Kinetic theory, evaporation-condensation equilibrium

It is instructive to consider just how mobile the surface atoms of a solid might be expected to be. Following the approach in Section III-2, one may first consider the evaporation-condensation equilibrium. The number of molecules hitting a 1-cm surface per second is from kinetic theory... 

It must also be realized that this thin surface region is in a very turbulent state. Since the liquid is in equilibrium with its vapor, then, clearly, there is a two-way and balanced traffic of molecules hitting and condensing on the surface from the vapor phase and of molecules evaporating from the surface into the vapor phase. From the gas kinetic theory, the number of moles striking 1 cm of surface per second is... 

The first theoretical equation relating the quantity of gas adsorbed to the equilibrium pressure of the gas was proposed by Langmuir [16]. Using the kinetic theory of gases, Langmuir balanced the rates of condensation and evaporation of the gas molecules at the solid surface, giving the volume adsorbed, V, as a fimetion of the gas pressure, P ... 

This is apparent if we consider the number of molecules that must evaporate each second from the surface to maintain the vapor pressure. At equilibrium, the number of liquid molecules that evaporate into the gas phase is equal to the number of gas molecules that condense at the liquid surface (which will take place in the intermediate phase). The number of molecules hitting the liquid surface is considered to condense irreversibly." From the kinetic theory of gases, this number can be estimated as follows ... 

From the kinetic theory of gases, an expression for the net-mass flux at the interphase can be derived based on the works of Hertz [223] and Knudsen [224]. From a statistical consideration under the assumption of a Maxwell-Boltzmann distribution for the velocity of the gas molecules, the maximum condensation mass flux can be calculated. The evaporation mass flux has to equal the condensation mass flux at equilibrium. The resulting Hertz-Knudsen equation for calculating the area specific net-mass flux is given below ... 

If 6 is the fraction of the total catalyst surface covered by adsorbed molecules at any instant, then the fraction of bare catalyst surface available for adsorption is (1 — 6). According to kinetic theory, since the rate at which molecules strike a unit area of a surface is proportional to the pressure of the gas, the rate of condensation of molecules should be determined both by the partial pressure and the fraction of bare catalyst surface or i(l — 6)p, where ki is a proportionality constant. If 2 is the rate at which molecules evaporate from a unit surface when the surface is fully covered, then for a fraction 0 of a fully covered surface, the rate of evaporation will be k2d. For adsorption equilibrium, these rates must be equal. Therefore,... 

Kinetic-molecular theory provides an explanation on a molecular level for this equilibrium. Evaporation from the liquid occurs as fast moving molecules on the surface escape from the liquid. In turn, molecules in the gas phase strike the liquid and condense, As the concentration (pressure) of gas molecules builds up in the gas phase, the rate of condensation increases. Eventually, a pressure is reached where the rate of condensation and rate of evaporation just balance, and equilibrium is achieved. The equilibrium pressure is denoted by p and is known as the vapor pressure. The magnitude ofp depends upon the substance, composition of the liquid, and any two of our thermodynamic variables such as temperature and total pressure. The criteria for equilibrium that we will now derive provide the thermodynamic relationships that will help... 

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