Gases: Boyle's and Charles' Laws
INSTRUCTOR RESOURCES
The CCLI Initiative
Learning Objectives
!
introduce the concepts and units of pressure, volume and temperature.
!
experimentally determine the relationship between pressure and volume, using the MicroLAB interface
system to collect and analyze the data.
!
experimentally determine the relationship between temperature and volume, using the MicroLAB
interface system to collect and analyze the data.
Procedure Overview
Boyle's Law
!
interface and syringe assembly set up and calibrated.
!
pressure/volume data pairs taken at three different central volume settings.
!
data analyzed and graphed, and questions answered.
Charles’ Law
!
interface and thermistor assembly set up and calibrated.
!
temperature/volume data pairs taken over wide temperature range.
!
data analyzed and graphed, and questions answered.
11
GASES: BOYLE’S AND CHARLES’ LAWS
PRESSURE VS VOLUME DATA WORK UP:
The pressure-volume data are stored on your disc under the file names you gave them.
Data Manipulations
1.
For each different PV set of measurements, open the file in the spreadsheet, and in column C, calculate
the product of P times V, then, right clicking on the Spreadsheet column for that data, click on Column
Statistics and determine the mean and standard deviation (the standard deviation represents the
?standard error” on the mean value) of the data in column C and record these in your lab book and in
T1 in your lab report. Calculate a percent error value on the standard deviation for each of the data sets
and add this to the table. Insert this table, T1, containing the data for each of the three PV data sets,
within the body of the Results and Conclusions section of your written report. The P vs. V table on your
experiment write up is an example of how this should be set up.
2.
Ensure that you have graphed your dependent variable on Y, and your independent variable on X for
each PV data set. Print these graphs with the spreadsheet data and the appropriate title as described
above. (Graphs G1.1, G2 and G1.3 set)
3.
Compare your graphs against the attached series of graphs to determine what mathematical transformation could
be used to linearize your data. (HINT: To decide on the transformation to use, think about what you physically
“felt” in the qualitative pressure/volume experiments as you adjusted the syringe plunger. CAUTION: Going for
the highest correlation coefficient is not always the best approach if the transform necessary to achieve it is not
realistic or does not conform to the experimentally observed conditions. It is possible to find a transform that will
give a perfect correlation, but may not correspond to the physics or chemistry of the experiment.) In column D,
make this transformation and plot new graphs with linear regression. (Remember to do the transform
on the independent variable and then graph the transform on the X axis.). (Graphs G2.1, G2.2 and
G2.3)
4.
Add the value of the ?slope” from each linear graph (G21 - G2.3) to table T1 for each of the three PV
data sets?
5.
Calculate the percent difference between the slope and the P*V product for each data set in table T1,
and add this value to table T1.
6.
Using PV = nRT, calculate “n” for each PV data point set of the three gas volume series, determine the
mean, standard deviation and % error on the mean for each, and add that data to your table of data.
12
GASES: BOYLE’S AND CHARLES’ LAWS
VOLUME VS TEMPERATURE DATA WORK UP:
The volume-temperature data are stored on your disc under the file names you gave it.
Data Manipulations for Charles’ Law
1. For each experiment run, graph the dependent variable on the Y axis and the independent variable on
the X axis. If the points of the scatter graph appear linear, then do a regression line through the data.
If the points are clearly not linear, then perform the proper transform to make the data linear. Print
this graph with the appropriate title as described above. (Graph 1.1 to 1.3).
2.
Plot a linear regression graph of temperature on Y and volume on X. Print this graph with the
appropriate title as described above. (Graph 4.)
3.
Using the Predict function under Analysis, for Graph 4, predict the temperature value for zero (0)
volume from the above graph. Enter the predicted value and the Y intercept value in Table 1.2 and
calculate their percent difference.
4.
Using the Add Formula function, calculate the corresponding Kelvin temperature and drag to
column C.
5. Using the Add Formula function, divide the temperature in Kelvin by the volume (This is the
reverse of the normal procedure, but for a purpose.), drag this to column D, then determine the mean,
standard deviation and percent error on the standard deviation of the data in Column D and enter it
in Table T1.2.
6.
Plot a linear regression graph of Kelvin on Y and volume on X. Print this graph with the appropriate
title as described above. Graph 5
7. Calculate the percentage difference between the mean and slope values in the above question and add
this value to T1.2.
