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| Langmuir Isotherm |
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| Langmuir adsorption isotherm is based on the following assumptions. |
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| i) Adsorption does not proceed beyond monolayer coverage. |
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| ii) All the sites available on the adsorbent surface are equivalent and the surface is perfectly uniform, that is flat. |
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| iii) The ability of a gas molecule to get adsorbed at a particular site is independent of the occupation of neighboring sites. This implies that there is no interaction between adjacent adsorbed molecules. |
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| iv) A dynamic equilibrium exists between the adsorbed molecules and the free gas molecules. |
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| Initially, since the surface is completely bereft of any gas molecules, every molecule of the gas that strikes the surface of solid may get adsorbed. After some time, only those gas molecules may get adsorbed which strike the part of the surface that is not already covered. This means, that initially the rate of adsorption is high and then decreases as less surface is available for adsorption. |
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| Since a dynamic equilibrium exists between the adsorbed molecules and the free gas molecules, it implies that the adsorbed molecules also undergo desorption, probably due to thermal agitation. When the rate of adsorption equals the rate of desorption, dynamic equilibrium is attained. |
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| If q is the fraction of the total available surface covered with gas molecules, at any instant, then (1-q) is the fraction of the surface of the solid which is empty. From kinetic theory of gases, it is known that the rate at which gas molecules collide per unit area of a surface is directly proportional to the pressure of the gas. The rate of adsorption depends on both the pressure of the gas and fraction of surface available for adsorption. Hence, |
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| Rate of adsorption = Ka (1-q) P …..(3) |
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| Rate of desorption = Kd (q) …..(4) |
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| At equilibrium, the rate of adsorption is equal to the rate of desorption i.e., |
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| Ka (1-q) P = Kd (q) |
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| Now, the extent of adsorption (x/m) is proportional to the fraction of surface covered. Therefore, |
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| This is the equation which describes the Langmuir adsorption isotherm. Here a and K are the Langmuir parameters and are characteristic of a particular system at a particular temperature. |
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| At very high pressure, the Langmuir isotherm acquires the limiting form. |
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| At very low pressure, |
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| i.e., the extent of adsorption is proportional to pressure. |
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| The parameters a and K can be determined by taking the inverse form of equation 7. |
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| A plot of m/x against 1/P gives a straight line with slope and intercept equal to 1/a and K/a respectively. |
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| Langmuir isotherm shows that at low pressures of the adsorbate, the extent of adsorption is linear and at high pressure the extent of adsorption is a constant. This form of isotherm is shown in figure 7.4. |
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| fig 7.4 - Langmuir adsorption isotherm |
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| v) Effect of temperature |
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| Most adsorption processes are exothermic; hence adsorption decreases with increasing temperature. This is especially true for physisorption. For chemisorption, extent of adsorption initially increases with temperature and then decreases. The plot of extent of adsorption versus temperature T at a constant pressure is called the adsorption isobar. How the extent of adsorption (x/m) varies with temperature for physisorption and chemisorption as shown in figures 7.5 (a) and 7.5 (b). |
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| fig 7.5(a) - Physical adsorption at a given pressure |
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| fig 7.5(b) - Chemical adsorption at a given pressure |
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| In chemisorption, the initial increase of x/m with temperature is due to the fact that like chemical reactions, chemisorption also requires activation energy. |
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| (vi) Activation of adsorbent |
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| Activation of an adsorbent implies enhancing the adsorptive powers of an adsorbent. This is done by either increasing the specific area of the adsorbent by breaking the solid adsorbent into fine pieces or activating the surface of the adsorbent by specific treatments. How charcoal is activated is already discussed in the section pertaining to nature of the adsorbent. |
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