Unit 13 - Modeling Instruction Program

```Unit 13 – Chemical Equilibrium
Instructional goals
1. Recognize that when a system reaches a state of equilibrium, processes continue to occur at the
microscopic level despite the fact that no further macroscopic changes take place.
2. Explain how initial unequal rates of forward and reverse processes can eventually result in the
equilibrium condition in which the rates of these opposing processes are equal.
3. Distinguish between equal rates of opposing processes and equal amounts (or distributions) of
the particles involved.
4. Explain that the same equilibrium condition will be reached regardless of whether the system
starts with reactants or with products.
5. Explain that the transfer rates between species dissolved in two non-miscible solvents depend on
the concentration in each solvent.
6. Generalize that the transfer rate for “condensed” phases (solids and liquids) is constant, but that
the transfer rate for “dispersed” phases (dissolved species, gases) depends on the concentration.
7. Given a chemical equation representing a system at equilibrium, write the expression for the
equilibrium constant.
8. Perform calculations involving the equilibrium constant and the concentrations of the reactants
and products.
Sequence
1. A kinetic view of liquid-vapor equilibrium. Introduce the equilibrium board game.
2. Vaporization of butane activity
3. Examine solubility equilibria. Lab: dissolving Ca(OH)2
4. Play the equilibrium board game to model solubility equilibrium.
5. Worksheet 2
6. Examine partition equilibrium involving two phases. Lab: solubility of I2.
7. Modify equilibrium board game to model partition equilibria.
8. Generalize rules for various equilibria. Worksheet 3(?)
9. Derive expression for equilibrium constant in terms of rates of forward and reverse reactions.
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10. Revisit BCA tables; modify to make ICE tables. Worksheet 4(?)
Overview
Students know that you cannot dissolve an unlimited amount of a solid in a fixed quantity of
solvent – at some point the solution becomes saturated. But what does this mean at the particle
level? Is there literally no more room for the solid particles to fit into the spaces between the
solvent particles, or is something else going on?
We first examine liquid-vapor equilibrium because the competing processes of vaporizing and
condensing can be modeled using essentially the same game as used in unit 11a – Energy &
Temperature. The biggest difference is that now the chips represent the particles of the
substance and the circles represent places they can occupy. If you chose not to do unit 11, you
should find that the students readily grasp the rules for positioning the chips and for transferring
them across the interface.
We move on to examples of solubility equilibria – first, solid-solution, then second, a case in
which a substance is partitioned between two solvents.
Instructional Notes
1. A kinetic view of liquid-vapor equilibrium.
Review
Even if you have shown the students what happens when liquid butane reaches equilibrium with
its vapor it would be a good idea to show the movie1 provided in the movie-pix folder to set the
stage for the following activity.
Apparatus
Equilibrium game board and chips (beans, macaroni or tiddly-winks)
Activity notes
Tell the students that they are to arrange 10 chips for A and 24 for B in a way that reflects a
liquid (B) in contact with its vapor (A) confined to half of the board for start of the game. Allow
them to wrestle with this a bit, providing hints about the difference in the spacing between
particles in the gaseous and liquid states. Eventually, make sure that they have filled the first
four columns in B (closest to the interface) and have two chips in each of the five columns
representing the particles of a gas. Students are likely to spread out the particles in the portion of
the board representing the liquid (B). Remind them that while the particles in a liquid are
mobile, they are packed just about as closely as those in a solid.
Remind the students that the liquid and gas are in equilibrium with each other. Remind them that
in the previous unit, we defined thermal equilibrium as the situation in which the same number
of chips are transferred by each player in each turn. Ask the students to devise transfer rules (for
B→A and for A→B) that result in the exchange of the same number of chips in each turn. With
some hints, they should reach the conclusion that for player B, the entire column closest to the
interface moves to the vapor, and player A transfers those chips in the first three columns closest
to the interface. The players are to exchange the chips simultaneously. These rules make sense
because only the particles in the top layer of the liquid can escape to the gaseous phase and the
1
See the movie 2-butane-vaporize.mov
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gas particles closest to the interface are the ones most likely to return to the liquid. Don’t get
hung up on why it works out that the number of columns in A that return to B is 3 – that’s just a
rule that works for this particular situation. What we would like to see if the same set of rules
models what we see for different situations.
Once the students are willing to accept that these rules work, show the movie clip “2-butanevaporize.mov”, making sure that they recognize that it is the increase in volume that initiated the
further vaporization of butane.
Now, have them distribute the chips in A over the full space (all 10 columns) and then play the
game, recording the results in the table in the file: 01-Vaporization activity.doc. This situation
represents increasing the volume, thereby reducing the concentration of the chips in the gaseous
phase.
Ask the students to state the number of chips that A and B have when they have re-established
equilibrium, then compare the concentration of the chips in A for the larger volume to that when
they had chips on only half the board. Elicit from them the conclusion that when equilibrium
between the liquid and its vapor exists, the pressure is constant.
