Determining the Thermal Expansion Coefficient of Gases Jochen K. Lehmann Universitat Rostock, Fachbereich Chemie, Hermannstr. 14, D-0-2500 Rostock, Germany Recently, a student experiment for determining the zero point of the absolute temperature scale was published by Strange and Lang 'in this paper. We improved the design of the apparatus, extended the experimental task t o determining the thermal expansion coefficient of gases, and applied this experiment in practical training courses for chemistry students. Extension of the Task We apply Gay-Lussac's law aceording to V =V0(l+ yoe)
(1)
v=vo+ voYoe with e=T-To
where V is the volume at the Celsius temperature 8; Vois the volume at 0 'C; yo is the thermal expansion coefficient; T is the temperature in Kelvin; and Tois the temperature in Kelvin at 0 'C. If we graph V as a function of temperature at constant pressure, we expect a straight line for an ideal gas. Its intercept ao at 8 = 0 'C gives VO; the slope a l is determined by Voand yo. The thermal expansion coefficient can be determined from the fit of the experimental data by
For an ideal gas, a value of yo = 0.0036610 K-'is expected.' If we assume that the volume of gas vanishes at T = 0, from eqs 1and 3 we obtain the following expression for the absolute temperature at 0 'C. Figure 1. Experimental arrangement forthe determination of Experimental Arrangement The simple experimental arrangement, designed by Strange and Lang, was improved to avoid systematic errors in handling and measuring (see Fig. 1).A glass flask of about 180 mL is large enough that we can ignore errors due to temperature transition in the tube across the surface of the thermostated fluid. We can also ignore errors in determining the volume of the system. The flask is fitted with a stopper, which holds the needle of a 60-mL svrinee. The svrinee has a l-mL scale. and its volume can tie estimated to an.accuracy of 0.2 m ~ : A hlown-alass double-U tube. filled with a vacuum . oumo . oil of low vapor pressure, allows control of the pressure inside the system so that it can be kept at eonstant atmospheric pressure. A glass tube, connected to a thermostat, covers the system; all parts of the apparatus are visible. At the bottom of this coveringtube, a glass loop is mounted for fixing the flask during the experiment.
'Strange, R. S.; Lang, F. T. J. Chem. ~duc.1889,66,t0~-1055. 'Brdicka, R.; Grundlagen derphysikalischen Chemie, DVW: Berlin, 1965;p 193.
ye).
The temperature of the thermostated fluid is measured outside the flask in the covering tube. Thermal equilibrium between gas and fluid is attained if the pressure inside the flask is eonstant. The temperature range should be as wide as possible and can easily include 15 to 60 OC. Temperature measurements should be carried out at steps of 3 to 5 K with an accuracy of 0.2 K. Measurements To prepare the flask, it is flushed with dried air via a narrow tube to displace the ambient air, which may contain water vapor. The syringe i s set to about 10 mL, and the system is assembled according to Figure 1.Next, the hook of the flask is inserted into the loop at the bottom of the coverine tube to fix the svstem. Then the coverine tube is connected to a thermostat and filled with thermostated water. During this operation, care must be taken to keeo the pressure &side the flask at atmospheric pressure. After completing the measurement, the system is disassembled, and the volume of the system is determined. We hang the flask with the upper hook on a gauge and weigh i t f i r s t empty and then filled with distilled water. The A
Volume 69 Number 11 November 1992
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-300 -250
-200 -150
-100
-50
0
50
Temperature (TI Figure 2. Data points for measuring run 3.
15
20
25
30
35
LO
L5
50
55
-I
Temperature IT1 Figure 3. Data points for measuring run 3 (expanded). Discussion
Students Results from V(0o)
vertical tube that attaches to the double-U tube must be filled to the level of its placement within the thermostated water. We marked this level on the tube with a small rubber ring. We recommend replacing the syringe and stopper with another stopper.
Although the experimental equipment is very simple and cheap, we found surprisingly low scatter among the data. The results are reproducible within 1%.Thus, yo or To generally show a systematic deviation of 3% from the expected value. This may be due to the influence of the nonideal behavior of the gas, represented by the temperature dependence of the virial coefficients, which cause a small positive curvature of the graph of V(0)in this temperature range. Fractions of liquid water that remain in the flask might also be a source of error, although we made some effort to avoid this. The increasing vapor pressure of water might counterfeit an increasing volume of gas and also lead to the observed deviations.
Results
Conclusion
Figures 2 and 3 show data points from a typical student experiment, and the table gives some representative data. Figure 2 shows the relatively large range for extrapolation to 0 volume. Figure 3 shows the scatter of the experimental data points. The slopes, intercepts, and deviations were obtained by linear regression. The average yo was determined: yo = 0.00379 (0.00004) K-'. The average Kelvin temperature a t 0 'C was also determined: TO= 263 (3) K.
Our experiences confirm the quality of the simple method and the results of Strange and Lang. We extended their suggestion to also derive the absolute temperature of 0 % as the temperature dependence of the volume. Comparing the results for yo and Towith the theoretical expected data, the student has a good means to check the reliability of his results and to discuss the influence of several effects, such as the nonideal behavior of the gas.
No. 1 2 3
intercept ao (mL) 176 (0.1) 178 (0.3) 174 (0.2)
slope
w (1o ~ / K )
To (K)
a1 (mUK)
0.668 (0.003) 3.79 (0.04) 0.674 (0.006) 3.78 (0.04) 0.664 (0.004) 3.81 (0.03)
263 (3) 264 (3) 262 (2)
(deviation in brackets)
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Journal of Chemical Education
