Introduction:

The Kinetic Molecular Model provides a context that allows us to combine Boyle's, Charles', and Avogadro's individual gas laws together into one unified ideal gas law, PV = nRT.  It is based on the assumption that the molecules experience no intermolecular forces and that the molecules themselves occupy no volume. These assumptions are valid at low pressure and high temperature. Under these conditions, the molecules are too far apart to "feel" attractive forces exerted by other molecules. Furthermore, since the molecules are far apart, the volume occupied by the molecules themselves is negligible compared to the total volume occupied by the gas.

In reality, intermolecular forces do exist and molecules do occupy space. The extent to which these factors cause a gas to deviate from the ideal gas law at a particular temperature and pressure will depend upon its molecular structure.  These deviation become severe when a gas is subjected to high pressure and/or low temperature.  Under these conditions, a gas begins to take on the characteristics of a liquid and the ideal gas law no longer applies.

Purpose:

The main purpose of this experiment is to identity an unknown gas by using the ideal gas law to determine its molar mass.  To accomplish this goal, you will need to make a series of mass pressure measurements that will then be plotted, ala Lord Kelvin.  You will then have to extrapolate this data to determine a value that can not be readily determined under normal conditions, i.e., the weight of a totally empty container.

Method:

Today's lab is loosely based on the Dumas method for determining the molecular weight of low boiling liquids (Section 12.10 of your Saunder's textbook).  However, instead of a liquid, you will be determining the molecular weight (molar mass) of a gas.  At a given temperature (T), pressure (P), and volume (V), the ideal gas law can be used to calculate the number of moles (n) of gas present (R is the universal gas constant, 0.082 L•atm/mol•K):

Remember also, that the number of moles of any substance can also be calculated by dividing the weight (in grams) of a compound by its molecular weight (MW):

Since both expressions are equal to n, they must be equal to each other:

This can be rearranged to give us the molecular weight of the gas as:

So to calculate the molecular weight of a gas, we SIMPLY need to know the weight of gas present, its temperature, its pressure, and its volume (R is a constant).

We will be using 2 liter plastic soda bottles to conduct this experiment.  The caps for these bottles have been modified with an automobile tire value which allows the pressure inside the bottle to be determined.  You will be using digital pressure gauges to measure the pressure inside the bottles.  However, these gauges are only accurate to ±0.5 psi and they only read in the range of 5-99 psi.  Also remember, that these gauges read relative to atmospheric pressure.  Which means you need to add 14.7 psi to each reading to determine the absolute pressure in the bottle.

Since the bottles are constructed of thin plastic with little insulating value, we will assume that the temperature of the gas inside the bottle is the same as the temperature of the lab.  Once the excess pressure in the bottle has been released, the pressure inside the bottle will equal the pressure of the room.  This can easily be determined by using a barometer.  The volume of a bottle can easily be determined by measuring the amount of distilled water it takes to fill the bottle.  Then knowing the temperature of the water, you can look up the density of water in the C.R.C.  This density can then be used to convert the mass of water to a volume.

The only thing left for us to determine is the number of grams of gas present in the bottle.  At first this may seem very easy, just weight the bottle with the gas, and then weigh the bottle without the gas.  The difference is the weight of the gas.  The problem is...how do I get the weight of the bottle by itself.  You could purge the unknown gas out of the bottle, but then it would be still be filled with whatever you purged it with.  Even if you attempted to remove the gas from the bottle with a large vacuum pump, the bottle would collapse and trap some gas.  What to do?  Take a page from Lord Kelvin and extrapolate!