2. Worksheet 1
Have the students examine the graph of the pressure of air vs. the number of puffs added to the
syringe. Remind them of the relationship between P and n that they found in unit 2. Next, they
should try to explain what is going on when “puffs” of butane are added to the syringe. To help
them explain why the pressure levels off, they should play the equilibrium game again, but they
will have to modify the rules (the exchange must take place sequentially, with A going first) in
order to get results that are consistent with the graph for 2, 4 and 6 “puffs”.
You may have to provide hints, but students should conclude that all the chips start out in player
A’s side of the board – use all 10 rows. Suggest that a “puff” could be represented by 5 chips.
In this scenario, the system gas phase becomes saturated at 4 “puffs”. Additional “puffs” added
to the system end up in the liquid phase. This explains why the pressure levels off, as the
concentration of the particles in the gas phase does not change.
At this point you should show the movie 3-butanecondense.mov. From this students should see that as the
concentration of gaseous butane gets high enough,
condensation becomes apparent.
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3. Solubility equilibrium – Ca(OH)2
Apparatus
250 mL beaker
NaCl (50g table salt will do)
10 vials containing 70 (±2) mg of Ca(OH)2
distilled water
stir plate and bar
LabPro and conductivity sensor
stirring rod
This activity can be performed as a demonstration2 if you have the means to project an image of
what is going on inside the beaker or as a lab that the students can do. Be advised that it will
require a bit of time (and a milligram balance) to mass out the samples of Ca(OH)2.
Pre-Activity discussion
Fill the 250 mL beaker with 100 mL of water; dissolve a teaspoon of NaCl into the water. Ask
the students what is taking place at the particle level. They should respond that the solid is
breaking up into Na+ and Cl– ions. To reinforce this, use Flash animation at
http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/molvie1.swf
Ask the students under what conditions does the reverse process (crystallization) occur. To those
who say that this only happens when the water is evaporated, remind them that they built a
model in which they proposed that both evaporation and condensation occurred when a liquid
was evaporating and that the process of evaporation appeared to stop when the rates of
evaporation and condensation were equal.
Continue adding more teaspoons of salt until no more will dissolve. Suggest to the students that
it’s reasonable to suppose that both dissolving and crystallizing can occur simultaneously, and
that when the rates of the opposing processes are the same, the solid appears to stop dissolving.
We say that the solution is saturated.
Suggest that we will examine the solubility behavior of Ca(OH)2, a substance that does not
dissolve very well in water. Because the substance breaks up into ions, we can monitor the
dissolving process by measuring the electrical conductivity of the solution.
Activity notes
Depending on the time and equipment available to you, you can do
this activity as a lab, as a demo, or simply show the presentation:
solubility.ppt.
Place 200 mL of distilled water in a beaker, add a stir bar and place
the beaker on a stir plate. Place the conductivity probe in the water,
and launch Logger Pro. The software should auto-detect the probe
and show the default data collection window. Under the
[Experiment] menu choose [Data collection] and then [Events with
entry]. Name column 1 mass Ca(OH)2; the units should be mg. Zero
the probe and begin collecting data. Add vials containing 70 mg of the Ca(OH)2, one at a time.
Wait a minute or so for the conductivity reading to stabilize, then [Keep] the reading and enter
the total mass of the solid added.
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A PowerPoint presentation (solubility.ppt) is provided that includes movies showing how this experiment was
performed in the event that you don’t have the time or the equipment to do it yourself.
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As the solid dissolves, the conductivity increases more or
less in a linear manner. Make sure that the students record
the appearance of the solution after each addition of the
solid. After the 5th edition, students should find that the
solution does not clear up after a while and the conductivity
begins to level off.
the solid. Stop collecting data, rinse off the probe, and
discard the solution down the drain. Students can print the
window or you can provide them sample data (see the file:
Ca(OH)2 data.cmbl).
Post-Lab discussion
Have the students label a couple key points on their graph with the observations they made
during the experiment (or demo). Have them estimate the maximum amount of the solid that
dissolved in the water. Ask them to consider what they think is taking place when no more
Ca(OH)2 appears to be dissolving.
4. Modeling solubility – the solubility game
Discuss with the students what might be a reasonable way to represent the particles in both the
solid and dissolved states. Display a solubility game board and suggest that the chips
representing the solid should be placed in the column or columns closest to the solid-solution
interface. The chips representing the particles in solution should be evenly distributed in the
solution space. For the purpose of this activity, B represents the solid and A represents the
solution.
Next, remind them that in the liquid-vapor game, they transferred the layer of liquid closest to
the interface to the gas, and that they transferred the chips in the first three columns (those
closest to the interface) back to the liquid. Suggest that they can use similar rules to model the
solubility of the solid, with an important exception. For this game to work with the relatively
small number of chips we have, the transfer has to be sequential (not simultaneous) with player
A going first. That is, at the very beginning, A can transfer 0 chips, and B transfers the 6 chips
in the first column (representing the first addition of Ca(OH)2).
Hand out the solubility activity data sheet. The first table looks like the one below.
6 chips
during a turn
at end of a turn
turn
A gives
B gives
A has
B has
0
0
6
1
0
6
6
0
2
3
4
5
6
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As the students play the game, you may have to ask them how they have decided to distribute
those chips that don’t divide evenly by the 10 columns in A’s side of the board. In any event, it
won’t take many turns for the players to find that they are exchanging the same number of chips
in each turn and at the end of the turn, all the chips are on A’s side of the board (in solution).
