Gibbs Free Energy: Pressure Change Calculations

In summary, the expression for an isothermal change in Gibbs free energy for a liquid when the pressure changes from Pi to Pf can be written as Gf=Gi + V(Pf-Pi). For a perfect gas, the expression is Gf=Gi + nRT Ln (Pf/Pi). These equations can be deduced using the variation of Gibbs free energy equation and the ideal gas law. It is important to note that for a liquid, a convenient equation of state must be used, while for a perfect gas, the ideal gas law can be directly applied. Additionally, it is worth mentioning that "free energy" is often used interchangeably with "Gibbs potential" or "free enthalpy."
  • #1
koomanchoo
8
0
would anyone happen to know what the expression for an isothermal change in Gibbs free energy for a liquid is when the pressure changes from pi to pf. Also an expression for when its a perfect gas?
i can't seem to figure them out.. and how would they be deduced?
i've come across one equation: Gf=Gi +nrtln(pf/pi) <- that i think may be for perfect gas. but I'm still unsure abotu the first expression.
thanks for any help.
 
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  • #2
For a pure sustance the variation of the Gibbs free energy, dG, is equal to
dG= VdP-SdT
where V,P,S,T are volume, pressure, entropy and temperature, respectively. At constant T, above equation becomes
dG= VdP
For an ideal gas PV= nRT, then
dG= nRT dP/P
Integrating at constant T between Pi and Pf
Gf=Gi + nRT Ln ( Pf/Pi)

Where Gf and Gi are the Gibbs free energy at T and Pf , and at T and Pi, respectively. You can assume any value for Gi .

for a liquid you may use a convenient equation of state valid for the liquid phase. If the liquid is incomprensible V is almost independent of pressure, then
Gf=Gi + V(Pf-Pi)
 
  • #3
And one more thing,it's called Gibbs potential or free enthalpy."Free energy" is the name for Helhmoltz potential customarily denoted by "F".

Daniel.
 

1. What is Gibbs Free Energy?

Gibbs Free Energy, also known as the Gibbs function, is a thermodynamic property that measures the maximum amount of useful work that can be obtained from a thermodynamic system at a constant temperature and pressure.

2. How is Gibbs Free Energy related to Pressure?

Gibbs Free Energy is related to pressure through the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature, and ΔS is the change in entropy. Pressure affects the enthalpy and entropy of a system, thus impacting the overall Gibbs Free Energy.

3. How do you calculate Gibbs Free Energy for a pressure change?

To calculate Gibbs Free Energy for a pressure change, you can use the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy and ΔS is the change in entropy. You will also need to know the change in pressure and the temperature of the system.

4. What is the significance of ΔG in pressure change calculations?

The change in Gibbs Free Energy (ΔG) is a measure of the spontaneity of a reaction or process at a given temperature and pressure. A negative ΔG indicates that the reaction or process is spontaneous, while a positive ΔG indicates that it is non-spontaneous. A pressure change can affect the spontaneity of a reaction or process, thus changing the ΔG value.

5. Are there any limitations to using Gibbs Free Energy for pressure change calculations?

Yes, there are some limitations to using Gibbs Free Energy for pressure change calculations. The calculations assume that the temperature and pressure are constant, which may not always be the case in real-world situations. Additionally, the calculations do not take into account any kinetic or kinetic energy effects.

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