evidence, not a fresh calculation. Keep the downloaded file with your worksheet so that you can reproduce the result later. We will now reopen the saved file from the beginning of the restore workflow. Because our three synthetic cases have already been downloaded, I clear only this temporary comparison from memory. The downloaded file is unchanged. Under Load studies or a comparison JSON, choose the solids comparison file that was just saved. You can instead select an individual study JSON if you only need one case. Loading a file should produce case labels to restore. It does not mean the main calculator has already recalculated the imported inputs. The three case labels have returned after loading the comparison. Select Restore beside case ten A, solid remains. Check that the controls return to one liter, zero point zero one zero mole of volatile material, zero inert gas, and the correct reference pressure. The stored interpretation should return with the inputs. Keep the distinction between opening a recorded result and solving the current state. In particular, switching the experiment during restoration can briefly display default results. Always finish restoration by pressing Calculate equilibrium again. The recalculated case again reports solid plus gas, a volatile partial pressure of ten kilopascals, and the same gas and solid amounts as our original record. That is the reproducibility check we wanted. In worksheet section D, retain the three rows, your independent material balance, and one explanation of partial versus total pressure. Use the next activity stop to repeat this workflow yourself. Your evidence should show that you can identify which phase is present, apply the finite inventory constraint, and reopen the inputs without relying on a screenshot alone.
Your action: Listen, then continue through the lesson.
Slide 17: Lab 10 evidence
Recording 24:18 | Follow the study route and activity cues
Use this list to decide what evidence belongs in your record. Start with the active mode and inputs, because they define the problem being solved. Next, record the gas amount and remaining solid, which establish whether both bulk phases are present. Keep species partial pressure separate from total pressure. Then check the volatile inventory independently: gas moles plus solid moles must equal the volatile total. The inert has its own conserved amount. The Lab plots sweep temperature, not time. The volatile partial pressure follows the sublimation-pressure curve wherever solid remains. A crossing or boundary on that plot describes a change across the stated conditions, rather than a measured time history. Save the study file so that the chosen conditions can be reproduced.
Your action: Listen, then continue through the lesson.
Slide 18: Lab 10 independent investigation
Recording 25:17 | Follow the study route and activity cues
Pause for about twenty-two minutes and complete D two through D four on worksheet page three. Open Lab ten using the link, and follow Lab guide pages one and two. Run all three specified cases yourself. Record phase presence, gas and solid amounts, partial pressure and total pressure. Use your calculator to check the capacity and the inert contribution, rather than copying the output alone. Inspect the temperature plots and explain where the finite inventory becomes important. Export your studies and reopen one saved file. Restore its controls, verify their values, and calculate again. Confirm that the result agrees with the saved case. Keep the comparison table and the calculation evidence. If a result differs from your prediction, explain the difference before moving on.
Your action: Pause for about 22 minutes. Complete worksheet p. 3, D2–D4 using Lab 10 and Lab guide pp. 1–2.
Slide 19: Lab 10 check
Recording 26:16 | Follow the study route and activity cues
Check the three cases against the table. Case ten A retains about zero point zero zero five nine nine one moles of solid, so its volatile partial pressure is ten kilopascals. Case ten B has no solid left and gives about four point nine eight nine kilopascals. Case ten C has the same volatile inventory and the same volatile partial pressure as case ten B. The added inert gas increases total pressure to about nine point nine seven seven kilopascals. This is a direct example of why total pressure cannot replace partial pressure in the sublimation condition. The values describe equilibrium endpoints under the stated model. They do not predict a sublimation rate, a transport resistance or the time needed for the vessel to reach equilibrium.
Your action: Listen, then continue through the lesson.
Slide 20: Break
Recording 27:15 | Follow the study route and activity cues
Take a ten-minute break here. Save your Lab ten files and your worksheet before leaving the screen. There is no calculation to complete during this break. When you return, open worksheet page four and Lab guide pages three and four. We will move from bulk sublimation to surface adsorption. That change requires a new variable: uptake per unit mass of adsorbent. The material-balance question will remain familiar. We will first evaluate an equilibrium relation at a specified pressure, then determine the pressure that can exist in a closed vessel with a fixed inventory. Keep the distinction between a state quantity and an amount in mind. Resume when you are ready to begin the adsorption section.
