Physical Chemistry Laboratory
Experiment I-1
Heat Capacity of Gases
References:
See relevant sections of undergraduate Physical Chemistry text.
P.E. Pierce, J. Chem. Educ., 39, 338-9 (1962).
Background:
Read the references carefully.
Know the following and their interrelations:
1)
Molar heat capacity at
a) Constant volume
b) Constant pressure
2)
Principle of calorimetry
3)
Equipartition Principle as applied to molar heat capacities of gases
Objectives:
•
•
Determination of the molar heat capacity of
a)
Monatomic gas in a flow calorimeter
b)
Diatomic gas in a flow calorimeter
Comparison of the experimental results with literature values and the predictions of the
"Equipartition Principle"
Chemicals:
Ar(g), N2(g)
Apparatus:
Gas regulator with gauges and needle valve.
Flow-meter of 1 to 10 L min-1 range with calibration chart for each gas used
Two thermometers (0-51°C range in intervals of 0.1°C)
Regulated DC power supply, 0.5 amp at 3 to 5 volts
Voltmeter (3 to 5 VDC)
Milliammeter (500 mA. DC)
Flow calorimeter (see diagram), consisting of three main components:
Physical Chemistry Laboratory
1) The flow calorimeter and heating circuit.
Experiment I-1
The flow calorimeter is simply an insulated glass tube provided with a side arm for
gas inlet. Two thermometers (0.1oC graduation) are fitted at the tube ends. The
lower thermometer, fitted tightly by a rubber stopper, measures the temperature of
the entering gas. The upper thermometer, which measures the temperature of the
heated gas fits loosely to permit the gas to exhaust. The heater inside the tube
(Nichrome wire B) heats a limited zone bound by silver baffles (shields). The heater
is powered by a regulated DC power supply (0-15 volts, 0-500 ma). The supplied
power is measured by a voltmeter (V) and an ammeter (A).
2) The flowmeter.
The flow rate of the gas entering the calorimeter is measured from the pressure
difference between the two ends of a capillary, as indicated by the difference in the
oil level in the flowmeter-manometer. The flow rate of a given gas through a
capillary of given length and bore radius is related to the pressure drop through the
tube according to the Poiseuille equation.
For each precalibrated flowmeter the flow rate corresponding to a given difference in
the oil level is read from a calibration curve for each gas. A trap (catch bottle),
downstream from the flowmeter, serves to collect oil in the case of overflow.
An additional oil manometer, open to the atmosphere, measures the difference of the
gas pressure (exit pressure) from barometric pressure. This difference is used to
correct for the gas pressure, under the experimental conditions, relative to the
barometric pressure at the time of the experiment.
3) The gas manifold.
The gas is fed from a cylinder through a gas regulator and a needle valve. The
pressure regulator and needle valve serve to control and to reduce fluctuations in the
gas flow, resulting in a reasonably constant flow rate.
Procedure:
1) Read the barometer at the beginning and the end of the experiment.
2) Record the flowmeter number.
3) Connect the nitrogen gas flow system and electrical circuits as shown in the attached figure. The
manometer and scale should be vertical.
4) Loosen (close) the diaphragm screw of the pressure reducing valve, then open the main gas
cylinder valve a small amount (a quarter turn or so). Close the needle valve and then tighten the
diaphragm screw until the low pressure gauge reads at least 17 psig, to ensure sonic flow
through the needle valve.
5) Compare the two calorimeter thermometers and obtain a relative calibration error for the upper
in terms of the lower at an intermediate flow rate.
6) Open the needle valve until a constant flow rate of 8 to 10 L min-1 is obtained. Readjust the
needle valve or diaphragm screw as necessary so that a constant value is maintained. Turn on
the heating circuit. Record the flowmeter manometer readings to 0.1 mm (∆h), the current, the
voltage, ∆hexit to 0.1 mm, time of day and upper and lower thermometer readings every few
minutes until ∆T between the upper and lower thermometer is constant for three successive
readings. After 10 to 15 minutes ∆T should be constant. Adjust current and voltage so that ∆T is
in the range of 7-11°C.
7) Repeat step (4) for at least 4 additional flow rates; about 8, 6, 4, and 2 L/min are suggested.
8) Repeat steps 3-7 with argon.
Physical Chemistry Laboratory
Experiment I-1
Treatment of results:
1) Convert ∆h for the flowmeter to flow rate n˙ mole/min using the appropriate calibration curve
and ideal gas law. The manometers are each filled with di-butylphthalate (d = 1.046 g/ml). The
∆hexit must be converted to mm Hg using the densities of mercury (13.55 g/ml) and that of
dibutylphthalate. The ∆hexit can then be used to calculate the pressure in the calorimeter from the
barometric pressure.
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˙ (J/min), the heating rate supplied by the electric heater. If the input impedence of
2) Calculate Q
the volmeter is low, then it will be necessary to correct the current for the small current through
the voltmeter. (Most modern meters have very high input impedence.)
Q˙ /"T for each flow rate and plot against n˙ , the corresponding flow rate.
˙ (J/min), n˙
4) Tabulate ∆h, V˙ (L/min), ∆hexit, T (low), corrected ∆T, V (volts), I (amps), Q
˙ /"T . Include an extra line showing the propagated errors in one of the sets of
(mol/min), Q
!
!data.
3) Calculate
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5) Calculate
the slope of line as (J/mole. deg.), this is
!
line is
the supposed!straight
C p . The equation of !
!
Q˙ /"T = C p n˙ + K
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where K is the proportionality constant in the equation for the rate of heat loss to the
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surroundings L:
L = K ∆T
Also calculate L at one flow rate.
6) Calculate the standard deviation in
C p from that of the slope for each of the two gases.
7) Compare your result with a literature value and the value expected from the equipartition
principle for translational and rotational energies only.
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John Miller! 8/4/06 11:51 AM
Comment: D to ∆