Molecules striking surface

Not all molecules striking a surface necessarily condense, and Z in Eq. VII-2 gives an upper limit to the rate of condensation and hence to the rate of evaporation. Alternatively, actual measurement of the evaporation rate gives, through Eq. VII-2, an effective vapor pressure Pe that may be less than the actual vapor pressure P. The ratio Pe/P is called the vaporization coefficient a. As a perhaps extreme example, a is only 8.3 X 10" for (111) surfaces of arsenic [11]. 

Let the concentration of solvent (B) in equilibrium with the silica gel surface be (c) g/ml. Let a fraction (a) of the surface be covered with a mono-layer of the polar solvent (B) and, of that fraction (a), let a fraction ( 3) be covered by a second layer of the polar solvent (B). The number of molecules striking and adhering to the surface covered with a mono-layer of polar solvent (A) and that covered with a mono-layer of solvent (B) per unit time will be (n ) and be (n") respectively. Furthermore, let the number of molecules of solvent (A) leaving the mono-layer surface and the bi-layer surface per unit time be ni and 2 respectively. Now, under conditions of equilibrium,... 

Air pollution problems in which adsorption is considered a unit operation involve gaseous contaminants. The number of molecules present at the carbon surface is dependent on the number that reach the surface and on the residence time of these molecules on the carbon surface. If n molecules strike a unit area of a surface per unit time, and remain there for an average time, t, then a number of molecules are present per unit area of surface ... 

Using cm as unit surface and seconds as unit time, n is the number of molecules falling on 1 cm /sec. The number n thus denotes the number of molecules striking each cm of the surface every second, and this number can be calculated using Maxwell s and the Boyle-Gay Lussac equations. The number n is directly related to the speed of the molecules within the system. It is important to realize that the velocity of the molecules is not dependent on the pressure of the gas, but the mean free path is inversely proportional to the pressure. Thus ... 

Langmuir (1916), whp put forward the fir quantitative theory of the adsorption of a gaS, assumed that a gas molecule condensing from the gas phase-would adhere to the surface fora short time before evaporating and that the condensed layer was only one atom or molecule thick. If 0 is the fraction of the surface area covered by adsorbed molecules at any time, the rate of desorption is proportional to 0 and equal to k 0 where is a constant at constant temperature. Similarly the rate of adsorption will be proportional to the area of bare surface and to the rate at which the molecules strike the surface (proportional to the gas pressurep). At equilibrium the rate of desorption equals the rate of adsorption... 

In addition, the rate that molecules strike the surface depends upon how many molecules there are per unit volume of solution. As the concentration rises, more and more molecules strike the surface per unit time. The rate of precipitation is proportional to the iodine concentration,... 

The solubility of a gas is proportional to its partial pressure, because an increase in pressure corresponds to an increase in the rate at which gas molecules strike the surface of the solvent. 

In pure n-heptane or pure chloroform the solute molecules can either interact directly with the surface of the adsorbed solvent or displace the adsorbed solvent and interact directly with the silica surface. In the case of the solvent mixture the solute molecules may interact with the surface of either solvent or displace either solvent and interact directly with the silica surface or any combination of these possibilities. For example some solute molecules might displace the layer of n-heptane and interact directly with the surface. At the same time, those solute molecules striking the layer of chloroform may interact only with the chloroform and not be capable of displacing it, as the molecular forces between the chloroform and the silica gel are greater than the molecular forces between the solute and the silica gel. 

An ultraclean environment is another major reason for generating high vacuum. At atmospheric pressure, every atom on a solid surface is bombarded with gas molecules at a rate of trillions per second. Even under a reasonably high vacuum, 10 atm, a gas molecule strikes every atom on a solid surface about once per second. If the surface is reactive, these collisions result in chemical reactions that contaminate the surface. The study of pure surfaces of metals or semiconductors requires ultrahigh vacuum, with pressures on the order of 10 atm. 

Derivation of the Langmuir Equation— Adsorption of a Single Species. The kinetic approach to deriving a mathematical expression for the Langmuir isotherm assumes that the rate of adsorption on the surface is proportional to the product of the partial pressure of the adsorbate in the gas phase and the fraction of the surface that is bare. (Adsorption may occur only when a gas phase molecule strikes an uncovered site.) If the fraction of the surface covered by an adsorbed gas A is denoted by 0Ay the fraction that is bare will be 1 — 0A if no other species are adsorbed. If the partial pressure of A in the gas phase is PA, the rate of adsorption is given by... 