Your action: Take a 10-minute break. Save your Lab 10 work before leaving the screen.
Slide 21: Adsorption and bulk phases
Recording 28:07 | Follow the study route and activity cues
Adsorption describes material associated with a surface. An adsorption isotherm gives uptake as a function of gas pressure at a specified temperature. In this lesson, q is absolute uptake measured in moles per kilogram of adsorbent. The pressure is the partial pressure of the adsorbate. To turn uptake into an amount in moles, multiply q by the adsorbent mass expressed in kilograms. For example, a value of one mole per kilogram on ten grams of adsorbent corresponds to zero point zero one mole adsorbed. That distinction will matter when we change adsorbent mass. A lower uptake per kilogram does not automatically mean fewer total adsorbed moles. The total amount depends on both uptake and the amount of adsorbent present.
Your action: Listen, then continue through the lesson.
Slide 22: Langmuir model
Recording 29:05 | Follow the study route and activity cues
The Langmuir equation writes uptake as the saturation uptake multiplied by b P, divided by one plus b P. Saturation uptake has units of moles per kilogram. The parameter b has reciprocal-pressure units, so the product b P is dimensionless. The ratio of uptake to saturation uptake is the fractional coverage in this model. It rises from zero toward one as pressure increases. At b P equal to one, the coverage is one half. The idealized interpretation involves a finite set of equivalent sites without lateral interactions. These assumptions help us understand the equation, but fitting the equation successfully does not establish a microscopic mechanism. Later, we will use it as a specified synthetic model and check its consequences through a vessel balance.
Your action: Listen, then continue through the lesson.
Slide 23: Henry limit
Recording 30:06 | Follow the study route and activity cues
At sufficiently low pressure, b P is much smaller than one. The denominator of the Langmuir equation is then approximately one, so uptake becomes saturation uptake times b times pressure. This gives the Henry adsorption coefficient as saturation uptake multiplied by b. With our chosen units, that coefficient is measured in moles per kilogram per kilopascal. A matched Henry line and Langmuir curve therefore share the same slope as pressure approaches zero. They do not necessarily agree at finite pressure. The word Henry also appears in gas-solubility equations, sometimes written as partial pressure equals a constant times liquid mole fraction. That convention defines a different constant. Always state the equation, phases and concentration basis rather than relying on the name alone.
Your action: Listen, then continue through the lesson.
Slide 24: Isotherm worked example
Recording 31:08 | Follow the study route and activity cues
Use the synthetic saturation uptake of two moles per kilogram and b equal to zero point one per kilopascal. Their product gives a Henry adsorption coefficient of zero point two moles per kilogram per kilopascal. At one kilopascal, b P is zero point one. The Langmuir uptake is about zero point one eight one eight moles per kilogram, while the Henry value is zero point two. At ten kilopascals, b P equals one. Langmuir uptake is then one mole per kilogram, exactly half of its saturation uptake. The Henry line predicts two moles per kilogram. This growing difference follows from the denominator in the Langmuir equation. Ten kilopascals is already well beyond a convincing small-b-P approximation for these parameters.
Your action: Listen, then continue through the lesson.
Slide 25: Isotherm attempt
Recording 32:05 | Follow the study route and activity cues
Pause for about ten minutes and complete E one through E three on worksheet page four. Keep the same synthetic parameters and compare pressures of five and forty kilopascals. Calculate both Langmuir and matched Henry uptake, then calculate Langmuir fractional coverage. Write the dimensionless product b P at each pressure. Use that product to judge the low-pressure assumption rather than deciding from the pressure number alone. Finally, describe what each model predicts as pressure becomes large. Ask whether the equation contains a saturation limit and whether a mathematical value outside that limit is physically credible for the model's intended domain. Show the substitutions and units. Attempt the calculation before continuing to the comparison table on the next slide.
Your action: Pause for about 10 minutes. Complete worksheet p. 4, E1–E3 before viewing the check.
Slide 26: Isotherm check
Recording 33:02 | Follow the study route and activity cues
At five kilopascals, b P is zero point five. Langmuir uptake is two thirds of a mole per kilogram, with coverage one third. The matched Henry line predicts one mole per kilogram. At forty kilopascals, b P is four. Langmuir uptake is one point six moles per kilogram and coverage is zero point eight. The Henry value is eight moles per kilogram. That large value comes from extending a linear low-pressure expression into a range where its assumption is not satisfied. Langmuir uptake approaches the specified saturation value of two moles per kilogram as pressure increases. The Henry equation has no plateau. The comparison illustrates model domains, rather than evidence that a real material actually follows either curve over this entire range.
