Chemical Thermodynamics 2013/2014. 7 th Lecture: Gibbs Energy and Fundamental Equations Valentim M B Nunes, UD de Engenharia. What have we learned (from the 2 nd Law!). We have seen that, in isolated systems, the entropy change give us the direction of an spontaneous transformation:.
7th Lecture: Gibbs Energy and Fundamental Equations
Valentim M B Nunes, UD de Engenharia
What have we learned (from the 2nd Law!)
We have seen that, in isolated systems, the entropy change give us the direction of an spontaneous transformation:
ΔStotal > 0 – spontaneous transformation
ΔStotal = 0 – equilibrium (reversible process)
But, systems of interest generally are not isolated. It will be convenient to have a criteria for spontaneous change depending only on the system.
Gibbs (1839-1903) introduced a new state function, that plays a key role in chemistry and in the study of chemical equilibrium:
Consider a system in thermal equilibrium with its surroundings:
By the second Law,
For any transformation in a closed system at constant p (p=pext)
Under constant T= Tsurr and constant p = pext, the criterion for spontaneity is:
This means that at constant p and constant T, equilibrium is achieved when the Gibbs energy is minimized.
Consider the process A B (keeping p and T constant)
ΔG < O – A B is spontaneous
ΔG = 0 – A and B are in equilibrium
ΔG > 0 – then B A is spontaneous
The second law is still valid. In some transformations the maximization of entropy can be obtained by “transferring” enthalpy to the surroundings
If Text is low (cold air masses) then |ΔSext| > | ΔSsyst|
Snowing: gas liquid solid
If we define now the Helmholtz energy, A, as:
The criterion for spontaneity under constant T = Tsurr and constant volume, V it will be:
Gibbs energy is, by far, more important that Helmholtz energy.
At constant temperature:
Since H = U + pV
Now, considering that the total work is the sum of expansion work and other types of work
As result, at constant p we finally obtain
The Gibbs energy change represents the maximum available work, or the useful work that we can obtain from a given process.
As for enthalpy we can also obtain standard Gibbs energy of formation, ΔGºf (at pº = 1 bar). For any element in their reference state, ΔGºf=0.
From the definition of G = H – TS we obtain:
These values are tabled, and are obtained from calorimetric or spectroscopic data!
We can now combine the first an second law; as we have introduced all the state functions for closed systems
From the 1st Law:
FUNDAMENTAL EQUATIONS: valid for reversible or irreversible changes for closed systems and only pV work.
Since H = U + pV
H = H(S,p)
G = H-TS
G = G(p,T)
Since G is a state function, and as we saw before G = G(T,p) then we can write:
And easily obtain:
Recalling that df = gdx + hdy is an exact differential if
and using the fundamental equations we obtain
Maxwell Relations: these equations allow us to establish useful thermodynamic relations between state properties!
We can now relate U and H to p-V-T data. For instance for U, we can calculate the ΠT value:
Generic equation of state!
For an ideal gas:
This proves that for an ideal gas U = U(T), that is function of T only !
For a van der Waals gas:
As we saw previously:
If we derivate now G/T we obtain:
Applying the Gibbs Helmholtz equation to a chemical reaction we obtain:
Where ΔH is the reaction enthalpy change.
And upon integration we obtain, at constant T:
For liquids and solids the molar volume, Vm, is small and approximately constant, so:
For a perfect gas (pV = nRT) we obtain:
Considering now that pi = pº (the standard pressure of 1 bar) and calculating the molar Gibbs energy, Gm (n=1), we obtain:
The molar Gibbs energy is also called the chemical potential, μ:
We have now all the “thermodynamic tools” that allow us to apply the thermodynamic principles to all kind of physical and chemical processes, like chemical equilibrium or phase equilibrium. That will be the syllabus for the next lectures…