Clausius Clapeyron Equations | Physical Chemistry PDF Download

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

(i)  Solid and Liquid, S  L, at the melt ing point of the solid.

(ii)  Liquid and vapour, L V, at the boiling point of the liquid.

(iii)  Solid and vapour, S  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  B at the given temperature and pressure. If G_A & G_B be the free energy per mole of the substance A & B in initial.
Then, G_A = G_B
Hence ΔG = GB - G_A = 0 ΔG = G_B - G_A = 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 G_A to G_A + dG_A and G_B + dG_B. Since the two phase are still in equilibrium hence,
C_A = dG_A = G_B + dG_B                                             [∵ G_A = G_B]
then dG_A = dG_B                                          …(a)

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

dG_B = V_BdP – S_BdT

Using equation (a) and (b)

we get: 

dG_A = dG_B

V_AdP – S_AdT = V_BdP – S_BdT 

V_A & V_B 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

Hence, 
Thus, 

This is Clapeyron equation.
Claypeyron equation for liquid  vapour equilibrium 

where       

 ΔH_V = heat of vapourisation
V_g = volume of gas
V_l = volume of liquid
 ⇒                                             [∵ Vg >> Vl]
& PV = RT (per mole)

⇒ 
⇒ 
⇒ 
⇒ 
⇒ 

This is Clasusius-Clapeyron equation.
Claypeyron equation for solid  vapour equilibria
 Solid  Vapour 
ΔH_S = heat of sublimation

V_g >> V_S &

Similarly the above equation, we get

⇒

Claypeyron equation for solid  liquid equilibria

Solid  Liquid 

ΔH_f = heat of fusion