Your action: Listen, then continue through the lesson.
Slide 27: Closed adsorption vessel
Recording 34:02 | Follow the study route and activity cues
For a closed adsorption vessel, total adsorbate inventory equals gas moles plus adsorbed moles. The gas term is pressure times accessible gas volume divided by R T. The adsorbed term is adsorbent mass multiplied by absolute uptake. Use the accessible gas volume in the ideal-gas term and convert adsorbent mass to kilograms before multiplying by uptake. The unknown pressure is the adsorbate partial pressure. At fixed temperature, volume, mass and inventory, the isotherm and this balance determine pressure together. For positive Langmuir parameters, both amount terms increase with nonnegative pressure, giving a single nonnegative solution. The balance uses absolute uptake. An excess-adsorption measurement needs a density and volume convention before it can replace that quantity.
Your action: Listen, then continue through the lesson.
Slide 28: Vessel worked example
Recording 35:05 | Follow the study route and activity cues
This worked example starts with a known pressure, rather than a known total inventory. At ten kilopascals, with saturation uptake two and b equal to zero point one per kilopascal, the Langmuir uptake is one mole per kilogram. Ten grams is zero point zero one kilograms, so adsorbed moles equal zero point zero one. The gas amount in one liter at three hundred kelvin is about four point zero zero nine millimoles. Adding them gives a required total inventory of about zero point zero one four zero zero nine moles. The next task reduces total inventory to zero point zero one mole while keeping the other parameters fixed. Do not carry the ten-kilopascal pressure across unchanged. It must satisfy the new balance.
Your action: Listen, then continue through the lesson.
Slide 29: Lab 11 predictions
Recording 36:03 | Follow the study route and activity cues
Pause for about five minutes and complete F one through F three on worksheet page four. Read Lab guide pages three and four before watching the demonstration. First predict the Langmuir pressure when the inventory is zero point zero one mole, less than the amount needed for ten kilopascals in the worked example. Next compare Langmuir with the matched Henry model. At the same positive pressure, the Henry expression predicts greater uptake. Use the closed balance to decide which model should therefore require a lower pressure for the same inventory. Finally, return to Langmuir and double adsorbent mass from ten to twenty grams. Keep temperature, accessible volume and total inventory fixed. Predict the pressure direction and explain why.
Your action: Pause for about 5 minutes. Complete worksheet p. 4, F1–F3 predictions before the Lab 11 demonstration.
Slide 30: Lab 11 demonstration
Recording 36:58 | Follow the study route and activity cues
We are now in the real Lab eleven interface. Keep worksheet page five and Lab guide pages three and four open. Begin in Explore isotherms, the upper calculator. The data fitting section lower on the page is optional for this lesson. Our main task is to compare two adsorption models and close a vessel balance. The chart displays four model curves, but the model selected in the menu is the one used to solve the closed vessel. The other curves are not additional phases and are not combined into that balance. Select Langmuir and check a capacity of two moles per kilogram and an affinity of zero point one per kilopascal. Use three hundred kelvin. The pressure units matter because the product of affinity and pressure must be dimensionless. Entering a pressure in pascals while retaining an affinity per kilopascal would change that product by a factor of one thousand. Identify the parameters as synthetic definitions at this temperature. Changing the temperature field does not generate a new temperature dependent parameter set. For our first comparison, set the minimum pressure to zero and the maximum to ten kilopascals so that the lower pressure curves are easy to see. The worksheet uses zero to one hundred kilopascals for your independent investigation. All three vessel roots are below ten kilopascals, so either admitted window gives the same roots. We will widen the range later. Expand Closed vessel, fixed temperature and free gas volume. Enter one liter of free gas volume, ten grams of dry adsorbent, zero point zero one zero mole of total adsorbate, and zero inert gas. This total inventory is the one used in the Lab investigation. It is different from the earlier worked example in which a pressure of ten kilopascals was given and the required total inventory was calculated. Here the pressure is unknown. The solver must divide the specified total amount between gas and adsorbed material. Press Compare and solve vessel after checking these inputs. For case eleven A, the equilibrium adsorbate partial pressure is about six point zero eight zero kilopascals. The uptake is about zero point seven five six two moles per kilogram. To obtain the total adsorbed amount, multiply that uptake by zero point zero one zero kilogram, not by ten. The result is about zero point zero zero seven five six two mole adsorbed. The gas contains about zero point zero zero two four three eight mole. Together these recover the total zero point zero one zero mole. Record the selected model, pressure, uptake, both amounts, and residual. Before changing the model, save the calculated Langmuir case with its interpretation and label. Then select Henry in the model menu. Enter a Henry coefficient of zero point