μ = μ⁰ +RTlnP
μ = μ⁰+ RTlncⱼ
μ = μ⁰ + RTlnxⱼ
The presence of intermolecular attractive and respective forces make a real gas deviate from ideal behaviour and it's molar volume V is not equal to RT/P ( gas equation) so other equations have to be used to find "V" in case of real gas.
Hence G.N Lewis decided to retain the general from equation μ=μ⁰ + RTlnPⱼ is used a new state function called fugacity (Latin - fleetless) "f" is nothing but effective pressure and takes into account the deviation of a real gas from ideal behaviour. It has dimensions of P and it applicable to Real gases.
Consider a liquid in equation with the vapour. For this equilibrium,
μ (l) = μ (v).
The molecules of the ligands tend to escape into vapour phase and the molecules in the vapour phase tend to escape into liquid phase. This escaping tenancy will be proportional to the pressure. The vapour these two escaping tenancy are equal, and system is equilibrium at constant.
This equation applicable both to ideal or non- ideal gases.
For ' n' moles,
( ∂G)T = v − dp
= RT/P.dp
(∂G) T = nRT. dlnP.
Upon the integration with the limits P₁ and P₂
∫ dɢ = nRT ∫ ₚᵖ₁² dlnP
(G) = nRTln P₂/P₁
G = G⁰ + nRTlnP
∆G⁰ = nRTln P.
If dG = nRTlnP is
Integrated with in limits P₁ and P₂
∆G = RTln P₂/P₁
This equation is not valid for real gases since 'V' is not exactly equal to R/P.
So the new function 'f' is introduced called fugacity function in place of P for real gases.
(dG)T = nRT ( dlnf)
G = G⁰ + nRTlnf.
Fugacity is a sort of fictitious P. Upon
∫ of the above equation with in limits f₁ and f₂
∆G = nRTln f₂/f₁
For one mole,
G = G⁰ + RTln f₂/f₁
∆G = RTln f₂/f₁
Fugacity and pressure,
If we take proportionality count as unity,
F = P
Fugacity at low P,
The ratio f/p = 1
Ɬ
P→0 f/P = 1
When pressure approaches is zero, (ie) at low P, fugacity and pressure are same only. They differ only at high P. Where the gases deviate from ideal behaviour.
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