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In the Laboratory
238 Journal of Chemical Education • Vol. 78 No. 2 February 2001 • JChemEd.chem.wisc.edu
Background
Several laboratory experiments evaluating absolute zero
in degrees Celsius have been used in freshman and upper-
level (physical) chemistry courses (1–5). They serve well in
proving the existence of the lowest possible temperature,
᎑273.15 °C, and in demonstrating several gas laws such as
Charles’s law. These subjects are covered in the textbook chap-
ter dealing with the gaseous state. The methods are based on
extrapolations of either volume (1–3) or pressure (4, 5) of a
given amount of a gas to zero volume or pressure after the
volume or the pressure of the gas is measured at several
temperatures. According to the gas laws,
V = kT or P = k′T(1)
T=1
kVor T=1
k′P
(2)
The volume or pressure of an ideal gas will be zero at the
absolute zero temperature.
The methods involving volume measurements (1–3),
which are inexpensive and simple, have been employed in
the freshman laboratory, while the methods involving pressure
measurements (4–6), which are more expensive, have often
been employed in the physical chemistry or instrumental
analysis laboratory. The old method of volume measurement,
while ingenious, involves a somewhat lengthy procedure (1).
In this method, errors can be easily introduced because the
volume of the air is determined indirectly by measuring a mass
of water using rather involved procedures. Only two data
points can be obtained in a single trial. A method of volume
measurement with a syringe (2, 3) is much simpler, but the
results are less precise, generating a standard deviation of
about 20 K (3).
We developed a new and elegant method of measuring
a gas volume to produce a much more precise result (with a
standard deviation of less than 10 K). Our method utilizes
reported values of the vapor pressure of water at various
temperatures in to extract the volume of dry air from the
volume of a sample of wet air. As many as 20 data points can
be collected in a single trial because the raw data of volume
can be obtained much more easily through direct readings
of gas volume in a graduated cylinder. Only the analysis of
data and calculations are somewhat more involved in this
method than in the previous methods (1–3).
Experimental Procedure and Method of Analysis
The biggest advantage of our method is that it requires
only very common, inexpensive glassware (a graduated cyl-
inder and a beaker), a thermometer, a heater (Bunsen burner or
hot-plate), and water. To begin the experiment, a small amount
of air (3–5 mL) is trapped inside an inverted graduated
cylinder in a water bath (1-L beaker) on a heater (Fig. 1).
The volume of the gas (dry air plus water vapor) inside the
cylinder is read at several temperatures while the bath is being
heated (or cooled). This part of the procedure is similar to
the experiment for determining the heat of vaporization of
water (7, 8).
The partial pressure of dry air inside the cylinder is given
by the following equation:
Pair = Ptotal – PH2O(3)
where Ptotal is equal to the barometric pressure and PH2O
represents the vapor pressure (VP) of water at the specific
temperature. PH2O can be found in VP tables from various
sources (8–11). If a VP value at a particular temperature is
not listed in the table, it can be found through the interpo-
lation method from two known VP values at the two nearest
A Simple Laboratory Experiment for the Determination W
of Absolute Zero
Myung-Hoon Kim*
Department of Science, Georgia Perimeter College, Dunwoody Campus, Dunwoody, GA 30338;
*
mkim@gpc.peachnet.edu
Michelle Song Kim
Roswell High School, Roswell, GA 30075
Suw-Young Ly
Department of Fine Chemistry, Seoul National University of Technology, Seoul 139-743, Korea
Figure 1. The experimental apparatus.
Thermometer
Beaker
Water Air and
water vapor
Inverted grad-
uated cylinder
Hot plate
In the Laboratory
JChemEd.chem.wisc.edu • Vol. 78 No. 2 February 2001 • Journal of Chemical Education 239
heated if the rate of heating is slow ( 0.5 °C/min or less) and if
the data are collected in a lower temperature range, typically
below 50 °C (Fig. 3).
