Effusion

Graham s law states that the rate of diffusion or effusion of a gas is inversely proportional 

This is essentially a restatement of Equation 11.14. Thus, lighter gases diffuse and effuse more rapidly than heavier gases. 

1 Methane (CH4) diffuses approximately 2.4 times as fast as a certain unknown gas. Which of the following could be the unknown gas  

Which gas effuses faster. He or Ar, and how much faster does it effuse  

---

It is a simple matter now to calculate number of particles per unit area, per unit time, that pass tln-ough a small hole in the wall of the vessel. This quantity is called the rate of effusion, denoted by n, and it governs the loss of particles in a container when there is a small hole in the wall separatmg the gas from a vacuum, say. This number is in fact obtained by integrating the quantity, 8 Af(v) over all possible velocities having the proper direction, and then dividing this number by A5f Thus we find... 

Figure B2.3.3. Crossed-moleciilar beam apparatus employed for die study of the F + D2 —> DF + D reaetion. Indieated in the figure are (1) the effusive F atom soiiree (2) slotted-disk veloeity seleetor (3) liquid-nitrogen-eooled trap (4) D2 beam souree (7) skimmer (8) ehopper (9) eross-eorrelation ehopper for produet veloeity analysis and (11) rotatable, ultralrigh-vaeuum, triply differentially pumped, mass speetrometer deteetor ehamber. Reprinted with pemrission from Lee [29], Copyright 1987 Ameriean Assoeiation for the Advaneement of Seienee.

For effusion through an orifice Graham drew the following conclusions. 

The results on effusion can apparently be accounted for quite easily in terms of the well known kinetic theory expression for the rate of incidence of molecules on unit area of a wall bounding a region occupied by gas, namely... 

As a consequence of these simple deductions, Graham s experiments c effusion through an orifice came to be regarded as one of the earliest direct experimental checks on the kinetic theory of gases. However, a closer examination of his experimental conditions reveals that this view is mistaken. As mentioned earlier, his orifice diameters ranged upwards from 1/500 in., while the upstream pressure was never very much less thai atmospheric. Under these circumstances the molecular mean free path len ... 

Comparing this with equation (A.2.2), it is seen to predict exactly the same dependence of che effusion rate on pressure and temperature. Furthermore, Che ratio of specific heats y depends relatively weakly on che nature of the gas, through its molecularity, so che prediction chat dV/dt 1/M, which follows from equation (A-2.2) and agrees with Graham s results, is not markedly inconsistent with equation (A.2.3) either. 

Effusion separator (or effusion enricher). An interface in which carrier gas is preferentially removed from the gas entering the mass spectrometer by effusive flow (e.g., through a porous tube or through a slit). This flow is usually molecular flow, such that the mean free path is much greater than the largest dimension of a traverse section of the channel. The flow characteristics are determined by collisions of the gas molecules with surfaces flow effects from molecular collisions are insignificant. 

Separator GC/MS interface. An interface in which the effluent from the gas chromatograph is enriched in the ratio of sample to carrier gas. Separator, molecular separator, and enricher are synonymous terms. A separator should generally be defined as an effusion separator, a jet separator, or a membrane separator. 

An effusive beam of atoms or molecules (see Ramsey, 1956 in fhe bibliography) is produced by pumping fhem fhrough a narrow slif, fypically 20 pm wide and 1 cm long, wifh a pressure of a few forr on fhe source side of fhe slif. The beam may be further collimated by suifable apertures along if. 

Such beams have many uses, including some imporfanf applications in specfroscopy. In particular, pressure broadening of specfral lines is removed in an effusive beam and, if observations are made perpendicular to fhe direction of fhe beam, Doppler broadening is considerably reduced because fhe velocify componenf in fhe direction of observation is very small. 

Why are fhese beams, or jefs, distinguished from effusive beams by fheir description as supersonic In some ways fhis description is rafher misleading, firsf because particles in an effusive beam may well be fravelling af supersonic velocities and, second, because fhe name implies fhaf somefhing special happens when fhe particle velocities become supersonic whereas fhis is nof fhe case. Whaf supersonic is meanf fo imply is fhaf fhe particles may have very high Mach numbers (of fhe order of f 00). The Mach number M is defined as... 

Fig. 4. Schematic of a high vacuum molecular beam epitaxy (MBE) chamber containing four effusion (Knudsen) cells. Also shown is a high energy electron...

Ba.rrier Flow. An ideal separation barrier is one that permits flow only by effusion, as is the case when the diameter of the pores in the barrier is sufficiently small compared to the mean free path of the gas molecules. If the pores in the barrier are treated as a collection of straight circular capillaries, the rate of effusion through the barrier is governed by Knudsen s law (eq. 46) ... 

A Back-Pressure Efficiency Factor. Because a gaseous diffusion stage operates with a low-side pressure p which is not negligible with respect to there is also some tendency for the lighter component to effuse preferentiahy back through the barrier. To a first approximation the back-pressure efficiency factor is equal to (1 — r), where ris the pressure ratiopjpj. 

According to Ktiudsen if a small circular orifice of diameter less than the mean free path of the molecules in a container, is opened in the wall of the container to make a connection to a high vacuum sunounding the container, the mass of gas effusing tlnough the orifice, of area A, is given by an equation derived from the kinetic theoty, where tire pressure is in amiospheres. 

---