Learning Scenario – Precipitate Model
(AgentSheets)
Basic Model:
Description
This is an agent model of a simple precipitation reaction of a solute in a
solvent. The model displays a number of particles that move randomly within a
liquid. Whenever two of these particles collide along the horizontal axis, they have a
chance of precipitating out. Precipitates will fall to the bottom of the tank and
coalesce. Parameters in this model determine the starting density of the particles
and the chance that they will precipitate out upon colliding.
Background Information
Many chemical reactions occur between two compounds that are dissolved in
water or another suitable solvent. Dissolved molecules have a greater ability to
move around and interact with one another than they would have if they remained a
solid. Where things get interesting, however, is when both of the reactants in a
chemical reaction are water-soluble, but their product is not. This creates a
situation where the compounds react in the water, but then their product either
sinks to the bottom as a solid or bubbles to the top as gas. This separation of
products from reactants is called precipitation.
Precipitate reactions have a large number of different applications in
chemistry. One of their most useful features is the ability to completely remove a
solute from water, something that is normally only possible by boiling and
recondensing the water. As a result, precipitate reactions are a very effective way of
removing certain types of impurities from water as part of a water treatment
process. Precipitate reactions can also be desirable for their quality that any
precipitate reaction will go to completion. Since the product is no longer a part of
the solution, it cannot react again to become a reactant. If the product of a reaction
is the only useful compound, a precipitate reaction will help ensure that all of the
reactant is used efficiently.
Science/Math
The fundamental principle behind this model is that the probability of an
event occurring is proportional to the number of different ways that it can occur,
given that all occurrences have equal probability. Thus, in this model the chance
that a particle will precipitate out is proportional to the number of possible pairs of
particles that could interact with one another. Each time tick, the following things
happen:
1) Each particle that has yet to precipitate moves in a random direction
2) Each particle that has precipitated moves down (if possible)
3) Any two particles that have not yet precipitated but are next to each other on
the horizontal axis have a certain chance of precipitating out.
Teaching Strategies
An effective way of introducing this model is to start with “pure” statistics
first to ensure that students understand the mathematics behind it. Ask students to
enumerate all potential pairs of results that can occur under the following random
simulations (order matters):
1) Flip 2 coins
2) Flip 1 coin and roll one 4-sided number cube
3) Roll 2 4-sided number cubes
4) Roll 1 4-sided and 1 6-sided number cube
5) Roll 2 6-sided number cubes
6) Roll 2 8-sided number cubes
When they are done, ask the following questions:
1) How many different pairs of results did you get for each simulation above?
2) Is there a relationship between the number of outcomes of each individual
random event and the number of pairs of outcomes? If so, what might that
relationship be?
3) If I asked you to tell me the number of possible pairs of results of rolling 2
20-sided dice, what would that be? You shouldn’t need to enumerate them
one by one.
4) If I increased the sides of the die by 50% to 30, what would happen to the
number of possible pairs? How do you know? What is the general
relationship between the number of sides of the die and the number of
possible combinations of rolls?
Implementation:
How to use the Model
There are two different parameters that can be manipulated to change the way this
model runs:
1) The “density” parameter determines the proportion of solvent cells that are
filled with solute when the pencil tool is used to refresh the container. This
determines the initial quantity of solute, and thus the reaction rate
2) The “stickiness” parameter determines the probability that two solute cells
that come into contact on the horizontal axis will “stick together” and
precipitate out of the solution. This also contributes to the reaction rate
These parameters can be manipulated by clicking on the dropdown arrow in
the upper-right hand corner of the worksheet and choosing “Simulation Property
Editor”. Users are able to input values directly or use the up and down arrows to
change each parameter by a preset amount. Changes to stickiness take effect
starting on the next tick, without requiring a reset of the simulation. Changes to
density affect the initial concentration of solute, so they do not take effect until the
simulation is reset.
To run the simulation, click the green play button at the bottom of the
worksheet. As the simulation runs, the results will automatically be displayed on a
graph. Users can also use the “Slow…Fast” slider bar to change the rate at which the
simulation runs. To move forward just one tick at a time, click on the gray
play/pause button next to the run button instead. For more information about
Agentsheets reference the Agentsheets tutorial at:
http://shodor.org/tutorials/agentSheets/Introduction.
Learning Objectives:
1) Understand the relationship between solute concentration and precipitation
rate in a precipitation reaction
2) Understand how reaction probability affects precipitation rate in a
precipitation reaction
Objective 1
To accomplish this objective, have students modify the simulation to add a
graph of the number of solute molecules that have not yet precipitated at a given
time, and then run the simulation several times with different initial solute
concentration levels. For each run, record the amount of time it takes for the solute
concentration to get (a) below half of the initial concentration, and (b) less than 50.