The rate of adsorption of CO is equal to the product of the flux of CO molecules striking the surface, F, and their sticking probability, S. That is,... 

In 1938, Brunauer, Emmett and Teller(12) and Emmett and de Witt(13) developed what is now known as the BET theory. As in the case in Langmuir s isotherm, the theory is based on the concept of an adsorbed molecule which is not free to move over the surface, and which exerts no lateral forces on adjacent molecules of adsorbate. The BET theory does, however, allow different numbers of adsorbed layers to build up on different parts of the surface, although it assumes that the net amount of surface which is empty or which is associated with a monolayer, bilayer and so on is constant for any particular equilibrium condition. Monolayers are created by adsorption on to empty surface and by desorption from bilayers. Monolayers are lost both through desorption and through the adsorption of additional layers. The rate of adsorption is proportional to the frequency with which molecules strike the surface and the area of that surface. From the kinetic theory of gases, the frequency is proportional to the pressure of the molecules and hence ... 

For a pure gas or liquid, Ri or Rz is extremely small, and is dependent only on the rate at which molecules strike the interface. This rate is given by the kinetic theory, and is extremely high and Ri or R is of the order 0.1 sec. cm. . However, for a solute such as CO2 diffusing from the surface of water, the concentration gradient of this solute below the surface may extend over an appreciable thickness Ax, so reducing k2 [see Eq. (3)]. Thus k2 will depend on D and on the thickness Ax of the unstirred... 

If a gas molecule strikes an empty space on the elementary crystalline space lattice it condenses and is held for a period of time (t) on the surface before it evaporates. This period of time between condensation and evaporation or the mean life of the molecule on the surface may vary from a small fraction of a second to an almost indefinite period. In those cases where the strength of union between adsorbate and adsorbing agent is weak and where the adsorbed molecule readily receives sufficient kinetic energy from shocks, provided by bombarding gas molecules and pulses from the solid adsorbate, to equal the latent heat of evaporation. 

Using a kinetic approach, Langmuir was able to describe the type I isotherm with the assumption that adsorption was limited to a monolayer. According to the kinetic theory of gases, the number of molecules striking each square centimeter of surface per second is given by... 

The constant k is N j InMRTY. Ths number of molecules striking and adhering to each square centimeter of surface is... 

In many theories, nevertheless, the (1 — 0) law has been used as the foundation on which to build elaborate superstructures, which must necessarily fall if the (1 — 0) law is invalid. Even from a theoretical analysis of what should happen when an incoming molecule strikes a surface which is partially covered, one should become suspicious of the (1 — 0) law. Should one not expect that an incoming molecule, which collides with an adsorbed atom (or molecule), is deflected by this atom and strikes a near-by bare spot where it can be adsorbed The view that the incoming molecule bounces off the surface if it collides with an adsorbed atom is in our opinion far too naive. 

At room temperature H2 molecules striking those crystallites of a platinum surface which have the highest work function (I) decompose into atoms. If a pure platinum surface is contacted by hydrogen, crystallites I will be covered by H atoms, those with a low work function, II, by H2 molecules, because the decomposition of H2 molecules on crystallites II requires a higher energy of activation than on crystallites I. The work function of crystallites I is lowered by the polarized H atoms that of crystallites II will not be changed essentially. All effects combined, the photoelectric emission therefore increases if hydrogen is adsorbed on a pure platinum surface. 

While the adsorption of benzene molecules before the maximum was reached increased the sensitivity, the molecules condensed on the platinum surface after the maximum had been reached decreased the sensitivity (C, D, and F in Fig. 28). The excess of the benzene molecules, however, can be desorbed in about 30 min. if no further molecules strike the surface E and G in Fig. 28). The work function was lowered by the adsorption of the optimum benzene layer from 4.54 volts (in J.) to 4.11 volts (in JS). The ir electrons were therefore displaced to the metal surface by the adsorption. 

One of the most useful applications of this formula is in the calculation of the number of molecules striking unit area of a surface in a given time. This calculation is of importance in connexion with the interaction of a gas with a solid substance, or in problems relating to contact catalysis, where we may require to know how many molecules strike the solid catalyst in each second. Suppose... 

At 315°C. the rate constant ki has a value of 7.0 X 1016 molecules/sec.-cm.2-atm. From the definition of kh this represents the rate of adsorption of methylcyclohexane per cm.2 of bare platinum surface at a methylcyclohexane partial pressure of 1 atm. From kinetic theory and statistical mechanics, one can calculate the number of molecules striking a unit area of surface per unit time with activation energy Ea. This is given by... 

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