two mole per kilogram per kilopascal. This is the product of the Langmuir capacity and affinity, so the two isotherms have the same limiting slope near zero pressure. Keep ten grams of adsorbent, the same volume, and the same total inventory. Press Compare and solve vessel again. Matching the low pressure slope does not make the two models identical over the full pressure range. The Henry calculation gives about four point one six five kilopascals for case eleven B. It predicts about zero point zero zero eight three three zero mole adsorbed and zero point zero zero one six seven zero mole in the gas. Its material balance closes, but that does not establish that the approximation is physically adequate. At this pressure, the Langmuir product of affinity and pressure is about zero point four two, which is not very small. The linear model stores more material on the adsorbent at a given pressure, so it reaches the fixed inventory at a lower pressure. Save this second case separately. For case eleven C, return the selected model to Langmuir and increase the dry adsorbent mass from ten to twenty grams. Keep the capacity, affinity, temperature, gas volume, and total adsorbate inventory unchanged. Compare this case with the original Langmuir case, eleven A, so that adsorbent mass is the only physical variable being changed in that comparison. Notice that editing a field invalidates the old result. Recalculate before recording or exporting anything. We are adding adsorbent surface capacity to a vessel with the same amount of adsorbate, not adding more adsorbate. With twenty grams of adsorbent, the Langmuir pressure falls to about two point eight four five kilopascals. The total adsorbed amount increases to about zero point zero zero eight eight five nine mole. Yet the uptake per kilogram decreases to about zero point four four three zero mole per kilogram. These changes are consistent. There is more adsorbent, but the lower gas pressure leaves each kilogram less heavily loaded. Multiply uptake by zero point zero two zero kilogram to recover the adsorbed amount. Add the gas amount, about zero point zero zero one one four one mole, and check the same total inventory. Save the third case, then widen the maximum chart pressure to one hundred kilopascals and calculate again to inspect the model shapes. The Henry line continues upward without a finite capacity. The Langmuir curve bends toward the specified capacity of two moles per kilogram. This helps explain the worksheet comparison at forty kilopascals, where the two predictions differ strongly. A wider plotting range does not supply experimental validation. The Freundlich and BET curves use their own synthetic parameters and domains. They are visible for context, but fitting them and interpreting isosteric heat are optional extensions today. The Study workspace now contains three named model studies: Langmuir with ten grams, Henry with ten grams, and Langmuir with twenty grams. For each one, use Your interpretation to record the balance and the reason for the pressure change. Export model study downloads a calculated study and retains it in this temporary comparison. Do not use Export data study from the separate fitting section for this activity. The saved cases keep the original zero to ten kilopascal calculation window even though we subsequently widened the current chart to inspect the isotherm shapes. Select Download comparison to save these three model studies together. Read the recorded fields carefully. In this lab the equilibrium pressure is recorded in kilopascals, the uptake in moles per kilogram, and the gas and adsorbed amounts in moles. The vessel input mass is stored in kilograms and the volume in cubic meters. This differs from some display units and from the pressure convention in the gas solid export. Do not compare raw field values across different labs without checking their definitions. A blank field is not automatically zero. To check that the study is reusable, clear the temporary comparison only after saving the file. Under Load studies or a comparison JSON, choose the downloaded adsorption comparison file. The file is read by the browser and the saved cases become available to restore. Keep the actual file on your computer with the worksheet. An in memory comparison alone may disappear when you leave the page. Saving a screenshot is useful for discussion, but it cannot replace the inputs, units, model selection, and interpretation needed to reproduce the calculation. After import, select Restore beside case eleven A, Langmuir ten grams. Verify that the selected model, capacity, affinity, temperature, inventory, and adsorbent mass have returned correctly. The plot range should also return to the saved zero to ten kilopascals. Restoring inputs is not the final calculation step. Press Compare and solve vessel to calculate the current state. If you edit any parameter after restoration, calculate again before treating the displayed result as evidence for that new case. The restored and recalculated Langmuir case again gives approximately six point zero eight zero kilopascals and the same gas and adsorbed amounts as before. This completes the full workflow from choosing a model to saving and reopening the result. In worksheet section G, reproduce the three cases yourself and verify each balance by hand. Explain why more adsorbent can increase the total adsorbed amount while decreasing uptake per kilogram. State the absolute uptake basis and the ideal gas assumption. The next activity stop gives you time to create and check your own evidence.
