GAS DENSITY

(Last Revision: September 2, 2004)

The method of gas density is used to determine the molecular weight of an unknown gas. The molecular weight is found by weighing a sample of gas in a known volume at a known pressure. An extrapolation procedure is used to find the molecular weight.

Atkins, "Physical Chemistry", 5th edition, 1994.

The ideal gas law is given by:

PV = gRT/M,

where P = pressure, V= volume, T = temperature, g = weight of the gas R = the ideal gas constant. This equation may be rearranged to give the density of the gas : r = g/V = PM/RT. Since the ideal gas law is only valid as the pressure approaches zero, an extrapolation procedure must be used to determine the molecular weight of a real gas. A convenient extrapolation is to plot r/P versus P (Where r is the gas density, g/V) and extrapolate to zero pressure to solve for the molecular weight.

Manometer, gas bulb, gas manifold, vacuum pump.

Unknown gas.

 

 

The gas is weighed in a glass bulb of the type shown in the figure. The bulb is first evacuated on the manifold using a vacuum pump to obtain a pressure of 1 mm Hg or less. The bulb is then filled with the gas at a measured pressure. The pressure is measured by reading the manometer. The barometer must also be read if an open end manometer is being used. In weighing the bulb a counterpoise should be used to compensate for buoyant effect of the air. If a counter poise is not used a buoyancy correction will have to be made. The bulb is weighed when evacuated and when filled with each of the pressures used.

In weighing the bulb, the following procedure is used. The stopcock to the bulb is closed after reading the pressure in the system. The bulb is removed and wiped with a clean lintless damp cloth and allowed to hang in the balance case for 5 to 10 minutes to come to constant weight.

The bulb is filled with gas by first evacuating the system, by opening stopcocks at A, C and D, and then filling the system with the gas through the double stopcock, D. The pressure is measured when the two stopcock, D, is closed.

For a closed end manometer, the observed pressure in mm Hg is corrected to 0 oC by the equation:

Po = P - P[at - b(t-ts)]/(1 + at) ,

where Po, P = corrected and observed pressures t = temperature of the manometer ts = temperature at which scale was calibrated, usually 20 o C a = mean cubical coefficient of expansion of mercury between 0 and 35 oC b = linear coefficient of expansion of scale material. The value of a is 181.8 × 10-6, and the value of b is 18.4 × 10-6 for brass and 5 × 10-6 for wood.

If an open end manometer is used, the pressure in the bulb is equal to the difference between the corrected barometric pressure and the manometer pressure corrected by the above equation. Don't forget to record the air temperature during each measurement.

The weights of the gas should be determined at four pressures going down to a pressure of about half an atmosphere. The volume of the bulb is found by filling the bulb with water at a known temperature and weighing the bulb. The density of the water can easily be found and the volume of the bulb determined.

If a counterpoise bulb of the same volume as the sample bulb was used no correction for buoyancy is needed. If no counterpoise bulb was used a correction for buoyancy must be made.

The weight of gas is found by difference between the filled and evacuated bulb. The molecular weight of the gas can be calculated at each pressure. To determine the true molecular weight, plot the molecular weight at each pressure against the pressure and extrapolate to zero pressure.

The following data were obtained during the performance of this experiment:

Barometric Pressure (corrected) = 740.2 Torr

Temperature = 25.2 oC

A wood scale open end manometer was used.

A counterpoise bulb was used in the weighings.

Weight of bulb plus water = 207.2648 g 

Trial
 
Wgt. Bulb empty (g)
 
Wgt. Bulb plus gas (g)
 
Manometer difference(mm Hg)
 
1
 
85.2653
 
86.0758
 
-20.1
 
2
 
85.2650
 
85.8738
 
132.5
 
3
 
85.2652
 
85.6506
 
360.4
 
4
 
85.2651
 
85.4124
 
588.6
 
 
             

NOTE: Negative pressure difference means the pressure is greater than the atmosphere.

Use the data given above to write a formal laboratory report as if you had performed the experiment in the laboratory. Turn the report in at the next period.