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Name ______________________________ Section _________ Date ___________________
GASES: BOYLE’S AND CHARLES’ LAWS
Boyle’s Law Questions
1. What is the name of the type of curves that are produced by the pressure / volume data? If you don’t
know this, then go to your algebra books, other students, a math major etc. to find out.
2. Discuss the relationship between the slope for each PV data set and the mean P*V product for that
data set, including whether they should be the same and why or why or not.
3. Can you explain the change in the difference between the slope and P*V product from the small
volume set to the large volume set? (HINT: Think about the defining conditions and the units for
the Ideal Gas Law constant!)
4. Which variable, pressure or volume, is measured with the least number of significant digits, i.e., what
is the limiting precision in this experiment? Look up Boyle’s Law in your text book. (Cite your
reference!) Are your data consistent with Boyle’s Law within the precision of this experiment?
Support this with data in your answer
14
Name ______________________________ Section _________ Date ___________________
GASES: BOYLE’S AND CHARLES’ LAWS
Boyle’s Law Questions (page 2)
5. The graphs of 1/X and 1/logX appear similar. Why is 1/logX not a good choice for modeling in this
experiment?
(T1 Include an expanded table like this in your Results and Conclusions section.)
Experimen
t
P*V
mean
Std.
Dev.
%err. on
P*V
mean
Lin.
Reg.
Slope
% Diff.
(P*V
vs.
slope)
“n”
Std.
% err.
mean
Dev.
on “n”
value
on “n”
mean
Small Vol.
Med. Vol.
Large Vol.
Answer the following Charles’ Law Questions
1. What type of curve do graphs 1.1 to 1.3 of volume versus temperature appear to produce?
2. What type of curve should it produce, and why? (Consider the physical changes that occurred as you
performed this experiment.)
3. In Data Manipulation step 3 above, you were to predict the value of the temperature at zero (0) volume.
Is your predicted value the same as the Y intercept in the Graph G1.2 to G1.3 linear fit equation?
Should it be? Why?
15
Name ______________________________ Section _________ Date ___________________
GASES: BOYLE’S AND CHARLES’ LAWS
Charles’s Law Questions (page 3)
4. What is the accepted value for this Y intercept? (Look up the value for absolute zero in your text. (Cite
your reference!)
5. This is the basis for the ?Kelvin” temperature discussed in the introduction. How does your value
compare with the accepted value?
6. Can you explain any differences? (HINT: Think about the precision of the measurements being made,
and how they affect the outcome.)
7. For Graph 5, what is the Kelvin temperature when the volume equals zero (0)? What should it be?
8. How do the ?mean” value of ?T(in K)/P” and the slope value from Graph 4 compare? Should they be
the same? Explain.
(T2 Include an expanded table like this in your Results and Conclusions section.)
Y intercept
Predicted
value
intercept
K/V Mean
Std. Dev.
16
% error on
Std. Dev.
L.R. slope
% Diff. (K/V
vs. Slope
GASES: BOYLE’S AND CHARLES’ LAWS
Tips and Traps
Boyle’s Law
1. It is imperative that an absolute pressure transducer be used in this experiment, rather than a differential
transducer. This is due to the fact that a range of approximately 1.5 times atmospheric pressure to less
than half atmospheric pressure is covered. Experience has shown that differential transducers do not
calibrate well across the positive to negative pressure range.
2. It is also imperative that the connecting tubing fit tightly at all connections, especially for the positive
pressure measurements. Very poor results will be obtained without this, and very good results will be
obtained with it.
3. Students should get very close to the values tabulated above with careful work.
Charles’ Law
1. It is imperative that a liquid with the lowest possible vapor pressure over the temperature range of 0 to
60 °C be used. The following compounds are listed in order of decreasing desirability, or increasing
vapor pressure. Ethylene glycol is probably the most economical for this purpose.
Compound
mp °C
°C @
Cost
Note
1 torr
&6
153.9
?
120
Triethylene glycol
&7
114
Diethyl phthalate
&3
Triethyl citrate
1,2,4-butanetriol
Tetrethylene glycol
$12.95/100g
nonhygroscopic
$11.60/25 g
hygroscopic
108.8
$9.05/5 g
nonhygroscopic
?
107
$10.65/5 g
?