Your action: Listen, then continue through the lesson.
Slide 31: Adsorption evidence
Recording 47:20 | Follow the study route and activity cues
A useful comparison needs more than a screenshot of a curve. Record the selected model, units and temperature because they define the meaning of each parameter. Then record pressure and uptake separately from the gas and adsorbed amounts. The uptake is measured per kilogram, while the vessel balance uses moles. Check the mass conversion explicitly. The sum of gas moles and adsorbed moles should reproduce the chosen inventory, within rounding and numerical precision. Keep a saved study and verify that reopening and recalculating it reproduces the result. Remember that two models can share a low-pressure slope without agreeing over the full range. Also, a correct numerical inventory balance verifies the calculation, but it does not prove that the chosen isotherm accurately represents a real material.
Your action: Listen, then continue through the lesson.
Slide 32: Lab 11 independent investigation
Recording 48:21 | Follow the study route and activity cues
Pause for about twenty-four minutes and complete G one through G four on worksheet page five. Open Lab eleven and follow Lab guide pages three and four. Run three cases with the same temperature, accessible volume and total inventory. Case eleven A uses Langmuir with ten grams of adsorbent. Case eleven B uses the matched Henry model with the same mass. Case eleven C returns to Langmuir and uses twenty grams. Record pressure, uptake, gas moles and adsorbed moles, then check each balance with your calculator. Compare the findings with your predictions and inspect the graph. Save your studies, reopen one, verify its controls and calculate again. Explain the difference between uptake per kilogram and total adsorbed amount when interpreting the mass change.
Your action: Pause for about 24 minutes. Complete worksheet p. 5, G1–G4 using Lab 11 and Lab guide pp. 3–4.
Slide 33: Lab 11 check
Recording 49:21 | Follow the study route and activity cues
The Langmuir case with ten grams gives about six point zero eight zero kilopascals. With the same inventory and mass, the matched Henry model gives about four point one six five kilopascals. Henry predicts more uptake at a common positive pressure, so it reaches this fixed inventory at a lower pressure. Returning to Langmuir and increasing mass to twenty grams lowers pressure to about two point eight four five kilopascals. Uptake per kilogram decreases, but total adsorbed moles increase because there is more adsorbent. Check the gas and adsorbed amounts in each row. Their sum is zero point zero one mole. The Henry result is useful for model sensitivity, but its finite b-P value requires caution about the low-pressure approximation.
Your action: Listen, then continue through the lesson.
Slide 34: Model scope
Recording 50:18 | Follow the study route and activity cues
The Lab includes additional models and analysis options, but they need their own assumptions. Freundlich is an empirical expression over a stated pressure range and has no saturation plateau. BET uses relative pressure and requires a justified fitting range and reference pressure. Isosteric heat requires comparing pressures at the same absolute loading across temperatures. Comparing arbitrary points on separate isotherms is not enough. Experimental fitting also needs measured data, uncertainty, units and a clear objective. Today's examples use synthetic parameters to examine equilibrium and inventory reasoning. They do not establish an adsorption mechanism or validate extrapolation. You can explore the extensions later, but no new fit, BET calculation or isosteric-heat calculation is required to complete this lesson. Choose one relevant limitation for your reflection.
Your action: Listen, then continue through the lesson.