We present a set of results from ten trials: ᎑276.01,
᎑277.58, ᎑287.90, ᎑287.80, ᎑263.93, ᎑276.14, ᎑285.50,
᎑273.05, ᎑277.58, ᎑272.19 °C. This yields an average and a
standard deviation of ᎑277.77 ± 7.56 °C. The absolute error
in the average is 4.6 °C with a relative error of 1.7% . In
general, a measurement with a larger volume of air yielded
better results (Fig. 4).
Systematic errors resulting from inaccuracy in the vol-
ume measurements with the cylinder were also investigated.
Figure 2. Plot of the raw volume (total) and corrected volume (air
only) of the trial. Twelve volumes are read in a temperature range
of 0 to 75 °C.
-300
-250
-200
-150
-100
-50
0
50
100
150
Temperature / C°
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Volume of Air / mL
Total Gas Volume
Air Volume Only
Least Squares of
Air Volume
htiwsisylanAriehTdnaataDlacipyT.1elbaT
teehsdaerpSorporttauQ
rrot5.637erusserPcirtemoraBehT
sixa-Ysixa-X
pmeT
)Cged(
)latot(V
)Lm(
)O2H(PV )rrot( )ria(P )rrot( )ria(V
)Lm(
.qStsaeL
Tged()CrorrEniT
)Cged(
-war- -detcerroc-
0.2752.7 06.45209.184 8347.4 35.9674.2
7.1600.6 05.16100.575 3486.4 02.56
᎑
05.3
0.0657.5 04.94101.785 6385.4 78.7531.2
0.0551.5 05.2900.446 2305.4 10.25
᎑
10.2
5.3408.4 15.6699.966 5663.4 60.2444.1
6.4305.4 52.1452.596 0842.4 24.3381.1
2.8204.4 86.8228.707 7822.4 10.23
᎑
18.3
4.3202.4 85.1229.417 9670.4 69.0244.2
2.8101.4 76.5138.027 8210.4 92.6119.1
9.889.3 44.860.827 4439.3 85.01
᎑
86.1
8.409.3 54.650.037 8568.3 85.5
᎑
87.0
0.008.3 06.409.137 3677.3
᎑
49.0 49.0
0000.010.672-
:tuptuOnoissergeR
tnatsnoC10.672-TPECRETNI
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temperatures, assuming a linear relationship in the narrow
range. A VP value should not be crudely estimated in a rough
fashion: use of accurate VP values is very important in the
calculations. This is particularly true for higher temperatures
at which a small variation in temperature brings about a large
change in VP.
Then, the partial volume of the water vapor is
V
H
2
O
=V
total
P
H
2
O
P
total
(4)
The partial volume of dry air can be found by subtracting
the partial volume of water vapor from the total gas volume:
Vair =Vtotal –VH
2
O=Vtotal
Ptotal –PH
2
O
Ptotal
=Vtotal
Pair
Ptotal
(5)
A plot of the Celsius temperatures (y axis) vs volumes of dry
air (x axis) is prepared:
T=P
nR V
air
(6)
The y intercept can then be found by extrapolation to give
absolute zero. The best result is obtained from the linear least
squares method. The moles of air trapped in the cylinder can
be found from the slope:
n=P
slope ×R
slope = P
nR
(7)
Details of the procedure and analysis are available online.
W
Results
Typical experimental data and results of data analysis
with a QuattroPro spreadsheet are presented in Table 1.
The temperature vs raw volume data are given in the first
two columns (bold and italicized); the barometric pressure is
given in the first row, 736.5 torr. The room temperature was
19.7 °C. Twelve volumes were read in a temperature range
of 0 to 80 °C. All calculations were done with the spreadsheet.
Theoretical temperature at each volume was calculated from
the slope (m) and the intercept (b) from the least-squares
method; these are given in the 6th column along with the
associated errors in the 7th column.
Plots of temperature vs raw volume (total) and corrected
volume (air only) from the trial are given in Figure 2. As
expected, the plot of temperature vs raw volume is curved
because of the increased vapor pressure (hence vapor volume)
at higher temperature. When the temperature is plotted against
the corrected volume (total volume minus vapor volume), a
well-defined straight line is obtained with an intercept (the
constant) of ᎑276.01 °C. This yields an absolute error of about
3°C and a relative error of 1%. The slope (m, the X coefficient)
was determined to be 72.84, from which the amount of air
trapped was calculated to be 1.62 × 10᎑4 mol using eq 7.
