MU Modeling Chemistry Workshop Day 5a

Lost my flow preparing for ChemED presentation, ChemED itself, #140edu and the subsequent post-PD summer laze, but better Nate than lever!

We started Day 5 by discussing an article by Ronald Gillespie that we’d read the night before. The article discussed topics that the author thought should be included in an introductory college chemistry course.  In groups, we whiteboarded what topics we would exclude for high school chemistry, and what topics we would add.

Next, we discussed the gas labs we’d done the day before. (P vs. V, P vs. T, P vs. n), and their respective relationships.

P \propto \frac{1}{V}

P \propto T(K)

P \propto n

V \propto T

 We discussed how we can use these relationships to make predictions about how changes in conditions will affect one of the variables. We used PVTn analysis tables, which look like this:

Students will fill in the initial conditions, final conditions, and an up or down arrow to indicate the effect of the change on each of the variables. For example, for the problem:

A sample of gas at a pressure of 0.556 atm and a temperature of 20^{\circ}C occupies a volume of 12.9 liters. If the gas is allowed to expand at constant temperature to a volume of 22.3 liters, what will be the pressure of the gas sample?

Students would record the information in the table

The analysis table is great for organizing information, and also for allowing students to apply the relationships they developed to begin to reason about what the answer should be. Based on the inverse proportional relationship between P and V, you would expect an increase of volume to result in a decrease in pressure. So, either

P_{initial}\times\frac{12.9 L}{22.3 L}=P_{final}


P_{initial}\times\frac{22.3 L}{12.9 L}=P_{final}

will result in a smaller number. In this case, in the first equation, the volume ratio is less than one, so it will decrease the pressure. So students can solve to find the answer.

The analysis works well also for combined gas law problems. For the problem

A sample of helium gas has a volume of 7.06 L at 45^{\circ}C and 1590 mm Hg. What would be the volume of this gas sample at STP?

Here, there are two variables changing: pressure decreases, and temperature decreases. But because P and V are inversely proportional, and P and T(K) are directly proportional, they have opposite effects on the volume. So the two approaches to solving this are to

  • Solve one variable, then use new value to solve for second, or
  • combine both into one equation
Using the second approach, you’d need to multiply the initial volume by a ratio of pressures that is greater than one, and a ratio of temperatures that is less than 1. Or,


I have used this approach to gas laws for two years, and I love it. Students use proportional reasoning rather than “plug and chug” and keeps students thinking about why they’re doing what they’re doing. This is one place where the textbook is unhelpful, because it quickly reduces this all to “Boyles law is P_1V_1=P_2V_2  “, etc. One text I’ve found that uses proportional reasoning here and elsewhere is Introductory Chemistry: An Active Learning Approach by Mark S. Cracolice and Edward I Peters. We were intent on adopting this text, but some logistical issues made it impossible (its HUGE, expensive, and paperback). It is a college text for non-majors, but takes a modeling-esque approach to quantitative problems, and is heavy with multiple representations. I hope they’ll come out with a HS friendly version. I’ve had my desk copy for less than a year, and its already falling apart, so you can imagine how it would fare in the hands of teenagers.

Anyway, back to the workshop. We whiteboarded some PVTn problems, and finished by whiteboarding “The Story So far,” and modifying our model to incorporate the new topics from this unit. Namely,

  • particles move at different speeds
  • hot particles move faster than small particles
  • when particles collide with each other, they don’t stick
  • when particles collide with the container with some frequency, this can be measured by pressure
  • Relationships between pressure, volume, temperature, and number of particles

We then started unit 3, but I’ll put it in the next post.

Blank PVTn Table Google Doc

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