Entropy Calculation for Reversible Processes

Entropy (S) is a measure of the number of different ways that the internal energy of a sample can be stored in the available energy levels.  Each different way corresponds to a microstate of the system.

The macrostate of a system is determined by temperature, pressure and amount of substance.  This does not change with time.   

However, as the videos below show, the particles of any system are continually moving and colliding with one another.  As a result, the distribution of the available energy between the particles in the system is continually changingA microstate is a snap shot of the distribution of energy at one point in time
 
The more different snapshots (microstates) possible, the higher the entropy. One factor which affects the number of microstates is the extent to which the particles in the sample can move.  Thus when considering the same substance, the entropy of a gas is higher than the entropy of the liquid which is higher than the entropy of a solid.

This means that the entropy of reaction for vaporisation and melting is positive, while the entropy of reaction for condensation and freezing is negative.

VisChem molecular animations courtesy of Dr Roy Tasker, University of Western Sydney. 1995.
This can be used to predict the sign of the entropy change ΔrS for reaction systems involving different substances  where the phases of reactants and products differ.

In general for reactions involving gases,
 
  • If there are more moles of gases in products ΔrS is positive.
    Example:  N2O4(g) 2NO2(g) (1 in reactants and 2 in products)
     
  • If fewer moles of gases in products ΔrS is negative.
    Example: 2NO(g) + O2(g)  2NO2(g) (3 in reactants and 2 in products)
     
  • If equivalent numbers of moles of gases are in reactants and products, ΔrS is small.
  • Example: H2(g) + Cl2(g) 2HCl(g) (2 in reactants and 2 in products)