Ideal Gas Law Introduction Lesson Plan
Keith Newman
Chemistry 511 – Final Project – 2006/2007
Objectives:
*
Students will be able to solve ideal gas law problems using
algebraic ratios.
*
Students will be able to predict the behavior of gases using the
ideal gas law.
*
Students will be able to explain the use of ideal gas laws and its
uses.
Standards:
Academic Standards for Science and Technology, Pennsylvania Department
of Education, Page 15 3.4.10. GRADE 10.
Academic Standards for Mathematics, Pennsylvania Department of
Education, Page 15 2.8.10. GRADE 10.
Background Information:
Being a math teacher, and not having the ability to strictly teach
science, I’ve decided to bring the math to the science by introducing
my students to the Ideal Gas Laws. Many of my 10th graders have a hard
time dealing with fractions, ratios, and literal equations. Since the
ideal gas law uses all of those skills, I’ve decided to create a math
lesson plan showing students that using science to explain math is a
great way to “own” the material.
The ideal gas law wasn’t exactly something that just popped up from
one person. The problem with doing science (especially when you are in
the pioneering stages) is that people have to take chances and
sometimes even have to go against the normal paradigms and think
outside of the box. This was true for these leading scientists: Robert
Boyle, Jacques Charles, Joseph Louis GayLussac and Amedeo Avogadro.
They were all involved in the revolution of figuring out how ideal
gases would behave in any given situation involving pressure, volume
and temperature. The interesting part about them is that it took all
of their workings to come up with what we now know as the ideal gas
law.
Boyle came to the conclusion that P times V is constant as long as
temperature stays constant (PV k). He also had a variation of his
law (Boyle’s Law) and used it to further explain his experiments with
his manometer. The variation is most commonly seen as , and is
most widely used when solving with known and unknown algebraic values
(Spark Notes). The manometer experiments by Boyle are considered to be
very dangerous today. At the time he would use the element Mercury,
which is very dangerous when exposed and ingested to humans. Still,
Boyle was able to prove that his part of the Ideal Gas Law was true by
showing pressure differences in his manometer.
About a hundred years later, Jacques Charles added another part of the
equation that said: volume over temperature is constant when pressure
is held constant. This also has another form just like Boyle’s Law and
can be expressed such as: (Spark Notes). Now, Charles knew
that the temperature had to be the absolute temperature because he
found that when you use Celsius you can have negative values and when
you use negative values in his formula you can get negative volume and
pressure which doesn’t make any sense. Therefore all temperatures we
use will be in Kelvin units (absolute temperatures, C + 273) (Spark
Notes). The problem with Charles is he didn’t really record his notes
for use by others. He was very interested in ballooning and used his
own discoveries to help him in his flights (E. Thall).
GayLussac realized a third component of the ideal gas law (also
several years after Charles figured this out) and said pressure over
temperature is constant when volume is constant (D. Nelson). This was
the key connection that became Charles’ Law because it’s the variation
of what was said by Charles but now used to fit our ideal gas law.
Since, we know where the P, V, and T come from in the laws talked
about above but, what are the “n” and “R” values all about?
We are using the widely accepted notion of Avogadro’s Law (the man who
brought everything together into the basic Ideal Gas Law of PV nRT)
that states the volume of a gas kept at constant temperature and
pressure will relate to the amount of moles of that gas are present
(Wikipedia: Avogadro Article). This is where the “n” value comes from.
It simply states we have “n” moles of this gas present. The problem
with Avogadro’s Law wasn’t that it was flawed but, other scientists
were not ready to accept the fact that the amount of molecules had
anything to do with how ideal gases behave (E. Thall).
The R value is simply how we handle unit conversions because we are
going from moles, temperature, volume, and pressure units. In this
lesson we will use liters for volume (L), atmospheres for pressure
(atm), n will be in units of the mole (mol), and as mentioned
previously, temperature is in Kelvin (K). Once they came up with the
ideal gas law they had to create a constant “R” to keep the equation
balanced in terms of units, basically a value that would basically
convert all those different units. Since we are using the above units
our constant is going to be R 0.08206 (Spark Notes). This
will work out very nicely algebraically once we are given our values
to input.
