CHAPTER 19 CHEMICAL THERMODYNAMICS SECTION 3 THE MOLECULAR INTERPRETATION OF ENTROPY

MOLECULAR MOTIONS & ENERGY Heat increases the motion of molecules. From Kinetic Molecular Theory, the average kinetic energy of the molecules of an ideal gas is directly proportional to the absolute temperature of the gas: ↑ temp. = ↑ speed of molecules = ↑ KE

Hotter systems have a broader distribution of molecular speeds – see Figure Molecules can undergo 3 kinds of motion: 1. Translational: entire molecule moves 2. Vibrational: atoms within a molecule vary their inter-atomic distances 3. Rotational: molecules may spin on an axis

BOLTZMANN’S EQUATION & MICROSTATES The entropy of a substance relates to the behavior of atoms and molecules through the application of statistical thermodynamics. Consider taking a “snapshot” of one mole of a gas having a set of 6.02 x positions and energies of the individual molecules to determine the thermodynamic microstate of the system. A microstate is a single possible arrangement of the positions and kinetic energies of the molecules in a specific thermodynamic state.

Continuing to take “snapshots” to see other possible microstates is not practical, so statistical analysis is used to describe the thermodynamics. Each thermodynamic state has a characteristic number of microstates (W) associated with it. The relation between the no. of microstates of a system (W) and its entropy (S) is expressed as: S = k ln(W) where k is Boltzmann’s constant = 1.38 x J/K Therefore, entropy is a measure of how many microstates are associated with a particular system or macroscopic state.

The entropy change accompanying any process is: ΔS = k ln(W final )– k ln(W initial ) = k ln(W final ) / k ln(W initial ) *So, any change in the system that leads to an increase in the number of microstates leads to a positive value of ΔS: entropy increases with the number of microstates of the system.

In general: the number of microstates available to a system increases with an increase in volume, an increase in temperature, or an increase in the number of molecules because any of these changes increases the possible positions and energies of the molecules of the system. An increase in entropy represents an increase in disorder or an increase in the dispersion (spreading out) of energy through the system. This is why, at the same temperature, a solid has less entropy than a liquid and a liquid has less entropy than a gas.

MAKING QUALITATIVE PREDICTIONS ABOUT ΔS An increase in the number of microstates, which means an increase in entropy parallels an increase in: 1. temperature 2. volume 3. number of independent particles

In summary, the entropy of the system is expected to increase for processes in which: 1. Gases are formed from solids or liquids 2. Liquids or solutions are formed from solids 3. The number of gas molecules increases during a chemical reaction

Predicting the Sign of ΔS Predict whether ΔS is positive or negative for each of the following processes, assuming each occurs at constant temperature: a)H 2 O (l)  H 2 O (g) b)Ag + (aq) + Cl - (aq)  AgCl (s) c)4 Fe (s) + 3 O 2(g)  2 Fe 2 O 3(s) d)N 2(g) + O 2(g)  2 NO (g)

Predicting ΔS Answers a)ΔS is positive b)ΔS is negative c)ΔS is negative d)ΔS is impossible to predict, but will be close to zero

Practice Exercise Indicate whether each of the following processes produces an increase or decrease in the entropy of the system: a)CO 2(s)  CO 2(g) b)CaO (s) + CO 2(g)  CaCO 3(s) c)HCl (g) + NH 3(g)  NH 4 Cl (s) d)2 SO 2(g) + O 2(g)  2 SO 3(g)

Practice Answers a)increase b)decrease c)decrease d)decrease

THE THIRD LAW OF THERMODYNAMICS The Third Law of Thermodynamics states that the entropy of a pure crystalline (solid) substance at absolute zero is exactly zero. This means – no thermal motion and only one microstate. Above absolute zero the degrees of freedom of the crystal increase and the number of possible microstates increases so entropy of the system increases. See Figure 19.14

Entropy increases with temperature because of increased motion (kinetic energy) that can be dispersed in more ways. Entropies of phases of a given substance follow the order: S solid < S liquid < S gas