Thermodynamics :  Entropy

Entropy (S) - A measure of the disorder in a system.  Entropy is a state function.

where k is a proportionality constant equal to the ideal gas constant (R) divided by Avogadro's number (6.022 x 10-23) and lnW is the natural log of W, the number of equivalent ways of describing the state of a system.

In this reaction, the number of ways of describing a system is directly proportional to the entropy of the system.

Entropy of Reaction (S)

• The difference between the sum of the entropies of the products and the sum of the entropies of the reactants:

In the above reaction, n and m are the coefficients of the products and the reactants in the balanced equation.

Second Law of Thermodynamics

Natural processes that occur in an isolated system are spontaneous when they lead to an increase in the disorder, or entropy, of the system.

Isolated system - System in which neither heat nor work can be transferred between it and its surroundings.  This makes it possible to ignore whether a reaction is exothermic or endothermic.

IfSsys > 0, the system becomes more disordered through the course of the reaction

IfSsys < 0, the system becomes less disordered (or more ordered) through the course of the reaction.

There are a few basic principles that should be remembered to help determine whether a system is increasing or decreasing in entropy.

• Liquids are more disordered than solids.
• WHY? - Solids have a more regular structure than liquids.
• Gases are more disordered than their respective liquids.
• WHY? - Gases particles are in a state of  constant random motion.
• Any process in which the number of particles in the system increases consequently results in an increase in disorder.

Does the entropy increase or decrease for the following reactions?

• INCREASES - The number of particles in the system increases, i.e. one particle decomposes into two.  In addition, one of the products formed is a gas which is much more disordered than the original solid.
• DECREASES  - The number of particles in the system decreases, i.e. there are four moles of gas reactants and only 2 moles of gas products.
• INCREASES - The number of particles in the system increases, i.e. the single reactant dissociates into two ion particles.  In addition, the ions in the ionic solid are organized in a rigid lattice structure whereas the ions in aqueous solution are free to move randomly through the solvent.
• DECREASES - The reactant changes from a gas to a liquid, and gases are more disordered than their respective liquids.

Third Law of Thermodynamics

The entropy of a perfect crystal is zero when the temperature of a the crystal is equal to absolute zero (0 K).

 At 0 K, there is no thermal motion, and if the crystal is perfect, there will be no disorder  Once the temperature begins to rise above 0, the particles begin to move and entropy gradually increases as the average kinetic energy of the particles increases.  When temperature reaches the melting point of the substance (Tm), there is an abrupt increase in entropy as the substance changes from a solid to a more disordered liquid.  Again the entropy increases gradually as the motion of the particles increases until the temperature reaches the boiling point of the substance (Tb).  At this point, there is another drastic increase in entropy as the substance changes from a confined liquid particles to radom motion gas particles.

Standard-State Entropy of Reaction (S)

• The entropy of reaction at standard-state conditions.

Standard-state conditions

• The partial pressures of any gases involved in the reaction is 0.1 MPa.
• The concentrations of all aqueous solutions are 1 M.

Measurements are also generally taken at a temperature of 25C (298 K)

Sample entropy of reaction calculations

1) Calculate the standard-state entropy for the following reaction given the following information.  Also, explain the sign ofS for the reaction.

 Compound S  (J/mol-K) NaCl(s) 72.13 Na+(aq) 59.0 Cl-(aq) 56.5

In the balanced reaction above, one mole of NaCl yields one mole of Na+ and one mole of Cl-.  We find theS by subtracting the entropy of the reactant from the sum of the entropies of the products:

The change in entropy for this reaction is positive. The disorder of the system increases because the number of particles increases as one solid reactant is converted into two aqueous particles.  Also, the ions in the ionic solid are positioned in a rigid lattice structure whereas the ions in solution are free to move around.

2) Calculate the standard-state entropy for the following reaction given the following information.  Also, explain the sign ofS for the reaction.

 Compound S  (J/mol-K) NO2(g) 240.06 N2O4(g) 304.29

In the balanced reaction above, two moles of NO2 combine to form one mole of N2O4.  We find theS by subtracting the entropy of the reactant from the entropy of the product:

The change in entropy for this reaction is negative.  The disorder of the system decreases because the number of particles decreases as two moles of gas reactant are converted to one mole of gas product.

Next:  "Gibbs Free Energy"