93
Experiment
10
Determination of the Molar Gas
Constant, R
OBJECTIVE
To determine the molar gas constant, R, by measuring the volume, pressure, and temperature of
a known mass of oxygen collected over water.
EQUIPMENT
0-100oC thermometer, 70-cm length of 4-mm tubing, ring stand with 3-in. iron ring, Bunsen
burner with wing top, spatula, pinch clamp, 15-cm length of 1/4-in. rubber tubing, one-hole no. 2 rubber
stopper, two-hole no. 6 rubber stopper, 600-mL beaker, 50-mL graduated cylinder, 500-mL round
bottom flask, 18 x 150-mm test tube, evaporating dish, crucible.
REAGENTS
3 g of KClO3, 0.2 g of MnO2
SAFETY AND DISPOSAL
Refer to the MSDS information available online when working with KClO3,1 MnO2,2 and KCl.3
Disposal for all compounds must be in accordance with local, state and federal regulations. Disposal
for KCl and MnO2 should be into a labeled laboratory waste container for inorganic chemicals.
INTRODUCTION
The volume, V, for a given mass of an ideal gas is directly proportional to its absolute
temperature, T, and inversely proportional to its pressure, P. If n is the number of moles of gas, the
relationship of volume, pressure and the number of moles is given by the ideal gas law,
PV = nRT
where R is a proportionality constant. Solving for R,
R = PV
nT
(10-1)
R is known as the molar gas constant. R has dimensions of energy per Kelvin per mole, and its
numerical value depends on the units used to express P and V. Thus, if P is in atmospheres and V is in
liters, R will be expressed in liter-atmospheres per Kelvin per mole.
In this experiment, the value of R will be determined by measurement of P, V, T, and n on a
sample of oxygen gas which will be produced by the reaction
2KClO3 (s) → 2KCl (s) + 3O2 (g)
The physical properties of oxygen gas, when measured at room temperature, closely resemble
those of an ideal gas. There is a loss of material in the reaction vessel as the reaction proceeds, because
Experiment 10 Determination of the Molar Gas Constant, R
94 oxygen is liberated as a gas. The number of moles of oxygen liberated, n, can be expressed as
n = loss of mass of material in a reaction vessel
molecular weight of oxygen
The volume, V, occupied by the sample of oxygen produced in the reaction is measured by the
displacement of water. For each milliliter of O2 liberated in the reaction, 1 mL of water is displaced.
The pressure, P, of the sample will equal the atmospheric pressure corrected for the vapor pressure of
water. The correction is needed because the sample of oxygen that is collected is saturated with water
vapor. Finally, the temperature, T, of the gas is measured with a thermometer when the system is at
equilibrium with its surroundings. When n, V, P, and T are all known, R may be calculated using eqn.
10-1.
PROCEDURE
Wear your safety goggles. Clean a test tube (18 x 150-mm) and set it in an oven to dry. In the
meantime, construct the items shown in Fig. 10-1 from lengths of 4-mm glass tubing. Be sure to firepolish the ends of all glass tubing, except the capillary tip. Review the material on handling glass tubing
and stoppers in the Laboratory Safety section and then assemble the apparatus shown in Fig. 10-2. Use a
few drops of glycerol or water to lubricate rubber
tubing or the holes of stoppers before you insert glass
tubing into them. Be sure that tube C extends a few
mm above the bottom of the 500-mL flask and that
Fig. 10-1
tubes A and B protrude slightly below the stoppers.
Forming glass
Wipe clean of excess glycerol both the glass tubing
tubing
and the inside of the test tube. Do not let the glycerol
lubricant come in contact with the KClO3. The
resultant mixture is potentially explosive.
Test the assembly for leaks by the following
procedure. Fill the reservoir flask (F) to the base of the
neck with water and return it to the assembled
apparatus. Remove the test tube and blow through
glass tube A so that enough air enters the flask to raise
the level of the water in tube C an inch or two above
the water level of the flask. Immediately close off the
system by bending back rubber tubing X. If the raised
level of water in tube C does not remain steady, there
is a leak in the system. Tighten all connections or
replace suspected parts (particularly the pinch clamp) and test again. Fig. 10-2. Assembled
apparatus
Carefully dry about 3 g of KClO3 by gently warming it in an evaporating dish above a small flame
for about 2 minutes. Similarly dry about 0.2 g of MnO2 in a clean crucible. Then, with a spatula,
carefully mix the MnO2 with the KClO3 in the evaporating dish.
Remove the dry test tube from the oven. When it has cooled to room temperature, pour the MnO2KClO3 mixture into it through a paper funnel. Take care that none of the mixture is left on the upper part
of the test tube where it might come into contact with the rubber stopper.
Determine the mass of the test tube and its contents on an analytical balance and record the mass
on your data sheet.
Open the pinch clamp and blow through glass tube A so that tube C, the rubber tube Y, and the
constricted glass tube (D) are completely filled with water. Close the pinch clamp. Now attach the test
tube containing the MnO2-KClO3 mixture to the apparatus. Carefully open the pinch clamp. At this point
a little water may flow out of the constricted tip. However, a continuous siphoning of water indicates a
Experiment 10 Determination of the Molar Gas Constant, R
95
leak. If such is the case, close the pinch clamp, tighten all connections, and repeat the procedure.
