APRIL, 1948
A QUANTITATIVE DEMONSTRATION OF GRAHAM'S LAW OF DIFFUSION LUIS F. LEROY University of Havana, Havana, Cuba
A
WELI~KNOWN qualitative lecture demonstration of Graham's Law of Diffusion1 consists of a beaker of hydrogen inverted over a porous clay cup containing air. The hydrogen diffuses into the cup faster than the air diffuses out; this produces a pressure within the cup, causing a water fountain, or pushing mercury in a Utube to close an electrical circuit and ring- a, bell, etc. (Figure 1). A quantitative demonstration of this law is indicated in Figure 2. An ordinary constant level device such as a Mariotte flask is used in conjunction with a meter stick to determine the amplitude of the water jet issuing in a horizontal plane from a fine hole made in a glass tube GRAHAM, T.,Trans: Edinburgh Soc., 1831-6; Phil. Trans.,
1835-54; Mem. Chem. Soc., 1843-48.
connected to the bottom of a water reservoir (Figure 2). From these data the velocity vl with which the water flows out from the aperture under atmospheric pressure is easily calculated. Neglecting air resistance, given g the acceleration due to gravity, t the time required for the water to fall the distance h (tine height of the opening above the meter stick) then: t =
mg=rc
In this same time interval the jet has advanced the distance zl in the horizontal direction, thus: vt = z,/k
If now the free end of the glass tube in the Mariotte
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flask is connected by rubber tubing to the glass tube of the porous cylinder, as indicated in the figure, the pressure of the gaseous mixture within it will be transmitted to the water; and the rate of flow of the jet will be increased in proportion to the diffusion rate of hydrogen with respect to air. In consequence a new value rn will be found greater than XI, and: The ratio vl/vz = x1/x2gives us a quantitative test of Graham's law. For the purpose of a lecture demonstration, several measurements should be made at differentpoints of the parabola formed by the water flowing out from the Mariotte flask. It will then be found that the most coincident values of v are those which correspond to measurements of x taken about midway along the height of the curve. This is readily understood if attention is called to the fact that with too low values of h there can be but poor precision in measurements, due to small absolute values of h and x with the corresponding large relat,ive errors. If too large values of h are t,aken, pre-
of actual determinations of v made in a lecture demonstration by the author himself, the following values can be presented: h, = 5 . 3 cm. h,= 9 . 5 c m . hs=12.0cm.
XI = 16.3 em. xz=21.8cm. w=24.5om.
01 = 156.6 cm./sec. un=156.5cm./sec. ua=156.5cm./sec.
which gives a mean value of v = 156.6 cm./sec. In these the values taken for h were always measured carefully to f 1 mm. vvhile the measurements along the x axis were made to the nearest 0.25 cm. Also g = 978.8 cm./sec. Aft,er connecting the free m d of the tube in t,he
Mariotte flask to the hydrogen diffusion cell by means of a rubber tubing, 6 M HCI is dropped along the safety tube in the hydrogen generator and the water jet allowed to flow freely. The acid must be poured nithout interruption so as to 6ll the jar rapidly with Hz and keep it constantly full of hydrogen a t ordinary atmospheric pressure. The water jet is seen then to advance along the meter stick placed horizontally just to a maximum value, which must be observed quickly; for in a few seconds the water jet begins to move backward as equilibrium is approached. For inasmuchas the time interval t = 4% is always the same for jets of different amplitudes in x,Graham's law can be written, as applied to the apparatus set up: Substituting actual experimental values found by the writer, XI = 21.8 cm. (at atmosphericpressure) andx2= 50.0 cm. (hydrogen pressure) for h = 9.5 cm., v e obtain: cision is gained in its measurements, but it is entirely d = 0.0663 (air = 1). Actually, the value for the lost in the determination of x due t o the loss in unifor- density of hydrogen compared t o air is 0.06947. Turmity in the shape of the jet a t such large values of x and bulence, gaseous impurities, etc., account for this disthe resistance of the air which should then be taken into crepancy, which is small enough t o allow for the pracconsideration. Thus, making a selection from a series tical demonstration of Graham's law. Figure 1
