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Langmuir contended the rate of adsorbate gas molecules colliding with the adsorbent surface is proportional to the partial pressure of the gas, and the probability of adsorption occurring is proportional to the fraction of empty sites. Additionally, he asserted the desorption rate is directly proportional to the fraction of occupied sites. Finally, he contended that at dynamic equilibrium, the rates of adsorption and desorption are equal.7 For a single adsorbate system, the rate equation is represented as: where pi is the adsorbate gas pressure, θ is the fractional surface coverage, and ka and kd are rate constants for adsorption and desorption respectively. θ is the ratio n*/ns where ns is the adsorption saturation capacity assuming only monolayer coverage. When ka and kd are combined together (since they cannot be experimentally determined individually), the Langmuir isotherm equation is represented as: where b is the ratio ka/kd (adsorption equilibrium constant). Equation 3.6 correctly approximates the asymptotic behavior that appears as sites fill up during adsorption for microporous systems. The adsorption equilibrium constant, b, is often found experimentally, and is directly related to the Henry’s constant ( =bns). Both b and decrease as temperature increases because adsorption is exothermic. Hence, isotherms at lower temperatures possess more curvature and appear higher than those at higher temperatures. 39PDF Image | LIMITS OF SMALL SCALE PRESSURE SWING ADSORPTION
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