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EAS1600 – Lab 04
“The Ideal Gas Law”
Objectives
In this lab we will investigate the behavior of air under different conditions – varying
pressures and temperatures. We will assume an ideal gas approximation, and will verify change
in the volume of air with pressure change at constant temperature (Boyle’s Law), and change
in the volume of air with temperature change at constant pressure (Charles’s Law). Also, the
Universal gas constant R* will be determined based on the experiments, and compared to
standard value.
At the end of this lab, you should be able to:




understand the concepts of kinetic theory and ideal gas,
know the limits and applicability of these concepts;
understand the Ideal Gas Law, recognize its different forms;
apply Ideal Gas Law to solve problems related to Earth’s Atmosphere
Theoretical background
Kinetic gas theory. The kinetic theory (also known as the collision theory) is a theory
that explains the state properties of gas, such as pressure, temperature and volume, based on
the behavior of microscopic gas particles (molecules). There are several basic assumptions that
are used in kinetic theory:
- A parcel of gas consists of molecules that are in a state of constant random motion; the
number of molecules is very large, so statistical approach can be applied.
- The distance between molecules is much larger than the size of the molecules.
- The only interaction between molecules (and between molecules and walls of the
container) is through elastic collisions; the molecules obey Newton’s laws of motion.
The behavior of gases at normal pressures and temperatures is explained very well by the
kinetic theory; an ideal gas is a gas that behaves according to kinetic theory.
Dalton’s law is a direct derivation from these principles. It states that the pressure exerted by
a mixture of gases is simply a sum of partial pressures, exerted by each of the gases, if they
were acting independently.
Boyle’s Law: Robert Boyle studied the relationship between the volume and pressure of an
ideal gas. He found that at constant temperature the pressure P of a gas is inversely
proportional to its volume V :
P×V = const.
In other words, if you double the pressure of a given amount of gas, its volume will decrease
by half. For example, at ~10 meters under water (two times the normal atmospheric pressure)
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there is twice the amount of air within a diver’s lungs. The lung’s size remains the same, but
the air compresses and doubles in amount.
Charles’s Law: Charles’s Law states that under conditions of constant pressure and quantity,
the volume V of a given amount of dry ideal gas is directly proportional to the absolute
temperature T, or
V
= const.
T
Gay-Lussac's law. Gay-Lussac's law, discovered in 1802, relates pressure and temperature of
an ideal gas, provided that the amount of gas and its volume are constant:
P  T,
or
P
 const
T
Avogadro's law states that all ideal gases, taken in equal volumes at the same temperatures
and pressures, will have the same number of molecules in them. One mole of an ideal gas
occupies approximately 22.4 liters at a temperature of 25C and at normal atmospheric
pressure.
Mole (denoted as mol) is the SI unit that measures an amount of substance. One mole contains
Avogadro's number (approximately 6.022×1023) of atoms or molecules.
Molar mass M is the mass of one mole of a substance. The unit of molar mass is grams per
mole (g/mol). Molar masses are usually calculated from standard atomic (or molecular)
weights of the substance, multiplied by the molar mass constant, 1 g/mol, which is used to keep
the units correct as the atomic weights are dimensionless. For example, the molar mass of pure
Sulfur (S, atomic weight is 32 atomic mass units) is:
molar mass (S) = 32 1 g/mol = 32 g/mol.
The Ideal Gas Law. The Ideal Gas law, first written in 1834 by Emil Clapeyron, is the
combination of Boyle's Law, Charles’s Law and Avogadro's Law. Expressed mathematically,
the Ideal Gas Law relates all 3 state variables and the absolute quantity of gas:
PV = nR*T,
where P is pressure; V is volume; n is the number of moles of gas; R* is the Universal gas
constant (R*= 8.31 J · K-1 · mol-1 ), and T is the absolute temperature (K).
Alternative forms of the Ideal Gas Law: besides the form shown above, the ideal gas law
can be expressed in several other ways:
P =  Rm T,
or
PV = NkT,
where  - density; Rm - specific gas constant equal to R*/M (for the dry air Rair  287 J kg-1 K-1);
N – number of molecules; k - Boltzmann's constant, k =1.38×10-23 J/K.