102
$20.00/25 g
hygroscopic
Dimethyl phthalate
+2
100.3
$13.05/5 g
? due to mp
Diethylene glycol
&10
91.8
$4.35/25 g
hygroscopic
&1 to 1
58
$13.25/100 g
toxic irritant, very
potent mutagen
Tetradecyltrimethylsilane
1,1,2,2-tetrabromoethane
2. Preparing the Charles’ Law tube: It is helpful to add a small amount of strongly colored organic
compound to a few ml of one of the above compounds. Consider the relative polarities of the two
compounds in choosing the dye to use. (Fuchsin works OK with 1,1,2,2-tetrabromoethane.)
3. Where feasible, it is preferable to heat 600 to 800 ml of water for calibration using a liter Erlenmeyer
flask before lab begins so that it is ready when the students need it.
17
GASES: BOYLE’S AND CHARLES’ LAWS
Suggested Answers to Questions
Boyle's Law Questions
1.
What is the name of the type of curves that are produced by the Pressure / Volume data? If you don’t
know this, then go to your algebra books, other students, a math major etc. to find out.
This type of curve, where one decreases while the other increases, is termed an “inverse”
relationship.
2.
Discuss the relationship between the slope for each PV data set and the mean P*V product for that data
set, including whether they should be the same and why or why or not.
The slope of the data which has been made linear represents the best estimate of the product of
pressure times volume. Ideally, they should be identical, but experimental error, especially in
defining precisely the volume and holding it constant while taking the instrumental measurement,
causing the deviations.
3.
Can you explain the change in the difference between the slope and P*V product from the small volume
set to the large volume set? (HINT: Think about the defining conditions and the units for the Ideal Gas
Law constant!)
The difference between the slope and the P*V product for each of the three different central
volume experiments is due to the increase in the number of mols of gas in the syringe. For
example, the PV product increased 1.47 times from a 20 ml central volume to a 30 ml central
volume, which is exactly how the number of moles increased.
4.
Which variable, pressure or volume, is measured with the least number of significant digits, i.e., what
is the limiting precision in this experiment? Look up Boyle’s Law in your text book. (Cite your
reference!) Are your data consistent with Boyle’s Law within the precision of this experiment?
Support this with data in your answer
The volume measurement is the least precise in this experiment. The syringe allows reading to
two digits, and estimating to a third, where as the MicroLAB interface collects data to at least five
significant digits.
The data obtained in these experiments is consistent with Boyle’s Law within the precision of this
experiment, as shown by the making the pressure versus volume graph linear by graphing
pressure versus the inverse of volume, Boyle’s law states that pressure is inversely related to
volume.
5.
The graphs of 1/X and 1/logX appear similar. Why is 1/logX not a good choice for modeling in this
experiment?
The logarithm function is based on powers of ten, and we do not have variations in the data in
orders of 10, so 1/logX would not be an appropriate function for making the data linear. In
addition, if that function is tried on the current data, the data is not linear.
Experiment
P*V
mean
Std.
Dev.
%err. on
P*V
mean
Lin.
Reg.
Slope
% Diff.
(P*V vs.
slope)
“n”
Std.
% err.
mean
Dev.
on “n”
value
on “n”
mean
Small Vol.
15596
979
6.3
12833
21.5
8.39E-4
5.3E-5
6.3
Med. Vol.
22958
627
2.7
21016
9.2
12.4E-4
3.4E-5
2.7
Large Vol.
34011
698
2.1
31013
9.7
18.3E-4
4.0E-5
18
2.0
GASES: BOYLE’S AND CHARLES’ LAWS
Suggested Answers to Questions
Charles’ Law Questions
1.
What type of curve does the graph of volume versus temperature appear to produce?
The data on the graph of volume versus temperature appears to be linear without any
transformation.
2.
What type of curve should it produce, and why? (Consider the physical changes that occurred as you
performed this experiment.)
Since Charles’ law indicates that volume and temperature are directly related, they should
produce a linear relationship without any transformation.
3.
In Data Manipulation step 3 above, you were to predict the value of the temperature at zero (0)
volume. Is your predicted value the same as the Y intercept in the Graph 3 linear fit equation? Should
it be? Why?
Ideally, the predicted value should be the same as the Y intercept value because they are both
based on the same linear fit curve.
4.
For the G3 type of graph, what is the accepted value for this Y intercept? (Look up the value for
absolute 0 in your text, (Cite your reference!) this is the ?Kelvin” temperature discussed in the
introduction.) How does your value compare with the accepted value?
