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My textbook reads as follows:

"When a gas is adsorbed, the freedom of movement of its molecules become restricted. This amounts to decrease in the entropy of the gas after adsorption, i.e. Entropy change is negative."

But now, I am unable to understand why it isn't a violation of the 2nd Law of Thermodynamics which states that the entropy change of a system can never be negative? Please guide.

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    $\begingroup$ Oh, no not again that... Entropy decreases locally by but raises globally - If this wouldn't be possible you wouldn't exist $\endgroup$ – Mithoron Feb 5 '15 at 17:38
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    $\begingroup$ This I think is the most commonly asked question about entropy! (Not the exact question, but the concept) $\endgroup$ – M.A.R. ಠ_ಠ Feb 5 '15 at 20:29
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The second Law of Thermodynamics states that the entropy of the universe always increases. $$\text{d}S > 0$$

In the case of adsorption the entropy of the system; the gas being adsorbed; decreases but the entropy of the surroundings;the rest of the gas and the surface (and everything else in the universe); increases and this outweighs the decrease in entropy of the system. $$\Delta S_{sys} < 0~~~~~~~~\Delta S_{surr} > 0$$ $$|{\Delta S_{surr}}| > |{\Delta S_{sys}}|$$

This is because adsorption is an exothermic process and so the surroundings are heated up and therefore increase in entropy. If you consider the Gibbs energy change for adsorption it will be negative becuase the negative $\Delta H$ term is larger than the positive $-T\Delta S$ term. This page goes through the maths of this very nicely. http://www2.chem.uic.edu/rjgordon/teaching/chem549/Entropy%20of%20adsorption.pdf

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