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Online exercises/activities
For additional information and animations take a look at the following web pages:
http://comp.uark.edu/~jgeabana/mol_dyn/ - Java animation of the molecular collisions.
For a deeper review of the kinetic theory, please take a look at
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/ktcon.html
This page contains an interactive chart that links together kinetic theory concepts. Clicking on
boxes with concepts will bring you to the detailed explanation page with formulas, graphs and
examples.
Safety precautions
There are several things to remember in order to stay safe during this lab:
-
Please be careful with glass beakers during the lab.
There should be no water spills on the table where the equipment is set up. Clean all
spills immediately.
Hot water is used in the experiment. Please be careful pouring hot water, as it can cause
burns if spilled on the skin. To fill the beaker with hot water, put the beaker on the lab
table and then slowly pour the water from the electric kettle.
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Part 1 - Boyle’s Law.
Equipment
The equipment for this experiment consists of a syringe held between two wooden blocks,
and two weights, 500 g and 1 kg. The syringe can be sealed by putting a small plastic plug at
the end.
Figure 1. Experiment set-up for Part 1 - Boyle’s Law.
Procedure:
1. Read the safety precautions before starting the lab.
2. Record the room temperature.
3. Weigh the upper (cap) wooden block (round wooden block with slot for the syringe
plunger end) and record its weight.
4. Insert the plunger end into the larger slot of the cap block, and then slide plunger end over
to the center of the cap block.
5. Turn the assembly so the syringe is positioned horizontally and draw 45 cm3 (1 ml = 1 cm3)
of air into the syringe (the plug should be removed to allow the air in) and then place and
tighten slightly the small plastic plug at the end of the syringe.
6. Place the assembly on the lab table with the stepped round wooden block on the table top.
7. The top wooden block works as the smallest weight now. Tap the syringe on the side
lightly, to compensate for a piston-to-wall friction. Record the volume (in V1 column) and
weight of the wooden block into the second row of Table 1.
8. Place the 500 g weight on the top block. After placing the weight, record the volume of air
in the syringe and the total weight applied to the piston. Tapping the syringe lightly will
help reduce errors due to friction. Make sure the weight is not going to fall off the upper
block when you are tapping!
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9. Repeat the previous step with 1 kg weight, and then with both 500 g and 1 kg weights.
Each time, record the volume of air in the syringe and total mass applied to the piston.
10. After all the weights have been added, remove them one by one, recording the volume (in
V2 column) in the corresponding row, as before. Tapping the syringe lightly will help
reduce errors due to friction.
Measurement results
Table 1. (4 points)
V1, cm3
V2, cm3
V=(V1+V2)/2, cm3
45
Total weight, kg
Note
0
Initial volume
Upper block
installed
Upper block +
500g
Upper block +
1000g
Upper block +
500g+1000g
Analysis of measurement results
Question 1. Using a ruler, measure the inside diameter of the syringe barrel. Calculate the area
A, using the formula: A= r2 where r is 1/2 of the diameter. Enter the answer into your
Clicker in units of m2 . (1 point)
Question 2. Calculate the number of moles of air, n, present in the syringe at the beginning of
your experiment. In your calculations use the following values: molecular weight of air = 28.96
g/mole and the density of air under standard conditions =1.23 kg/m3. Enter the answer into
your Clicker. (3 points)
Next, calculate the pressure inside of the syringe, P, for each data point by using the
relationship: P = F/A + P0 , where F = mg is the gravitational force exerted by the weight;
A is the area of the syringe barrel, and P0 is atmospheric pressure (remember, the atmospheric
pressure is present all the time !!!). Write your results in table 2 (below) . (For reference, g =
9.81 m/s2 ; 1Pa=1 N/m2=1 kg·m-1·s-2 ; 1 ml =1 cm3= 10-6 m3; Standard atmospheric pressure
is 101325 Pa =101.325 kPa =1013.25 hPa = 1013.25 mbar.)