Slide 35: Unseen case brief
Recording 51:28 | Follow the study route and activity cues
The final calculation transfers the method to new parameters. Keep the worked solutions closed and read H one through H four on worksheet page six. For the gas-solid case, use three hundred and ten kelvin, two liters and a sublimation pressure of five kilopascals. Compare volatile inventories of zero point zero zero two and zero point zero zero eight moles. Add zero point zero zero one mole of inert gas to each. For adsorption, use a different synthetic material with saturation uptake three moles per kilogram and b equal to zero point zero five per kilopascal. At twenty kilopascals and three hundred and ten kelvin, use two liters of accessible gas volume and five grams of adsorbent. Calculate the inventory required by that state.
Your action: Listen, then continue through the lesson.
Slide 36: Unseen attempt
Recording 52:28 | Follow the study route and activity cues
Pause for about twenty minutes and complete H one through H four. Use the equations from the earlier slides, but make your own calculation before opening the answers. For gas-solid equilibrium, determine the gas capacity first. Then find gas and solid amounts, volatile partial pressure and total pressure with the inert included. Check the species inventory in each case. For adsorption, evaluate the isotherm at the specified pressure. Convert five grams to kilograms, then calculate gas moles, adsorbed moles and total inventory. Predict what happens to pressure if adsorbent mass doubles while that inventory stays fixed. An exact new pressure is not required. Finally, state one shared assumption and one difference between bulk gas-solid equilibrium and surface adsorption.
Your action: Pause for about 20 minutes. Complete worksheet p. 6, H1–H4 before viewing the unseen-case check.
Slide 37: Unseen check
Recording 53:27 | Follow the study route and activity cues
The gas capacity is approximately zero point zero zero three eight eight zero moles. The smaller volatile inventory therefore completely vaporizes. The larger inventory leaves about zero point zero zero four one two zero moles of solid and maintains a volatile partial pressure of five kilopascals. The inert contribution is about one point two eight nine kilopascals. Add it to obtain the total pressures shown. For adsorption, uptake at twenty kilopascals is one point five moles per kilogram. Gas moles are about zero point zero one five five one nine, and adsorbed moles are zero point zero zero seven five. Their sum is about zero point zero two three zero one nine moles. Doubling adsorbent mass at that fixed inventory lowers pressure.
Your action: Listen, then continue through the lesson.
Slide 38: Choosing an equilibrium description
Recording 54:27 | Follow the study route and activity cues
Use these four questions whenever you approach a new equilibrium problem. First, identify the physical process. Bulk phase transfer, surface uptake and chemical reaction require different descriptions. Second, state the constraints. Temperature and pressure are not interchangeable with temperature and accessible volume. Third, identify the model and its conventions, including standard states, gas ideality, uptake basis, units and pressure range. Finally, use material balances to determine amounts and check whether the proposed phases are actually present. A solubility composition, a sublimation pressure or an isotherm loading supplies only part of the description. None replaces an inventory balance. In your reflection, report a numerical result with its units, one supporting check and the assumptions needed for the interpretation. That combination makes the result useful and reproducible.
Your action: Listen, then continue through the lesson.
Slide 39: Exit ticket and feedback
Recording 55:36 | Follow the study route and activity cues
Pause for about ten minutes to complete section I on worksheet page six and submit the Session four exit ticket and feedback. Use the link or scan the Q R code. Explain what happens to gas pressure when bulk solid runs out. In the evidence answer, include one Lab ten comparison and one Lab eleven numerical balance, with settings and units. Report your actual study time, including the activities, and tell me about any access problems or explanations that need improvement. The form does not ask for your name, student I D or email. Submit once and wait for the message Response received. The next slide is a receipt and saved-work check, not another submission request.
Your action: Pause for about 10 minutes. Complete worksheet p. 6, I and submit the Session 4 exit ticket and feedback once. Wait for Response received.
Slide 40: Receipt and saved work
Recording 56:28 | Follow the study route and activity cues
Check that the form shows Response received. If you already have that confirmation, do not submit a second response. Save your completed worksheet, including the predictions, calculations and corrections, together with the Lab ten and Lab eleven comparison tables. Keep the study J S O N exports and a note of one result that you reproduced by reopening and recalculating a saved case. Record your actual study time as well. The recording, worksheet and Lab investigations together form this week's lesson. There is no additional compulsory after-class assignment. The appendix remains available if you want to examine an extension. In the next session, we will continue using the same habits: identify the process and constraints, calculate carefully, and check the interpretation against conserved quantities.
Your action: Listen, then continue through the lesson.