Lecture 6: Entropy and Gibbs Free Energy Concept
Review:
o Concept of efficiency of engine
o The concept of entropy
o Entropy change during reversible and irreversible paths.
Today:
o Entropy variation with
o Temperature
o Pressure
o Composition
o Reaction
The Carnot’s concept of engine revisited
Efficiency
Entropy
Entropy is a state variable!
Temperature dependence of Entropy
Using the usual conditions such as isobaric or isochoric paths we can see that:
Just as in case of ΔH the above formulae apply as long as system remains in single phase. On the other hand if system undergoes a phase transition, at constant temperature and pressure.
Thus overall temperature dependence of the entropy will include the changes involved at the phase transition.
Such an approach is valuable for calculating entropy at arbitrary temperature for a single component system.
Pressure Dependence of Entropy
For solids and liquids entropy change with respect to pressure is negligible on an isothermal path. This is because the work done by the surroundings on liquids and solids is miniscule owing to very small change in volume. For ideal gas we can readily calculate the entropy dependence on the pressure as follows:
Entropy of Mixing
Consider two non-reacting gases A and B initially at identical pressure, P separated from each other. If we allow them to mix they will do so spontaneously and it is difficult to separate them. The mixture will have identical pressure P, but we can think of it as if it’s made up sum of partial pressures of A and B. We can calculate the net change in the entropy of this system.
This is a very important relation used frequently in problems involving solutions.
Entropy Changes involved in chemical reactions
Consider a general reaction
o S is the standard molar entropy of formation at 25oC. Tables of heat of formation are in appendix A5-A7. Unlike enthalpy of formation, entropy of formation of elements in not zero at 25 C.
o Entropy increases in a reaction that leads to increased number of particles and vice versa
o If the reactants are charged and the reaction takes place in aqueous medium resulting in decreased net charge, then it leads to an increase in entropy. This is because polar water molecules are ordered in a specific way around charged species.
o Whether, a reaction occurs spontaneously or not cannot be predicted solely based on the change in entropy.
Gibbs Free energy
Gibbs developed the precise criterion for a spontaneous reaction or process, in general. Gibbs Free Energy is a new measure of energy:
Since it is made up of state variables, it is also a state variable and is extensive in nature. In general this free energy is especially valuable when we are considering processes that are carried out at constant temperature and pressure. Consider the following
Thus ΔG at constant temperature and pressure equals the ability of system to perform useful work other than the simple PV work.
Gibb’s criterion for Spontaneous Process.
Thus, at constant T and P, the system can do useful work on the surrounding if the sign of w rev is negative. This means that the sign of ΔG must be negative for the process to take to place. On the other hand, if the process is directed in the opposite direction, that is, surrounding does work on the system then sign of ΔG is positive. While if the system is in equilibrium with surrounding then the maximum reversible work that either surrounding or system can do is zero. Then ΔG is zero. These are the three fundamental criteria.