Q5(d). Signs of Δ H, Δ S and Δ G for spontaneous adsorption
What would be the sign; negative, positive or zero; for Δ H, Δ S and Δ G for the process of spontaneous adsorption of gas on solid surface at constant temperature. Give reasons.
Answer in brief
Δ G negative (the process is spontaneous); Δ S negative (the gas loses translational motion on the surface); hence Δ H must be negative (adsorption is exothermic), with |Δ H|>T|Δ S|.
Key points
- Δ G<0: at constant T and p a spontaneous process lowers the Gibbs energy. Adsorption occurs by itself, so Δ G<0
- Δ S<0: a gas molecule moving at random in three dimensions becomes held on the surface: it loses translational (and some rotational) motion. Fewer arrangements are possible, so the system becomes more ordered: Δ S<0
- Δ H<0: from Δ G=Δ H-TΔ S, with -TΔ S>0, a negative Δ G is possible only if Δ H is negative and larger in size than T|Δ S|: Δ H<0 (exothermic)
- new attractive forces (van der Waals in physisorption, chemical bonds in chemisorption) form between the molecule and the surface, releasing energy: typically about -20 kJ mol⁻¹ for physisorption and about -200 kJ mol⁻¹ for…
The full model answer
Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.
- Δ G<0: at constant T and p a spontaneous process lowers the Gibbs energy. Adsorption occurs by itself, so Δ G<0
- Δ S<0: a gas molecule moving at random in three dimensions becomes held on the surface: it loses translational (and some rotational) motion. Fewer arrangements are possible, so the system becomes more ordered: Δ S<0
- Δ H<0: from Δ G=Δ H-TΔ S, with -TΔ S>0, a negative Δ G is possible only if Δ H is negative and larger in size than T|Δ S|: Δ H<0 (exothermic)
- Physical picture: new attractive forces (van der Waals in physisorption, chemical bonds in chemisorption) form between the molecule and the surface, releasing energy: typically about -20 kJ mol⁻¹ for physisorption and about -200 kJ mol⁻¹ for chemisorption.
- None is zero: Δ G=0 would mean equilibrium, not spontaneous adsorption; Δ S=0 and Δ H=0 are ruled out by points 2 and 3.
Consequence: since Δ H<0, adsorption decreases with rise in temperature at a given pressure (Le Chatelier), and the extent at equilibrium falls until Δ G becomes zero.
Application. charcoal in gas masks and silica gel in desiccators adsorb best when cold; adsorbed gases are driven off by heating (regeneration of adsorbents), and the heat released is measured as the isosteric enthalpy of adsorption.
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All parts of Question 5
- 5(a) Degeneracy of the hydrogenic level with E=-R_H/3610 marks
- 5(b) van der Waals constants of ethylene from T_c and p_c10 marks
- 5(c) Half-life of two parallel first-order reactions10 marks
- 5(d) Signs of Δ H, Δ S and Δ G for spontaneous adsorption10 marks
- 5(e) Decay routes of an electronically excited molecule: Jablonski diagram10 marks