Raoult's law 1

Raoult's lawEstablished by François-Marie Raoult in 1882,[1] Raoult's law states:

The vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component andthe mole fraction of the component present in the solution.[2]

Once the components in the solution have reached equilibrium, thetotal vapor pressure p of the solution is:

and the individual vapor pressure for each component is

wherepi is the partial pressure of the component i in the mixture (in thesolution)

p*i is the vapor pressure of the pure component ixi is the mole fraction of the component i in the mixture (in thesolution)

Consequently, as the number of components in a solution increases, theindividual vapor pressures decrease, since the mole fraction of eachcomponent decreases with each additional component. If a pure solute which has zero vapor pressure (it will notevaporate) is dissolved in a solvent, the vapor pressure of the final solution will be lower than that of the puresolvent.

This law is strictly valid only under the assumption that the chemical interactions between the two liquids is equal tothe bonding within the liquids: the conditions of an ideal solution. Therefore, comparing actual measured vaporpressures to predicted values from Raoult's law allows information about the relative strength of bonding betweenliquids to be obtained. If the measured value of vapor pressure is less than the predicted value, fewer molecules haveleft the solution than expected. This is put down to the strength of bonding between the liquids being greater than thebonding within the individual liquids, so fewer molecules have enough energy to leave the solution. Conversely, ifthe vapor pressure is greater than the predicted value more molecules have left the solution than expected, due to thebonding between the liquids being less strong than the bonding within each.The vapor pressure and composition in equilibrium with a solution can yield valuable information regarding thethermodynamic properties of the liquids involved. Raoult’s law relates the vapor pressure of components to thecomposition of the solution. The law assumes ideal behavior. It gives a simple picture of the situation just as theideal gas law does. The ideal gas law is very useful as a limiting law. As the interactive forces between moleculesand the volume of the molecules approaches zero, so the behavior of gases approach the behavior of the ideal gas.Raoult’s law is similar in that it assumes that the physical properties of the components are identical. The moresimilar the components are, the more their behavior approaches that described by Raoult’s law. For example, if thetwo components differ only in isotopic content, then the vapor pressure of each component will be equal to the vaporpressure of the pure substance times the mole fraction in the solution. This is Raoult’s law.Using the example of a solution of two liquids, A and B, if no other gases are present, then the total vapor pressure pabove the solution is equal to the weighted sum of the "pure" vapor pressures of the two components, pA and pB.Thus the total pressure above solution of A and B would be

Raoult's law 2

DerivationWe define an ideal solution as a solution for which the chemical potential of component is:

,where µ*i is the chemical potential of pure i.If the system is at equilibrium, then the chemical potential of the component i must be the same in the liquid solutionand in the vapor above it. That is,

Assuming the liquid is an ideal solution, and using the formula for the chemical potential of a gas, gives:

where ƒi is the fugacity of the vapor of and indicates reference state.The corresponding equation for pure in equilibrium with its (pure) vapor is:

where * indicates the pure component.Subtracting both equations gives us

which re-arranges to

The fugacities can be replaced by simple pressures if the vapor of the solution behaves ideally i.e.

which is Raoult’s Law.

Ideal mixingAn ideal solution can be said to follow Raoult's Law but it must be kept in mind that in the strict sense ideal solutionsdo not exist. The fact that the vapor is taken to be ideal is the least of our worries. Interactions between gasmolecules are typically quite small especially if the vapor pressures are low. The interactions in a liquid however arevery strong. For a solution to be ideal we must assume that it does not matter whether a molecule A has another A asneighbor or a B molecule. This is only approximately true if the two species are almost identical chemically. We cansee that from considering the Gibbs free energy change of mixing:

This is always negative, so mixing is spontaneous. However the expression is, apart from a factor –T, equal to theentropy of mixing. This leaves no room at all for an enthalpy effect and implies that ΔmixH must be equal to zero andthis can only be if the interactions U between the molecules are indifferent.It can be shown using the Gibbs–Duhem equation that if Raoult's law holds over the entire concentration range x =0–1 in a binary solution then, for the second component, the same must also hold.If the deviations from ideality are not too strong, Raoult's law will still be valid in a narrow concentration rangewhen approaching x = 1 for the majority phase (the solvent). The solute will also show a linear limiting law but witha different coefficient. This law is known as Henry's law.The presence of these limited linear regimes has been experimentally verified in a great number of cases.

