The Second Law defines the criteria needed for a chemical or physical process to occur without outside help. This is called spontaneity. A spontaneous process is one in which the change can happen without external intervention. Although a spontaneous process can occur, it may not happen in a reasonable time, depending upon the kinetics of the process. The thermodynamic definition of spontaneity is unrelated to time!
For a spontaneous process, energy flows from high concentration to low concentration.
The measure of this type of energy flow is called entropy.
Entropy, given the symbol S, has units of J/mole·K and is a state function.
Entropy is linked to heat: heat is the agent that carries entropy (and energy) from one place to another, either from the system to the surroundings or from the surroundings to the system.
Thus, the Second Law of Thermodynamics can be stated as:
For a spontaneous process, the total entropy of the system plus the surroundings increases.
Entropy is quite different from energy: it is not conserved, i.e., entropy can be created during chemical or physical changes.
We are able to measure both the change in entropy during a process and the absolute entropy of substances.
Thus, for any process, the change in entropy is defined by the amount of entropy created by the process and the amount of entropy moved by the heat flow:
ΔS = Sfinal – Sinitial
ΔS = Screated + Sheat flow
The amount of entropy created is generally not known, but the contribution from the heat flow is simply:
Sheat flow = q T
q is the heat and T is the absolute temperature.
This gives a mathematical statement of the Second Law:
For a spontaneous process ΔS > q T
For processes at equilibrium, there are changes occurring at the microscopic level, but there is not net macroscopic change. This means that there is no spontaneous process available. In Second Law terms, this means that there is no entropy being created at equilibrium, although the heat flow may move entropy around.
Mathematically:
For a spontaneous process ΔS = q T
The implication of this statement is that all equilibrium processes are connected to entropy changes!
Most chemical processes are run at constant pressure, so
For a spontaneous process at constant pressure ΔS > qp T
(qp is the heat at constant pressure.)
Remember that qp = ΔH, so
For a spontaneous process at constant pressure ΔS > ΔH T
or, ΔH – TΔS < 0
for a spontaneous process at constant pressure.
This is such an important function that we give it a name:
ΔG = ΔH – TΔS
ΔG = Gibb's Energy.
ΔG is used to determine the spontaneity of any process at constant pressure.
ΔG > 0 for a nonspontaneous process
ΔG < 0 for a spontaneous process
ΔG = 0 for a process at equilibrium
ΔG is a measure of the change in entropy of the universe for a constant pressure process.
The Third Law defines entropy in terms of statistics.
On a molar basis,
S = RlnW
R = gas constant (units of J/mole·K)
W = the number of arrangements of the energy of atoms or molecules can take without changing the total energy in a system. This is also known as the degeneracy.
At absolute zero for a perfectly ordered crystalline substance, W = 1 (there is only one way to arrange the atoms in a perfect substance, hence there is only one way to distribute the energy)
This means that at T = 0, S = Rln(1) = 0.
The Third Law, then, gives us a method to find the absolute entropy for any substance: cool the substance to as close to absolute zero as possible and then measure the heat change as the substance is warmed up (remember, ΔS = q/T = Sfinal – Sinitial, but Sinitial = 0 if we start at T = 0).
Absolute entropies for substances are tabulated at standard conditions.
The tabulated values of the absolute entropy allow us to calculate the change in entropy for chemical reactions:
ΔS° = ∑products miS°fi – ∑reactants mjS°fj
mi and mj are the stoichiometric coefficients from the balanced reaction and Si° and Sj° are the absolute entropies of the products and reactants.
ΔS° will be positive if the chemical process leads to an increase in the number of ways to disperse energy.
This will happen if:
There are more moles of products than moles of reactants (there are more ways to distribute energy because there are more particles after reaction).
The number of moles of gaseous products is greater than the number of moles of gaseous reactants (gases can distribute energy in more ways because of the large mobility of the particles, so have a disproportionate effect on the change in entropy).
A change in phase from s to l, l to g, or s to g.
These guidelines can be used to help determine if a calculated entropy change makes sense.