If it is not possible to actually perform an experiment at a given set of conditions, then carry it out at some more convenient conditions and extrapolate.  In our case, it would be very difficult to remove all of the air from our bottle, so we will carry out a series of experiments at higher pressures.  With the valve cap tightly fastened on to your bottle, it is possible to pressurize the bottle to 50 - 75 psi.  Note:  As a Safety consideration, your instructor will pressurize your bottle for you.  After the bottle has been pressurized, weigh it.  This weight represents the amount of gas present plus the weight of the empty bottle.  Remember, Avogadro's law says that the pressure is directly proportional to the amount of gas present.  Now release some of the pressure and weigh the bottle again.  The weight will be less since some of the gas has been released.  However, the weight of the bottle itself is constant.  You will need to repeat this process to collect 10 - 15 data points. Try to spread you data out so you have readings from 5 to 50 psi.  The larger the spread in your data and the more points you have, the greater confidence you have in extrapolating it.  Mr. Plot is particularly useful for this lab, but any spreadsheet can be used to generate a plot similar to the one below:

Procedure:

Please read the following procedure carefully before coming to lab.  This experiment is technique intensive.  None of the individual steps are difficult, however, if they are not performed in the proper order, spurious results will be obtained:

1. When you come into lab you will choose a 2 liter plastic soda bottle that contains an unknown gas (be sure to write the unknown number and any observations down in your notebook).
2. Release any excess pressure in your bottle by turning the top.  You will notice that the bottle becomes cooler as the high pressure gas escapes (Joul-Thompson cooling).  Allow the bottle to warm back up to room temperature and release any excess pressure.  Repeat this process until no excess pressure is apparent.
3. Weigh your bottle to 0.001g.  This initial weight reading is very important to correctly identifying your unknown gas!
4. Have your instructor pressurize your bottle to 50 - 75 psi with compressed air.  (Note:  that it does not matter if we mix your unknown gas with compressed air, because by Dalton's law of partial pressures.)
5. Release a small amount of gas through the valve stem.
6. Determine the pressure in the bottle with the digital pressure gauges (remember to add 14.7 psi to your readings).
7. Weigh the bottle to 0.001g.
8. Repeat Steps 5, 6 & 7 until you have collected 15 - 20 pressure/weight readings (the more readings you have, the better your results).  You also want to keep collecting data until the pressure in the bottle falls below 5 psi (at this point the digital gauge will not work anymore).  This should only take a few minutes.  Remember to write all of your data directly into your notebooks.
9. Conduct a second trail by repeating Steps 4, 5, 6, 7, & 8 with the same bottle.
10. After all of your pressure/weight reading are complete, carefully release any remaining pressure from the bottle and remove the valve cap assembly.  Make sure you are ready to proceed because once the bottle gets wet, its volume changes and it can not be used for any further pressure/weight readings.  It may be prudent to do a quick check of your data using Mr. Plot before proceeding.
11. Remove the valve cap assembly and fill your bottle to the very top with distilled water.  Screw the valve cap assembly back on and be sure to wipe off any water that might spilled.
12. Place the bottle on the '4800 g' balance and record its weight.  The difference between this weight and the weight of the empty bottle (y-intercept from pressure/weight plot) is the mass of the water.
13. Record the temperature of the water in the bottle (to 0.1°C).  You can use a C.R.C. or this Table of Water Density to find the density of water at this temperature.
14. Record the temperature of the lab (to 0.1°C) by leaving a thermometer on a paper towel for several minutes.
15. Record the barometric pressure in the lab.
16. After you have finished with your first unknown, go back and pick out a different unknown and repeat this entire process. Note:  DO NOT dispose of the distilled water in your first bottle.  Save it so you can use it to fill your second bottle.

Use the following tables to guide your data collection:  

Calculations:

For each trial calculate the following from your data (show all calculations):

• The true volume of your 2 liter bottle
• The weight of your empty 2 liter bottle.  Include graphs (use your pressure data as the x-axis, and your weight data as the y-axis) and linear regression results.
• Absolute temperature of the lab.
• Molecular weight of your unknown gas.

• Based on your molecular weight, what is the identity of your unknown gas?  Does this make sense?
• How good a correlation did you obtain from your pressure/weight readings?  Where there any points that seemed out of line?
• How did the two trails compare?
• Was the volume of your bottle actually 2 liter?  Why was it different?
• What do you think is the biggest source of error in this experiment?