Determination of R: The Gas Law Constant

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Determination of R: The Gas Law Constant
Objective: To gain a feeling for how well real gases obey the ideal gas law and how to determine the
ideal gas law constant, R.
Apparatus
Balance
Bunsen burner and hose
Test tube
250 mL beaker
8 oz wide mouth bottle
Rubber stoppers
Pinch clamp
Clamp
Barometer (or readings)
Glass tubing
Rubber tubing
Thermometer
Ring stand
Chemicals
Potassium Chlorate (KClO3)
Manganese (IV) Oxide (MnO2)
Introduction:
Most gases obey the ideal gas equation, PV=nRT, quite well under ordinary conditions, that is, at room
temperature and atmospheric pressure. Small deviations from this law are observed, however, because
real gas molecules are finite in size and exhibit mutual attractive forces. The van der Waals equation,
Where a and b are constants characteristic of a given gas, takes into account these two causes for
deviation and is applicable over a much wider range of temperatures and pressures than the ideal gas
equation. The term nb in the expression (V-nb) is a correction for the finite volume of the molecules;
the correction to the pressure by the term n2a/V2 takes into account the intermolecular attractions.
In this experiment you will determine the numerical value of the gas law constant, R, in its common
units of L-atm/mol-K. This will be done using both the ideal gas law and the van der Waals equation
together with measured values of pressure, P, temperature, T, volume, V and number of moles, n, of an
enclosed sample of oxygen. Then you will perform an error analysis on the experimentally determined
constant.
The oxygen will be prepared by the decomposition of potassium chlorate, using manganese (IV) oxide
as a catalyst:
If the KClO3 is accurately weighed before and after the oxygen has been driven off, the weight of the
oxygen can be obtained by difference. The oxygen can be collected by displacing water from a bottle,
and the volume of the gas can be determined from the volume of water displaced. The pressure of the
gas may be obtained though the use of Dalton’s law of partial pressures, the vapor pressure of water,
and atmospheric pressure. Dalton’s law states that the pressure of a mixture of gases in a container is
equal to the sum of the pressures that each gas would exert if it were present alone.
Patmospheric = PO2 + PH2O vapor
SAFETY WARNING!!!!
KClO3 is very dangerous to work with. Be careful not to apply too much friction when scooping out
the powder.
KClO3 is a strong oxidizing agent and will react readily when heated with certain easily oxidizable
substances such as grease and rubber. DO NOT HAVE KClO3 and MnO2 come in contact with the
rubber stopper or a severe explosion may occur. Make certain that the clamp holding the test tube is
secure so that the test tube cannot move.
Procedures:
1. Add a small amount of MnO2 (about 0.02 g) and approximately 0.3 g of KClO3 to a test tube and
accurately weigh to the nearest 0.001 grams. Please also pre-weigh a dry beaker (it will be used to
collect the water displaced by the experiment).
2. Add ~200 mL of distilled water into the bottle.
3. Assemble the apparatus as illustrated in the figure, but do not attach the test tube. Be sure that tube
B does not extend below the water level in the bottle.
4. Attached a rubber bulb to tube B and apply pressure through it so that water may travel into tube A.
Close the clamp when tube A is filled.
5. Mix the solids in the test tube by rotating the tube, being certain that none of the mixture is lost
from the tube, and attach tube B as shown in the figure. AGAIN, read the safety warning about
KClO3 and rubber stoppers.
6. Fill the beaker about half full of water, insert tube A in it and open the pinch clamp. Lift the
beaker until the levels of water in the bottle and the beaker are identical. Then close the clamp,
discard the water in the beaker, and dry the beaker.
The purpose of equalizing the levels is to produce atmospheric pressure inside the bottle and test
tube.
7. Set the beaker with tube A in it on the bench and open the pinch clamp. A little water will flow
into the beaker, but if the system is airtight and has no leaks, the flow will soon stop and tube A
will remain filled with water. If this is not the case, check the apparatus for leaks and start over.
Leave in the beaker the water that has flowed into it; at the end of the experiment, the water levels
will be adjusted and this water will flow back into the bottle.
8. Heat the lower part of the test tube gently (be certain that the pinch clamp is open) so that a slow,
but steady stream of gas is produced, as evidenced by the flow of water into the beaker. When the
rate of gas evolution slows considerably, increase the rate of heating, and heat until no more
oxygen is evolved.
Allow the apparatus to cool to room temperature, making certain that the end of the glass tube is in
the beaker is always below the surface of the water. Some of the water will flow back into the
bottle, which is normal.
Equalize the water levels in the beaker and the bottle as before and close the clamp.
