Measuring the Molar Mass of an "unknown" gas

Introduction:

It is easy to calculate the molar mass of a substance if you know its formula – you simply add up the atomic masses of all of its component atoms. But what if the substance is unknown so you have no formula to work with? This experiment shows how you can find out the formula for an "unknown" gas – the gas from a disposable lighter. This procedure will show how you can use the ideal gas law, PV  = nRT to calculate the number of moles (n) of a gas from its measured pressure (P), volume (V), temperature (T) and the ideal gas constant (R = 8.31 kPa L mol-1 K-1).

Materials:

Procedure:

  1. Put on your goggles.
  2. Although you may be tempted to do so, do not light the lighter. Doing so will burn up some of the gas which we need for this experiment. This will change its mass.
  3. Find and record the mass of the lighter.
  4. Measure and record room temperature.
  5. 3/4 fill an ice cream pail with room temperature water. Completely fill the gas eudiometer or graduated cylinder with room temperature water from the pail, cover the end tightly with the palm of your hand, and invert it in the pail so that the end is under the water. If you use a graduated cylinder as an eudiometer, make sure that you push the palm of your hand into the mouth hard enough that you block off the indentation of the spout. You should have no air bubbles in the cylinder or eudiometer. Clamp the eudiometer in place, so that the mouth is just under water, and the top calibration mark is just above or right at the water level in the pail.
  6. Put the lighter into the disposable syringe. Attach the tubing to the syringe. Gently push down the plunger until it is almost, but not quite touching the lighter valve extension. Caution: don’t push the plunger in far enough to release any gas at this time. Put the tubing up into the neck of the eudiometer tube. Make sure that it is a bit above the level of water in the pail.
  7. Record the volume level on the syringe markings of the plunger at this time. Then, release gas from the lighter into the inverted eudiometer by pressing in the plunger of the syringe. Fill the eudiometer with gas until the water has been displaced to just above the highest calibration mark on the eudiometer (in other words, if you have a 50 mL eudiometer, fill it to about 48 mL). Make sure not to overfill the eudiometer, or you will not be able to measure the gas volume.
  8. The end of the vinyl tube must be 4 or 5 cm above water level at this point. Pull the plunger back until it is at exactly the same volume level marking on the syringe as it was at the start of step 7. Now remove the syringe and tubing assembly from the eudiometer. Caution: if you do not have the tube above the water you will suck water back into the syringe, and get the lighter wet.
  9. Adjust the height of the eudiometer until the level of water inside the eudiometer tube is the same as the water level in the pail. At this point the pressure inside the eudiometer is the same as that of the atmosphere. Record the volume level of the water inside the eudiometer.
  10. Dry the outside of the syringe. Disassemble it, being careful to get no water on the lighter. Find and record the mass of the lighter now.
  11. Measure and record the atmospheric pressure from the barometer.
  12. If there is time, repeat the entire experiment twice.

Calculations:

  1. Calculate the mass of gas that went into the eudiometer.
  2. You will probably have to convert the reading of your barometer into SI pressure units. If the barometer read in mm Hg, then this relationship can be used to do the conversion:

    3. 760 mm Hg = 101.3 kPa

    For example, if the room pressure was 700 mm, you could use this ratio:

    700 mm Hg   =  x kPa
    760 mm Hg 101.3 kPa
  3. The gas in the eudiometer is a mixture:

This can be expressed using Dalton’s law of partial pressures as:

Proom = PButane + Pwater vapor

You measured the Proom with the barometer. The Pwater vapor depends only on the water temperature, and can be found from this table.

Temperature (oC) Pressure (kPa)   Temperature (oC) Pressure (kPa)
15 1.71   23 2.80
16 1.81   24 2.99
17 1.93   25 3.16
18 2.06   26 3.36
19 2.20   27 3.59
20 2.33   28 3.77
21 2.48   29 4.00
22 2.64   30 4.24

Use Dalton's law of partial pressure to calculate the pressure of the butane in the tube. This corrected pressure will be the value of P to use in the ideal gas equation.
  1. Calculate the number of moles of gas in the flask, using the ideal gas law to solve for n. Make sure to use a value for R in the correct units. Don’t forget to convert the room temperature into K.
  2. Calculate the molar mass of butane. This is equal to the measured grams of gas (calculation step 1), divided by n (calculation step 4): g/n = g/mol.
  3. Find the actual formula for butane and calculate its molar mass. Using this as the accepted value, calculate your percentage error. Explain what systematic errors may cause your answer to differ from the accepted value.

Copyright © 1998 - 2008 David Dice