Based on your experiment, determine the Universal Gas constant R*. Write your results in
Table 2. Plot the volume, V, versus 1/P for each data point in Excel®. Print out the plot and
turn it in with your lab. (4 points)
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Table 2. (6 points)
Average
Force F,
Volume
N
V, cm3
Pressure
P, Pa
1/P
P×V, Nm
T×n
R* 
P V
T n
Note: temperature should be in K in order to get proper value for R* in units of J K -1 mol -1
Question 3. Enter the average value of the gas constant R* obtained in your experiment, into
the Clicker, in units of J K -1 mol -1. (1 point).
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Part 2 - Charles’s Law
Equipment
The equipment for this experiment consists of a 500-ml glass beaker, a syringe held in a beaker
with a rectangular wooden block, hot water, and a thermometer. The syringe can be sealed by
putting a small plastic plug at the end.
Figure 2. Experiment set-up. Part 2 - Charles’s Law.
Procedure:
1. The lab instructor will prepare the hot water (~ 80 C) in the electric kettle. Fill your
2.
3.
4.
5.
6.
7.
glass beaker with hot water up to the 450 ml mark. Please be careful not to burn
yourself.
Draw 40 cm3 of air into the syringe and place the plug at the end. Make sure there is no
water inside of the syringe, as this can affect your measurements.
Place the thermometer into the smaller hole of the rectangular block.
Place the syringe and the thermometer into the hot water, such that the rectangular
block would sit on the rim of the beaker as a support. Allow 2-3 minutes for
equilibration and then take a temperature and volume reading.
Record the volume in the syringe and the temperature in Table 3.
To get an accurate volume measurement, first push on the piston slightly and then
release it. Record the volume (V1). Then, pull back on the piston slightly and release it.
Record this second volume (V2) and the average of the two volumes. One of the team
members should hold the beaker and wooden block securely, while the other student
takes the measurements.
Allow the water to cool and take successive volume and temperature readings every
10 C or so. Write your results in Table 3. To speed up the cooling, you can add ice or
cold water into the beaker when the temperature is below 50 C. Remove the excess
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water using another syringe with a tube extension. Mix water and give it some time to
equilibrate before taking the measurement.
Measurement results
Table 3. (5 points)
V1, cm3
V2, cm3
V=(V1+V2)/2, cm3
T , C
T,K
Analysis of measurement results
Plot the dependence of volume V, on temperature T (use temperature in K ! ) using Excel®.
Add an appropriate trend line to the plot, together with equation. Print out the plot and attach it
to your lab. (4 points)
Question 4. Should the V (T) graph you plotted in this experiment give you a straight line?
Answer by typing “Y” for yes, or “N” for no, using the Clicker. (1 point).
Question 5. What is the number of molecules in one mole of air? Choose one from the following
and enter the letter that corresponds to your answer into Clicker (2 pts).
A.
B.
C.
D.
E.
The number of molecules in one mole depends on the pressure and temperature.
The number of molecules in one mole is proportional to the temperature.
The number of molecules in one mole is equal to Avogadro’s number.
The number of molecules in one mole is different for different gases
The number of molecules in one mole is equal to the molecular mass of gas in atomic mass
units (amu).
Question 6. Assuming the atmospheric pressure is equal to 1013.25 mb and room temperature is
20 C, what is the number of molecules inside of the syringe at the beginning of your experiment?
Assume that R* = 8.3145 J/mol K. Enter the number into your Clicker in units of 11020, i.e. if
the answer is 21020, enter “2” (3 points)
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Name ____________________________________ Lab section________________
Question 7. How many grams does a mole of some gas weigh? Choose one from the following and
enter the letter that corresponds to your answer into Clicker (2 pts).
A.
B.
C.
D.
E.
The number of grams is equal to Avogadro’s number.
The number of grams will depend on the temperature and pressure.
The number of grams will be equal to the volume of gas in liters divided by 22.4 .
The number of grams will be equal to the standard molecular weight of gas.
The number of grams will be constant for any gas and equal to R, universal gas constant.
Question 8. In your experiment on Charles’s law, the following relationship was observed: (Choose
one from the following and enter the letter that corresponds to your answer into Clicker) (2 pts).
A.
B.
C.
D.
E.
PV=const.
RT=const.
R/T=const.
T/V=const.
P/T=const.