The accepted value for this relationship is -273.16 °C. (Students should cite a page in their
textbook for this reference.) If they have done their work very carefully, they should get close to
this value. Experimental results could vary from -100 to -300 or wider.
5.
Can you explain any differences? (HINT: Think about the precision of the measurements being made,
and how they affect the outcome.)
It is very difficult to insure that the temperature inside of the flask is in equilibrium throughout,
and thus that we are really measuring the true volume and temperature.
6.
How do the ?mean” value of ?T(in K)/P” and the slope value from Graph 4 compare? Should they be
the same? Explain.
The “mean” value of “T(in K)/P and the slope from graph 4 should be the same. The linear fit
is the best estimate of the “true” value for that parameter.
Mean of T(in K)/V
Standard Deviation
Percent Error
"Slope" from graph
60 to 80
up to 2 or 3
up to 5%
60 to 80
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GASES: BOYLE’S AND CHARLES’ LAWS
Sample MicroLAB Program for Charles’ Law Experiment
Pressure versus volume (Boyle’s Law): Volume is entered from keyboard, then both pressure and volume
are recorded automatically by the MicroLAB system when the Enter key is pressed.
Experiment name: Boyle’s Law.
Sensors: Keyboard (Volume): X axis, Col. A, DD on top, Units = ml; Pressure: Y1 axis, Col B, DD on
bottom, units = torr.
Special program:
Repeat upon receiving keyboard input (Starts repeat loop triggered by keyboard input.)
Read Sensors (Reads all variables selected in Data Sensors/Variables and stores in a data grid.)
Until Stop Button is pressed (Ends program.)
Comment: Pressure may or may not be recalibrated, at instructors discretion.
The following program may be used to collect the Charles’ Law data.
Temperature versus volume (Charles’ Law): Volume is entered by keyboard, then both temperature and
volume are recorded automatically by the MicroLAB system when Enter is pressed.
Suggested name: Charles Law
Sensors: Keyboard (Volume): X axis, Col. A, DD on top, units = ml; Temperature: Y1 axis, Col B, DD
on bottom, units = °C.
Example Program: (Program for Charles’ Law to determine the volume-temperature relationship.)
Repeat upon receiving keyboard input (Starts repeat loop triggered by keyboard input.)
Read Sensors (Reads all variables selected in Data Sensors/Variables and stores in a data grid.)
Wait until Switch A is pressed (Allows temperature to continue to rise until volume increment obtained.)
(W hen Switch A is pressed, a window will open with a prompt to enter a value. W hen Enter is pressed, the
program will loop through to the Wait Until step and wait there until Switch A is pressed again.)
Until Stop Button is pressed (Ends program.)
Comment: Temperature probe recalibration required. Volume is read from the scale and entered via the keyboard.
20
GASES: BOYLE’S AND CHARLES’ LAWS
Boyle’s Law Sample Data
Sample Main Screen for Boyle’s Law experiment. Note that as volume increases, pressure
decreases, in accordance with Boyle’s Law.
MicroLAB graph showing the linear curve graph for pressure versus 1/volume, verifying
Boyle’s Law.
21
GASES: BOYLE’S AND CHARLES’ LAWS
Charles’ Law Sample Data
No MicroLAB data was available at the time of compilation, so data taken on a LabWorks interface from
several years ago was hand entered into MicroLAB.
Charles' Law data, heating
Main Screen for hand entered data for
Charles’ Law experiment.
Kelvin /Volume statistics for the Charles’ Law
experiment showing mean of 88.5.
Kelvin temperature vs volume graph with Y intercept of
34.1 K. Actual value should be 0, but it has been
extrapolated over 280 degrees from a range of about 35
degrees.
22
GASES: BOYLE’S AND CHARLES’ LAWS
Laboratory Preparation (per student station)
Boyle’s Law
•
Y tube with short rubber tubing attachments (see Figure 2)
•
screw clamp (attached to tubing on one leg of the Y tube)
•
60 ml syringe
•
MicroLAB interface pressure sensor
•
MicroLAB program which will accept volume inputs from the keyboard and read pressure values.
Charles’ Law
•
temperature probe
•
1 ml pipet, top end cut off to about 0.5 inches above the first calibration mark, prepare as per instructions
under Tips and Traps.
•
for possible organic compounds, see Tips and Traps
•
stirring hot plate with stirring bar
•
ice
•
hot water
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