Ask the following questions:
1) Based on your results, approximately how long does it take for a 10% density
solution to precipitate half of its solute? How about a 20% density solution?
A 50% solution? Which was the fastest? Does that make sense?
2) How long did each of the previous solutions take to get less than 50 solute
molecules left? Which was the fastest? Does that make sense?
3) In a simple inverse equation of the form 1/x, it should take exactly the same
time to cut the amount of solute in half regardless of the starting point. Is
that what you observed? If not, is there any other equation that might model
the results more effectively?
4) What is the number of ways that a pair of particles can interact? How does
this relate to the equation that seems to model the results here?
Objective 2
To accomplish this objective, have students set the “stickiness” of the
particles to (a) 1.0, (b) 0.5, (c) 0.25, and (d) 0.1. Then, run the simulation several
times at each stickiness level and record the amount of time it takes for the solute to
get below half and less than 50 in each case. Ask the following questions:
1) Based on your results, approximately how long does it take for a solution to
precipitate half of its solute with each stickiness level? What is the
approximate relationship between the two? Does that make sense?
2) How did changing the stickiness of the particles affect the results of the
simulation? What equation would best approximate this relationship? Does
that make sense?
3) How do the two parameters differ in their effects? Why do you think that the
relationship between concentration and reaction rate is 1/x2, while the
relationship between stickiness and reaction rate is only 1/x? Hint: think
about which events the two parameters affect and how many ways those
events can happen.
Extensions:
1) Investigate ways of increasing reaction rates without changing the
fundamental reaction
2) Extend the model to a new reaction with two types of reactants that must
interact in order to precipitate
Extension 1
Have students brainstorm other ways that chemists might try to increase
reaction rates without increasing the concentration of solute. Common ideas might
include increasing the temperature, stirring/shaking, or removing the precipitate
from the reaction as it forms. Have students implement their ideas in the
AgentSheets model as effectively as possible. For instance, higher temperatures
would increase movement rate, while stirring/shaking might change movement
probabilities to be biased in one direction or another. Have students test their new
simulations, and then ask the following questions:
1) How did your implemented change affect precipitation rates? Was this what
you expected? Why or why not?
2) To what extent does increasing the movement rate of particles increase the
precipitation rate?
3) In the real world, increasing the temperature of a reaction only changes the
collision rate by a small amount, but it vastly increases the reaction rates
nonetheless. How is that possible? What other parameters might
temperature affect?
Extension 2
Have students create a new agent within the model and change the agent
behavior such that agents can only precipitate if they interact with a different agent,
not one of their own. Have students test their new simulations, and then ask the
following questions:
1) Compared to the single-reactant model, are precipitation rates in this new
model higher, lower, or the same for an equal concentration? Why do you
think this is?
2) Change the concentration of both reactants to the same levels that you did
before with the single solute, and re-run the simulation. What relationship
do you see between concentration and precipitation rates now? Does that
make sense given our earlier statistical reasoning? Why or why not?
3) Change the stickiness and re-run the simulation. What relationship do you
see between stickiness and precipitation rates now? Does that make sense
given our earlier statistical reasoning? Why or why not?
Related Models
Second-Order Chemical Kinetics
http://www.shodor.org/refdesk/BioPortal/model/ASsoChemKinetics?level=introd
uctory
This is a closely related model to the Precipitate Model that simulates a
chemical reaction wherein two compounds react to form two products. As with the
precipitate model, the relationship between the concentration of the compounds
and the reaction rate is quadratic rather than linear. The main difference is that
second-order chemical kinetics has the potential to be a reversible reaction. In such
a situation, the relationship between concentration and reaction rate would still be
linear, but it would go to equilibrium rather than completion. This model is best
used as an extension of the precipitate model, to introduce multiple reactants and
the concept of reversibility.
Beginning Enzyme Kinetics
http://www.shodor.org/refdesk/BioPortal/model/NLBasicEnzymeKinetics?level=i
ntroductory
This model builds on the precipitate model but takes it in a slightly different
direction. Here, rather than needing any two particles to collide in order to react,
the reactant must bind with an enzyme before it can transform into a product. The
enzyme is not consumed or changed in any way by the reaction. In theory, if the
number of enzymes is approximately equal to the number of reactants, this reaction
will evolve by the same mathematical logic as the precipitate model. However, the
concentration of enzymes is usually extremely small compared to the concentration
of reactants, so it acts as a rate-limiting step and the actual reaction is
approximately linear. This model should be used to help students understand the
role of assumptions in chemistry. Depending on whether there is an equal quantity
of both types of reactants or a larger amount of one reactant, the mathematical
equation for the rate of the chemical reaction can be completely different. Similarly,
small changes in the rules of the precipitate reaction can have large effects on the
way it unfolds.