For the next round, leave the chips in A’s space and add another 6 chips to B’s side. As before,
students soon find that, while the rate of exchange may have increased, the substance continues
to dissolve. By the 4th increment of 6 chips, however, some chips end remains in B’s space at
the end of each turn; solubility equilibrium has been reached. Ask the students what will happen
if another 6 chips are added to B. By playing the game, they will find that the additional chips
end up in the solid; despite the fact that both dissolving and crystallizing continues at the particle
level, the solution is “saturated”.
For their report, students should show their tables for 1, 3 and 5 additions of chips representing
the solid. They should also explain why the solution is not saturated after the 3rd addition of
solid, but is after the 5th addition.
5. Worksheet 2
This worksheet gives the students a chance to examine what takes place when a large amount of
the solid is added all at once. The students begin by placing 30 chips in the first five columns on
B’s side of the board. They play the equilibrium game until it “gets boring”; i.e., they decide
when it’s reasonable to stop. This should occur when 20 of the chips have moved to A’s side.
Then, in the 2nd round of the worksheet, the 30 chips are distributed evenly over the columns on
A’s side of the board. The rules of play are the same as before, with A transferring chips to
begin the turn and B returning chips to end the turn. As before, the students need to resolve the
matter of how to distribute the chips that do not divide evenly over the 10 columns. As the
number of chips remaining in A’s space approaches 20, it is likely that you may have to prod the
groups that randomly positioning the 21st chip means that eventually it should find its way into
the first 3 columns so that it ends up in B’s space. Once A has 20 chips and B has 10, the
exchange rules guarantee no further change.
Now, have the students plot (using Logger Pro, Excel or manually) the number of chips in the
solid (B) and in solution (A) at the end of each turn. They should do this both rounds on separate
graphs. The surprising result is that whether one starts with all the material in the solid or in
solution, once equilibrium is reached, the concentration of the particles in solution is the same.
The file: solubility-amnt.cmbl shows results for both rounds.
Next, have the students plot the number of chips exchanged (A→ B and B→ A) during each turn
of both rounds of the game. The file: solubility-rate.cmbl shows results for both rounds. Try to
elicit from the students that while the rate of dissolving remains constant, the rate of crystallizing
depends on the concentration of particles in solution. As the concentration of particles in
solution increases (in round 1), the difference between the rates of dissolving and crystallizing
decreases.
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6. Solubility of iodine activity
Apparatus
3 shell vials
dropper bottle with 0.060M KI solution
dropper bottle hexane
dropper bottle with I2 in isopropanol (5g of I2 added to 100 mL of isopropanol and stirred for
30 min will insure that the solution is saturated)
bottle for storing waste solutions
Pre-lab discussion
Inform the students that this time they will examine the behavior of a substance that dissolves in
both aqueous and organic phases.
Lab performance notes
Students should place the vials on a sheet of white paper to help them judge the intensity of the
color of the iodine in both phases. Be sure to get the students to reach some consensus about the
number of drops of iodine that were extracted by the hexane. Be sure to ask the students why
they think that no more iodine went into the hexane layer. Students might suggest that the
hexane is “saturated”. Be sure that they make a prediction about the color of the hexane layer
once they have added it to vial 3 and provide an explanation for their prediction.
Have the students pour the contents of their vials into the waste bottle. When done, add a crystal
of Na2S2O3 to the bottle and shake until the thiosulfate has reduced the I2 to I–. The aqueous
layer can be drained from the mixture using a separatory funnel, and discarded down the drain.
The hexane layer can be added to kitty litter and then stored in waste area in your stockroom.
Students should find that the intensity of the color of the hexane layer is much darker than it was
in vial 2. When they add more drops of I2 to vial 1, they should agree a total number of 6 drops
of I2 in the aqueous layer in vial 1 should match the intensity of iodine in the aqueous layer in
vial 3.
7. Modeling solubility – the solubility game again
Have the students discuss how they could play the solubility game to model the results of their
experiment. They should reach the conclusion that the chips need to be distributed in both
aqueous and organic phases. In the previous lab, once the solution became saturated, the
concentration of A was constant, regardless of the total amount of particles. The exchange rule
that they used to describe the solid Ca(OH)2 or the liquid butane cannot work in this case. This
time, the ratio of concentrations [A]/[B] is constant, regardless of the amount. To model this, the
students must be led to conclude that the amount transferred in both directions depends on the
concentration of iodine in that phase.
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8. Summary of what weʼve learned thus far
1. When a macroscopic process (such as vaporization or dissolving) appears to stop, opposing
processes continue to take place at the microscopic level, but at equal rates, so that the net
change is zero/
2. The relative amounts of particles in each phase in a system at equilibrium do not appear to
depend on the initial conditions. Whether one starts with all the particles in A or in B, once
equilibrium is reached, the distribution of the particles in each phase is the same.
3. It appears that a constant transfer rate is appropriate for condensed phases (pure liquid, solid),
while a relative transfer rate was appropriate for dispersed phases (gas, solute).