Classroom Activity:
Students will now have direct instruction on how to use the ideal gas
laws. This will include manipulating the ideal gas laws to solve for
P, T, V, and n. Once we establish those three formulas algebraically,
students can be given problems to solve for the unknown variable.
Formulas to know:
Sample Problems:
Find the volume of 2.40 mol of gas whose temperature is 50.0 °C and
whose pressure is 2.00 atm. Remember to change from Celsius to Kelvin!
Find the pressure of 3.00 mol of gas whose temperature is 60.0 °C and
whose pressure is 5.00 L.
Find the temperature of 1.50 mol of gas whose pressure is 4.00 atm and
whose volume is 7.50 L.
Find the number of moles of a certain ideal gas whose volume,
temperature, and pressure are 3.00 L, 25.0 °C, and 2.00 atm,
respectively.
Inquiry Process:
After students have been practicing the ideal gas law problems they
will be introduced to some inquiry questions that help them understand
how varying values will change the equation. This helps their math
inquiry skills by using inductive reasoning. Inquiry questions will be
as a group assignment (groups were assigned in the beginning of the
marking period based on student performances with each group have one
high, one low and two intermediate achievers).
1.
What happens to temperature if pressure goes up and volume remains
the same?
2.
What happens to temperature if pressure goes down and volume
remains the same?
3.
What happens to pressure if volume remains the same but
temperature goes up?
4.
What happens to pressure if volume remains the same but
temperature goes down?
5.
What happens to pressure if volume goes up and temperature remains
the same?
6.
What happens to pressure if volume goes down and temperature
remains the same?
7.
What happens to volume if pressure is held constant but
temperature goes up?
8.
What happens to volume if pressure is held constant but
temperature goes down?
Reflection:
Students are required to turn in a one page journal reflection that
details how their group went about answering the questions and what
hardships they encountered. Students should also include a summary of
what role members of the group took in evaluating these questions. The
entry must also include a brief description on their understanding of
the ideal gas law. If they are having difficulties with their own
understanding of it, then they must detail what issues they are having
problems with and a course of action to address those issues.
Extension Questions:
Why does a baseball bounce better in the summer than in the winter?
What does a larger container do to pressure?
I would also further the students extension with this activity from
wikihow.com. This activity is fairly simple to demonstrate and is
another real life demonstration of these formulas in action.
WikiHow, Various (2007). Crushing a Can with Air Pressure Activity.
http://www.wikihow.com/GetKidsInterestedinSciencebyCrushingaCanWithAirPressure
Assessment:
In addition to a standard computational exam, students will be given a
set of problems similar to the ones found in the example set. With
those problems, they must use the following Java based applet to
determine the answers. They are to use screen captures using “Print
Screen” function and written explanations to answer the questions.
PhET Website (2007). Physics Education Technology website.
http://phet.colorado.edu/webpages/simulationsbase.html
Students can now “play” with the ideal gas laws in a Java based
applet. This allows for students to visually see the numbers they are
crunching as trapped gases and connects them even further to the
content.
Resources:
Sparknotes, Uncredited (2007). Ideal Gas Law History and Equation
Summary. http://www.sparknotes.com/chemistry/gases/ideal/summary.html
Nelson, D. (2007). Lecture Notes PDF format.
http://www.aos.wisc.edu/~dnnelson/AOS101Lecture3.pdf
Wikipedia, Uncredited (2007). Avogadro’s Law.
http://en.wikipedia.org/wiki/Avogadro%27slaw
Thall, E. (2007). Thall’s History of Gas Laws.
http://mooni.fccj.org/~ethall/gaslaw/gaslaw.htm
PhET Website (2007). Physics Education Technology website.
http://phet.colorado.edu/webpages/simulationsbase.html
WikiHow, Various (2007). Crushing a Can with Air Pressure Activity.
http://www.wikihow.com/GetKidsInterestedinSciencebyCrushingaCanWithAirPressure