Raoult’s Law become a special case of Henry’s Law when K=P⁰ , but where do these laws differ from each other?

There’s a statement in my text book which I’m having trouble understanding.

The statement:

As a real solution approaches the limit of infinite dilution its components behave more ideal. The solvent obeys Raoult's law whereas solute (minor component) obeys Henry's law for dilute solutions.

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  • $\begingroup$ This is screenshot from NCERT textbook I believe? $\endgroup$ – Gaurang Tandon Feb 14 '18 at 2:44
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    $\begingroup$ To my understanding is Raoult's law used to describe the component with the higher concentration in a mixture. Henry's law, on the other hand, will describe the compound with the lower concentration better. $\endgroup$ – Justanotherchemist Feb 15 '18 at 13:56
  • $\begingroup$ @GaurangTandon No, this a photo\scan from Cengage Physical Chemistry: Part 2, 2nd ed., p. 2.16 by K. S. Verma. $\endgroup$ – Apoorv Potnis Feb 18 '18 at 7:38
  • $\begingroup$ This is discussed here: quora.com/… and i think it is reasonably clear. $\endgroup$ – AMM Feb 20 '18 at 9:43

Raoult's law can be seen to be valid for ideal liquids. The assumption behind Raoult's law is that both the liquid phase and the vapour phase behave ideally. This means that the interaction between any two molecules in the liquid and the vapour have no interaction. The Raolt's law just states the mole fraction of a component in the liquid phase is proportional to the mole fraction of the same component in the vapour phase. This is valid only for mixtures of ideal liquids. When you add a very small amount of impurity in a solvent (equivalent to infinite dilution) the interaction between the impurity and the solvent molecule is minuscule or technically infinitesimal. Therefore, the liquid still behaves ideally. Hence Raoult's law is applicable for the solvent.

Whereas Henry's law is also defined for a ideal mixture only this time the assumption is that the mole fraction of the component is tending to zero. this means that when very few molecules a present in a vast space, the interaction between them is almost zero. This makes the system ideal. therefore, an infinitesimally small quantity of impurity does not feel any interaction with another molecule of the same impurity in the solvent. Therefore, Henry's law is used for the solute. That is why Henry's law constant have huge values. Huge values makes sure that even small amount of the solute is accounted for when calculating the mixture properties.

For further clarity, please refer to chapter 6 of 'Molecular Thermodynamics of Fluid phase equilibria' by John M.Prausnitz et. al.

  • $\begingroup$ I would argue against the use of the term infinitesimal in any context of physical chemistry except maybe "infinitesimal" fluctuations around the equilibrium, which is explained by any serious textbook as a simpler notation for time derivatives. As far I as I know, there is no record of other uses in the thermodynamic literature and mathematicians surely wouldn't approve it since infinitesimals are only well defined in the extended reals. $\endgroup$ – Vinícius Godim Feb 19 '18 at 3:01

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