6. Adsorption Equilibria Rules

For gases and their mixtures, the rules, limits, and consistency tests are [TM88]

  1. Unary isotherms should reduce to Henry’s law at the limit of zero pressure.

  2. In spite of incorrect limits at zero pressure, both the Toth and DR equations are accurate for calculating spreading pressure provided the pressure is sufficiently high.

  3. At fixed temperature and pressure, thermodynamically consistent \(x\)-\(y\) diagrams intersect each other at least once. This can be derived by considering the Gibbs adsorption isotherm at constant spreading pressure.

  4. Mixed gas isotherms should display continuity with single-gas isotherms. That is,

    \[\lim_{y_i\to 1} q_\text{t} = q_i \;(\text{constant}\; P, T)\]

    where \(q_\text{t}=\sum_iq_i\) is the total loading. Discontinuities generate inaccurate values of adsorbate vapor pressure that lower the quality of calculations of mixed-gas adsorption.

  5. Isothermal selectivity curves for different vapor compositions should intersect at the limit of zero pressure.

  6. Activity coefficients in the adsorbed phase are functions of spreading pressure as well as composition.

  7. Imperfections in the gas phase led to corrections in fugacity that are small compared to the effect of nonidealities in the adsorbed phase. In most cases, vapor-phase imperfections may be ignored unless the pressure is above 500 kPa and experimental error is less than a few percent.