Sips isotherm Isosteric heat

Since the Sips and Toth empirical equations fit the equilibrium data reasonably well, it may be possible to use the isosteric heat as a function of loading as a criterion in choosing the correct isotherm equation. Using eq. (3.2-19g) and the optimal parameters in Table 3.2-6 for the Toth equation, we obtain the following equation for the isosteric heat at 283 K with values tabulated in Table 3.2-7 ... 

The isosteric heats calculated by the Toth equation are lower than those calculated by the Sips equation (Table 3.2-5). The above table shows the percentage differences between the values calculated by the Sips and Toth equations. The difference is seen to be significant enough for the isosteric heat to be used as the criterion to better select the isotherm equation. 

Take the example of propane on activated carbon, we plot the isosteric heat (eq. 3.2-19f) versus the fractional loading for the Toth equation using the parameters obtained in Table 3.2-6 (Figure 3.2-11). Just like the case of the Sips isotherm, the isosteric heat decreases with loading, and it shows a weak temperature dependence. 

We see a distinction between the isosteric heat calculated from the Toth equation and those calculated from the Sips and Unilan equations, despite of the fact that the three isotherm equations describe the equilibrium data fairly well. This distinction in the isosteric heat curve could be utilised in the matching between the... 

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