New
York
I
This experiment has been performed a t City College by about 500-600 physical chemistry students during the past few years, with satisfactory results. Viscosities of some common gases are determined with good precision to within 5-10Yo of the values reported in the literature. The mean free path, collision diameter, and collision number can be calculated from the results, to give the student an increased understanding of the kinetic-molecular hypothesis.
of gas flowing through the capillary in unit time. du = dN(RT/P,)
Substituting back into ( 2 ) dN -=dl
rP9r4 16ZqRT
(3)
As the gas is evacuated, the pressure in the constantvolume system decreases. Again using the ideal gas law, dN
=
-dP(V/RT)
where V is the volume of the system being evacuated. Substituting this into (3) and rearranging gives TO Vacuum
c Capillary
The simple apparatus is shown in the diagram. The large bulb is evacuated through a capillary and the pressure is measured a t various time intervals. For an ideal gas, if the system has a constant volume, the relationship between pressure, time, and viscosity is
where 7 is the viscosity, r is the radius, L the length of the capillary, t the time. P the pressure in the bulb, P , the initial pressure, and V the volume of the bulb. Since r, L, and V are constant for any particular combination of bulb and capillary, the graph of 1 / P versus t is a straight line with a slope of k/?. Eqn. (1)is derived by combining Poiseuille's equation for laminar gas flow with the ideal gas law. From the Poiseuille equation.
(4)
dP = (-rP4Vl6LqV)dt
The assumptions of the derivation are constant volume for the system and ideality and laminar flow for the gas. If the pressure is measured with a U-tube manometer, the system volume will change by 10-20 ml, during the experiment. However, with a 500-ml bulb, this may be considered negligible. For most common gases (except for COz and NH8), deviations from ideality a t atmospheric pressure are within 1-2% and may be ignored. There is a possibility of turbulence a t high flow rates, but with capillaries of 5-20 cm in length, the results have been satisfactory enough to assume that the flow is indeed laminar. The experimenter evacuates the system through the bypass, flushes it with gas, and evacuates it again to remove all residual air. He then refills the system with gas and evacuates it through the capillary, taking pressure measurements a t convenient time intervals, until the pressure drops by only about 0.1 cm per minute. He obtains the viscosity from the slope of the straight line graph of 1 / P versus t. To avoid a measurement of the capillary radius and the manifold volume, k , the apparatus constant may be determined from the known viscosity of a reference case, i.e., dry laboratory air. Alternatively, the calculation of the apparatus constant may be omitted and the viscosity, relative to that of air, may be computed from the inverse ratio of the slopes of the 1 / P versus t graphs. s = slope2 m slopel
where dv/dt is the volume rate of gas flowing through the capillary, P is the pressure at the capillary inlet (i.e., the manometer pressure), P, is the pressure at the capillary outlet, and Po is the pressure at which the gas volume is measured. I n this experiment, the gas is evacuated with either a pump or an aspirator, so that P , is effectively zero and can be eliminated from the equation. From the ideal gas law, do, the volume of gas measured a t Po, pmsing through the capillary in unit time, is expressed m terms of d N , the number of moles
A broken thermometer stem is a convenient capillary. The stopcocks may be replaced with T-tubes, pressure tubing, and screw-clamps, but control and leak prevention become more difficult. Good results have been obtained with hydrogen, oxygen, ethylene, and various freons. As an optional experiment, runs may be made a t ice- and boiling-water temperatures, to demonstrate the increase of viscosity with temperature. The accuracy of the measurements is not sufficient to show the square root relationship, however. Volume
42, Number 12, December 1965
/
663