Pour about 50 mL of water into the 600-mL beaker. Make sure the constricted tip is below the
surface of the water, open the pinch clamp, and then raise the beaker until the water levels in the beaker
and in the reservoir flask are the same. Still keeping the levels equal, close the pinch clamp. The pressure
of the air within the apparatus is now equal to the barometric pressure. Discard the water in the beaker
and put the beaker back under the constricted tip. Then open the pinch clamp and leave it open.
Have your instructor check the apparatus before you proceed. Cautiously heat the MnO2-KClO3
mixture by moving the flame back and forth across the test tube so that the evolved oxygen gas displaces
the water from the flask at a steady rate. The mixture will gently bubble and turn dark. Throughout this
procedure the constricted tip must remain under the water which has been displaced by the oxygen. (The
appearance of a white fog in the test tube or splattering of the contents indicates that heat is being
applied too strongly -- use a steady low flame.) Do not allow the water level in flask (F) to fall below the
tip of tube (C).
When 200- 250 mL of water has been collected in the beaker, stop heating. Allow the test tube to
cool to room temperature with the pinch clamp remaining open and the tip (D) under water. Then
equalize the water levels in the beaker and in the flasks as before, and close the clamp.
In a graduated cylinder, carefully measure the volume of water collected in the beaker. (Note 101). Express this volume in liters and record it on your data sheet as the volume of evolved oxygen gas.
Measure the temperature of the water and record it on the data sheet as the temperature of the evolved
oxygen. Detach the test tube, taking care not to spill any of its contents, weigh it on the analytical
balance, and record its mass. Record the barometric pressure (this value will be provided by the
laboratory instructor). See Appendix B, Table 2 for the vapor pressure of water at the recorded
temperature and subtract this value from the barometric pressure to obtain the pressure of the "dry"
oxygen.
From the loss in mass of the test tube and its contents, calculate the number of moles of oxygen
liberated. Calculate the volume per mole and the gas constant, R.
Optional calculations. Report the results of the determination of the gas constant, R, to your
instructor, who win list the results of the entire class. Copy these data onto the report sheet. Review the
material on uncertainty and error analysis in the Mathematical Treatment of Data section and compute:
1. the mean of the results
2. the deviation of your value from the mean
3. the standard deviation
4. the 95% confidence level
Show the details of all calculations and complete all items asked for in the report sheet.
NOTES
10-1. The volume of the displaced water may be determined alternately from its mass and density.
Weigh the beaker and water on a platform balance and then weigh the empty beaker. See Appendix B,
Table 3 for the water density at the recorded temperature.
FURTHER READING
1. http://www.sciencelab.com/msds.php?msdsId=9927704 (KClO3, last accessed November 2013)
2. http://www.sciencelab.com/msds.php?msdsId=9924585 (MnO2, last accessed November 2013)
3. http://www.sciencelab.com/msds.php?msdsId=9927402 (KCl, last accessed November 2013)
4. Bastrop, O., Demandt, K, and Hansen, KO., “The Thermal Decomposition of KClO3, Textbook
Errors.”, J. Chem. Educ., 39 (1962) 573
Experiment 10 Determination of the Molar Gas Constant, R
96 NOTES
Experiment 10 Determination of the Molar Gas Constant, R
97
Name _____________________________________ Lab Section _____________ Date_____________
REPORT ON EXPERIMENT 10
Determination of the Molar Gas Constant, R
DATA AND RESULTS
mass of test tube, KClO3, and MnO2 catalyst
_____________________________
mass of test tube and residue
_____________________________
mass of oxygen evolved
_____________________________
moles of oxygen evolved, n
_____________________________
temperature of oxygen, T
_____________________________
barometric pressure
_____________________________
vapor pressure of water at T
_____________________________
pressure of “dry” oxygen
_____________________________
volume of water collected=volume of oxygen
_____________________________
volume per mole of oxygen, V/n
_____________________________
gas constant, R
_____________________________
Optional calculations: class-determined values of R
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mean value
________________________________
deviation
________________________________
standard deviation
________________________________
95% confidence level
________________________________
Show the details of all calculations; use extra sheets if necessary.
Experiment 10 Determination of the Molar Gas Constant, R
98 QUESTIONS
(Submit your answers on separate sheet if necessary.)
1.
Does the pressure of air initially in the flask introduce an error? Explain your answer.
2.
Is it necessary to consider the pressure of water vapor initially in the flask? Explain your answer.
3.
Briefly discuss whether each of the following "mistakes" would produce a high result, a low
result, or make no difference in the value obtained for the gas constant, R.
i. The water level in the flask dropped below the tip of tube C.
ii. Loss of some potassium chlorate from the test tube.
iii. Incomplete decomposition of the potassium chlorate.
iv. The correction for the vapor pressure of water was omitted in the
calculation.
v. Failure to use the MnO2 catalyst.
4.
Why is it necessary to equalize the pressure of the receiving beaker and the flask
before measuring the delivered volume of water?
Experiment 10 Determination of the Molar Gas Constant, R