Part 3 . Ideal Gas Behavior (computer simulation)
Procedure:
Open the website with Java simulation at this address:
http://www2.biglobe.ne.jp/~norimari/science/JavaApp/Mole/e-gas.html
(Make sure to activate Java plugin if asked, in order for simulation to work properly)
In this simulation you can control the pressure (P), temperature (T), and number of gas molecules
(N) using the control sliders at the bottom of the simulation screen. The volume (V) of the gas
will be determined by these three variables. The volume will change as you alter T, P, or N .
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Name ____________________________________ Lab section________________
Experiment 3.1 Constant temperature (T) and number of molecules (N)
Set the temperature to 60 K and the number of gas molecules to 45. Change the pressure as given
in the data table below and record the resultant volume of the gas. (Note: As you change the
pressure, wait until the volume stabilizes. At lower pressures this may take a few minutes.)
Pressure
Volume
10
15
20
25
30
35
40
45
Construct a graph of this data in Excel®: enter the pressure and volume values in two columns
and construct a scatter plot; add a trend line. (4 points)
Calculations and questions :
Question 9. What is the volume when pressure is 15 units? Enter the answer into Clicker (2 pts).
Question 10. What is the volume when pressure is 25 units? Enter the answer into Clicker (2 pts).
Question 11. What is the volume when pressure is 40 units? Enter the answer into Clicker (2 pts).
Question 12. What is the manipulated variable in this procedure? Enter the first letter (e.g. P for
pressure) into Clicker (2pts).
Question 13. What is the responding variable in this procedure? Enter the first letter (e.g. P for
pressure) into Clicker (2 pts).
Question 14. What connection did you observe between pressure and volume of the gas in this
experiment? Choose one from the following and enter the letter that corresponds to your answer into
Clicker (2 pts).
A. Pressure and volume are linearly dependent. As pressure increases, volume also increases.
B. Pressure and volume are not dependent.
C. Pressure and volume are inversely proportional. As pressure increases, volume decreases.
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Name ____________________________________ Lab section________________
Experiment 3.2: Constant pressure (P) and number of molecules (N)
Set the pressure to 30 units and the number of gas molecules to 30. Change the temperature as
given in the data table below and record the resultant volume of the gas.
Temperature
Volume
0
10
50
100
150
200
250
300
Construct a graph of this data: enter the temperature and volume values in two columns and
construct a scatter plot; add a trend line. Copy this plot and a plot from the previous
experiment and put them on the new Excel® spreadsheet. Print out both plots on the same
page and turn them in with your lab. (4 points)
Calculations and questions :
Question 15. What is the volume when temperature is 10 units? Enter the answer into Clicker (2 pts).
Question 16. What is the volume when temperature is 150 units? Enter the answer into Clicker (2 pts).
Question 17. What is the volume when temperature is 300 units? Enter the answer into Clicker (2 pts).
Question 18. What is the manipulated variable in this procedure? Enter the first letter (e.g. P for
pressure) into Clicker (2pts).
Question 19. What is the responding variable in this procedure? Enter the first letter (e.g. P for
pressure) into Clicker (2pts).
Question 20. What connection did you observe between temperature and volume of the gas in this
experiment? Choose one from the following and enter the letter that corresponds to your answer into
Clicker (2 pts).
A. Temperature and volume are linearly dependent. As temperature increases, volume also
increases.
B. Temperature and volume are not dependent.
C. Temperature and volume are inversely proportional. As temperature increases, volume
decreases.
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Name ____________________________________ Lab section________________
Problems for individual work
Question 21. What are two possible ways to decrease the volume of a gas in a sealed but
expandable container (e.g. stretchable balloon)? (2 pts.)
1)
2)
Question 22. How would you increase the pressure of a gas in a sealed rigid container? (2pts.):
Conclusions on the lab (individual work)
1. Discuss your findings (the value of the Universal Gas constant) from Part 1. How does your
value compare with the standard value? (4 pts.)
2. What are the possible reasons for your results (product of P and V) in the experiment in Part 1
(Universal Gas constant) to be different from the theory? (4 pts).
3. Discuss the behavior of the air in your experiments in Part 1 and 2. Can it be considered as an
Ideal Gas? (4 pts.)
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Name ____________________________________ Lab section________________
4. Does simulation in Part 3 realistically represents the behavior of real gas? Why do you think
so? Explain. (4 pts.)
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