Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

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Chemistry : Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

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Clausirs Clapeyron Equation: The two phases in equilibrium may be any of the following types:

(i)  Solid and Liquid, S Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev L, at the melt ing point of the solid.

(ii)  Liquid and vapour, LClausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev V, at the boiling point of the liquid.

(iii)  Solid and vapour, S Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev V; at the sublimat ion temperature of the solid. “The equal amounts of a given substance must have exactly the same free energy in the two phases at equilibrium with each other.”

Consider t ype equation A Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev B at the given temperature and pressure. If G& GB be the free energy per mole of the substance A & B in initial.
Then, G= GB
Hence ΔG = GB - GA = 0 ΔG = GB - GA = 0
If temperature of the system raise from T to T + dT then pressure raise from P to P + dt, in order to maintain the equilibrium. The free energy of substance raise from GA to GA + dGand GB + dGB. Since the two phase are still in equilibrium hence,
CA = dGA = GB + dG                                            [∵ GA = GB]
then dGA = dGB                                          …(a)

According to thermodynamics, dG = VdP – SdT 
then dGA = VAdP – SAdT                            …(b)

dGB = VBdP – SBdT

Using equation (a) and (b)

we get

dGA = dGB

VAdP – SAdT = VBdP – SBdT 

 Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev 

V& VB be the volume of A and B.

 If q heat exchanged reversibly per mo le of substance during the phase transformat ion at temperature t, then change in entropy. Δ

Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
Hence, Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
Thus, Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

This is Clapeyron equation.
Claypeyron equation for liquid Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev vapour equilibrium 

Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

where       

 ΔH= heat of vapourisation
Vg = volume of gas
Vl = volume of liquid
 ⇒  Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev                                           [∵ Vg >> Vl]
& PV = RT (per mole)

Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

⇒ Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
⇒ Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
⇒ Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
⇒ Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
⇒ Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

This is Clasusius-Clapeyron equation.
Claypeyron equation for solid Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev vapour equilibria
 Solid Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev Vapour 

ΔHS = heat of sublimation

 Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

Vg >> V&Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

Similarly the above equation, we get

Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

Claypeyron equation for solid Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev liquid equilibria

Solid Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev Liquid 

ΔH= heat of fusion

 Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev
Clausius Clapeyron Equation - Thermochemistry Chemistry Notes | EduRev

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