9. Weigh the beaker with the water and get a temperature of the water. Using the temperature, match
the density and calculate the volume of water that was displaced with the chart. This is the volume
of oxygen produced.
If your temperature is 24.5oC round up to 25.0oC or if it is 24.3oC round down to 24.0oC.
Record barometric pressure. The vapor pressure of water can be found by the temperature of the
water from the chart.
10. Remove the test tube from the apparatus and accurately weight the tube and contents. The
difference in mass between this and the original mass of the tube and contents is the mass of the
oxygen produced.
11. Waste Disposal: Please do not throw any of the contents in a waste bin. Return the tube to Mr. Yip
for proper disposal.
Data












Mass of test tube + KClO3 + MnO2
Mass of test tube + contents after reaction
Mass of oxygen produced
Mass of beaker
Mass of beaker + displaced water
Mass of water
Temperature of water
Density of water
Volume of water = Volume of O2 gas
Barometric pressure
Vapor pressure of water
Pressure of O2 gas
Calculations
 Calculate the gas law constant, R, from your data using the ideal gas equation.
 Calculate the gas law constant, R, using the van der Waals equation.
o For O2, a = 1.360 L2atm/mol2 and b = 31.83 cm3/mol
o Be sure to keep your units straight.
 Error analysis: Determine the maximum and minimum value of R consistent with the
experimental reliability of your data from the ideal gas law:
Assume that the reliabilities for the various measure quantities in this experiment are as
follows:
P = 0.1 mmHg
V = 0.0001 L
T = 1oC
m = 0.0001 g
o To determine the maximum value of R, use the maximum values that the pressure
and volume may have and the minimum values that the mass and temperature may
have. Similarly, calculate the minimum value of R from the minimum values of P
and V and the maximum values for m and T. Determine the average value of R and
assign an uncertainty range to this average value.
o Example: Assume that the measured quantities were as follows: P = 705.5 torr, T =
20oC. V = 242.9 mL, and m = 0.3002 g. What would be the maximum and
minimum values of R, the average value of R, and the uncertainty range to be
assigned to this average value?
Solution: First put the measured quantities into proper units as follows:
705.5 torr
= 0.928 atm
760 torr
V = 242.9 mL = 0.2429 L
P=
m = 0.3002 g
T = (20o C + 273) K = 293 K
Therefore
(705.6 torr/(760 torr/atm))(0.2430 L)(32.00 g/mol)
(0.3001 g)(292 K)
= 0.0823 L-atm/mol-K
Maximum R =
(705.4 torr/(760 torr/atm))(0.2428 L)(32.00 g/mol)
(0.3003g)(294K)
= 0.0816 L-atm/mol-K
Minimum R =
The average value for R is therefore,
0.0823 + 0.0816
Average =
L-atm/mol-K
2
= 0.0820 L-atm/mol-K
Since the maximum and minimum values of R differe from the average by 0.0004,
R is written as R = 0.0820  0.0004 L-atm/mol-K
Questions
1. Write a paragraph about some of the sources of error in your experiment. Indicate the ones that
you feel are the most important.
2. Which gas would you expect to deviate more from ideality, H2 or HBr? Please explain your
answer.
3. How might the solubility of O2 in water affect the value of R you determined? Please explain.
4. You have a 0.5576 gram mixture of KClO3 and a non-reactive compound. You place the
compound in our experimental setup and get the following results.
mass of O2 = 0.08420 g
a. If the mixture were pure KClO3, what is the theoretical yield of O2 that would be
produced?
b. What is the mass percent of KClO3 in the mixture?
Grading Rubric
Prelab (10 points)
Data table (5 points)
Calculations (20 points)
Questions (10 points)
NAME _________________________________
DATE _________________________________
Prelab - Determination of R: The Gas Law Constant
1. Under what conditions of temperature and pressure would you expect gases to obey the ideal gas
equation?
2. Why do you equalize the water levels in the bottle and the beaker?
3. Why is the corrective term to the volume subtracted and not added to the volume of the van der
Waals equation?
4. Given the following data from Mr. Yip’s freshman college lab experience.
Weight of the Test Tube + KClO3 + MnO2
Weight of Test Tube + Contents After Reaction:
Weight of 125 mL flask + water
Weight of 125 mL flask
Weight of Water
Temperature of Water
Barometric Pressure:
21.5854 g
21.5012 g
198.8 g
131.6 g
67.2 g
25 O C
763 mm Hg
Solve for the R constant on the back of the paper. Please SHOW ALL UNITS AND WORK!!!!
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