Problem 1

At low pressures, the amount adsorbed is given by:

$$\theta \simeq KP_A$$

where K is the equilibrium constant for the adsorption process (Langmuir).

1. For $\epsilon = 7.5$, at each of T = 0.9, 1.0 and 1.1, use simulations to determine the pressure range over which the adsorption isotherm is linear, and measure its slope. (Hint: at T=1.0, this is the same problem as done in Example 1.

2. From these data, you should be able to determine the standard molar enthalpy and entropy of adsorption at low coverage, using the van't Hoff equation:

$$\ln\frac{K(T_2)}{K(T_1)} = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$$

and the relationship

$$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ = -RT\ln K$$

3. How does your enthapy of adsorption compare with the wall-fluid interaction strength? Also, explain the sign (positive or negative) of your value for the entropy.