Raoult's law 3

In a perfectly ideal system, where ideal liquid and ideal vapor are assumed, a very useful equation emerges ifRaoult's law is combined with Dalton's Law.

Non-ideal mixingRaoult's Law may be adapted to non-ideal solutions by incorporating two factors that will account for theinteractions between molecules of different substances. The first factor is a correction for gas non-ideality, ordeviations from the ideal-gas law. It is called the fugacity coefficient ( ). The second, the activity coefficient ( ), is a correction for interactions in the liquid phase between the different molecules.This modified or extended Raoult's law is then written:

Real solutions

Many pairs of liquids are present in which there is nouniformity of attractive forces i.e. the adhesive andcohesive forces of attraction are not uniform betweenthe two liquids, so that they show deviation from theRaoult's law which is applied only to ideal solutions.

Negative deviation

When adhesive forces between molecules of A and Bare greater than the cohesive force between A and A, orB and B, then the vapor pressure of the solution is lessthan the expected vapor pressure from Raoult's law.This is called a negative deviation from Raoult's law.These cohesive forces are lessened not only by dilutionbut also attraction between two molecules throughformation of hydrogen bonds. This will further reducethe tendency of A and B to escape.

Raoult's law 4

For example, chloroform and acetone show such an attractionthrough a strong dipole-dipole interaction.

Positive deviation

When the cohesive forces between like molecules are greater thanthe adhesive forces, the dissimilarities of polarity or internalpressure will lead both components to escape solution more easily.Therefore, the vapor pressure will be greater than the expectedfrom the Raoult's law, showing positive deviation. If the deviationis large, then the vapor pressure curve will show a maximum at aparticular composition, e.g. benzene and ethyl alcohol, carbondisulfide and acetone, chloroform and ethanol.

References

Chapter 24, D A McQuarrie, J D Simon Physical Chemistry: A Molecular Approach. University Science Books.(1997)

E. B. Smith Basic Chemical Thermodynamics. Clarendon Press. Oxford (1993)[1] Barnett, Martin K. (2001), A Dictionary of the History of Science, Informa Health Care, p. 287. Extract. (http:/ / books. google. com/

books?id=JKMNuwMAmr4C& pg=PA287& lpg=PA287& dq=raoult's+ law+ history+ of+ discovery& source=bl& ots=FkH_LvtyiA&sig=NLtAO9FyUjkE-LDqh1_wwXzIYJU& hl=en& ei=PrBATLiXKcP-8AbqlZXUDw& sa=X& oi=book_result& ct=result& resnum=6&ved=0CDIQ6AEwBTgK#v=onepage& q& f=false)

[2] A to Z of Thermodynamics by Pierre Perrot. ISBN 0198565569

Article Sources and Contributors 5

Article Sources and ContributorsRaoult's law  Source: http://en.wikipedia.org/w/index.php?oldid=471052804  Contributors: Alansohn, Andre Engels, Aushulz, AxelBoldt, Brane.Blokar, Bubbachuck, CDN99, Chuckiesdad,Club house, Da Joe, Derek Ross, Dirac66, Drunken Pirate, FlamingSilmaril, Fthibault, Gentgeen, George Rodney Maruri Game, George moorey, Gescott14, Giftlite, GregRM, Hesacon, Icairns,Josh Parris, KI, LilHelpa, Longhair, Looxix, MagnInd, Mathmoclaire, Mbeychok, Mboverload, Mbursey1, Med, Mgiganteus1, Milio, Mnmngb, Nathan Johnson, Noldoaran, Pdch, Petergans,Physchim62, PhysicsJoe, Purgatory Fubar, Rifleman 82, Shalom Yechiel, Shoefly, Social tamarisk, Sodium, Strait, Tarif Ezaz, The wub, Ttownfeen, Uncle Dick, V8rik, Vsmith, Wikineer,Wsloand, 93 anonymous edits

Image Sources, Licenses and ContributorsImage:Graph-for-raoults-law.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Graph-for-raoults-law.jpg  License: Public Domain  Contributors: Devon Fyson, George mooreyImage:Negative-deviation-from-raoults-law.jpeg  Source: http://en.wikipedia.org/w/index.php?title=File:Negative-deviation-from-raoults-law.jpeg  License: Public Domain  Contributors:99of9, George moorey, Jeff G.Image:Positive-deviation-from-raoults-law.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Positive-deviation-from-raoults-law.jpg  License: Public Domain  Contributors: Georgemoorey

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