The data for this trial are obtained while the water bath
is being cooled. It is found, however, that one can obtain a
good result even from data collected while the cylinder is being
In the Laboratory
240 Journal of Chemical Education • Vol. 78 No. 2 February 2001 • JChemEd.chem.wisc.edu
Proportionate errors in the volume readings of the gas (for
example, all measured volumes are 3% larger, or smaller, than
true volumes) did not introduce any error in the results.
However, nonproportionate errors in the volume readings (for
example, all measured volumes are 0.1 mL larger, or smaller,
than true volumes) did introduce a substantial error in the
result. The larger volumes yielded a lower value of absolute
zero and the smaller volumes yielded a higher value. Therefore,
taking volume readings by looking down without leveling the
eyes with the meniscus in the cylinder will result in a higher
value of absolute zero because the measured total volumes
will be smaller than the true volumes.
This experiment is a good application and demonstration
for many gas laws (ideal gas law, Charles’s law, Avogadro’s
law, and Dalton’s law of partial pressure).
Acknowledgments
We thank Dale Manos for assistance with QuattroPro
and Maureen Burkart for editing the manuscript. MSK
thanks Ned Granville (RHS) for guiding the Science Fair
Project. This work won in the Physics Division at the Georgia
Science and Engineering Fair (University of Georgia, Athens,
GA, April 9–11, 1999). MSK also thanks Alice Schutte for
the use of the chemistry laboratory and the equipment for
the project. This paper was partially supported by the research
fund of Seoul National University of Technology.
WSupplemental Material
Details of the experimental procedures and analysis
(including a template of the Quattro Pro spreadsheet) for the
instructors and for the students are available in this issue of
JCE Online.
Literature Cited
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2. Timberlake, K. C. Laboratory Manual: General, Organic and
Biological Chemistry, 6th ed.; HarperCollins: New York, 1996;
pp 175–184.
3. Mills, J. L.; Mitchell, R. E. General Chemistry Experiments;
Morton: Englewood, CO, 1987; p 49.
4. Strange, R. S.; Lang, F. T. J. Chem. Educ. 1989, 66, 1054–1055.
5. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments
in Physical Chemistry, 5th ed.; McGraw- Hill: New York, 1989;
pp 86–95.
6. Garrett, D. D.; Banta, M. C.; Arney, B. E. J. Chem. Educ.
1991, 68, 667–668.
7. Roberts, J. R. Jr.; Hollenberg, J. L.; Postma, J. M. General
Chemistry in the Laboratory, 3rd ed.; Freeman: New York, 1991;
pp 241–253.
8. Hunt, H. R.; Block, T. F.; McKelvy, G. M. Laboratory Experi-
ments for General Chemistry, 3rd ed.; Saunders: New York,
1997; pp 169–175.
9. CRC Handbook of Chemistry and Physics, 63rd ed.; Weast, R. C.;
Melvin, J. A., Eds.; CRC Press: Boca Raton, FL, 1982; pp
D-196–D-198.
10. Lange’s Handbook of Chemistry, 13th ed.; Dean, J. A., Ed.;
McGraw-Hill: New York, 1985; pp 10-26–10-27.
11. Handbook of Mathematical, Scientific, and Engineering Formulas,
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Education Association: Piscataway, NJ, 1986; pp 726–727.
Figure 4. Plots from other trials with various volumes of air. Trials
with larger volumes of air yield more accurate results in general.
-300
-250
-200
-150
-100
-50
0
50
100
150
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
Volume of Air / mL
Temperature / C°
Figure 3. Effect of rate of the heating. The dashed lines are from
the least squares method with the data from the entire temperature
range, from 20 to 80 °C. The solid lines are obtained with data
from a lower temperature range, from 20 to 50 °C.
-300
-250
-200
-150
-100
-50
0
50
100
150
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
at 2 deg/min
at 0.5 deg/min
Volume of Air / mL
Temperature / C°
