Understanding Spontaneity and Entropy in Thermodynamics

1. Spontaneity, Entropy, and Free Energy

2. Spontaneous Processes and Entropy • First Law • “Energy can neither be created nor destroyed“. • The energy of the universe is constant. • Spontaneous Processes • Processes that occur without outside intervention. • Spontaneous processes may be fast or slow. • Many forms of combustion are fast • Conversion of diamond to graphite is slow

3. Entropy (S) • A measure of the randomness or disorder. • The driving force for a spontaneous process is an increase in the entropy of the universe. • Entropy is a thermodynamic function describing the number of arrangements that are available to a system. • Nature proceeds toward the states that have the highest probabilities of existing. • The most likely is the most random.

4. Positional Entropy • The probability of occurrence of a particular state depends on the number of ways (microstates) in which that arrangement can be achieved. • Positional entropy increases from solid to liquid to gas. Ssolid < Sliquid << Sgas

5. Solid state: molecules are close together with relatively few positions available. • Gaseous state: molecules are far apart, with more positions available. • Liquid state is closer to the solid state than gaseous state. Ssolid < Sliquid << Sgas

6. Second Law of Thermodynamics • "In any spontaneous process there is always an increase in the entropy of the universe" • "The entropy of the universe is increasing" • For a given change to be spontaneous, Suniverse must be positive Suniv = Ssys + Ssurr

7. Temperature and Spontaneity • Entropy changes in the surroundings are primarily determined by heat flow. • Exothermic reactions in a system at constant temperature increase the entropy of surroundings. • ∆Ssurr = positive • Endothermic reactions in a system at constant temperature decrease the entropy of surroundings. • ∆Ssurr = negative • The impact of the transfer of a given quantity of energy as heat to or from the surroundings will be greater at lower temperatures.

8. ∆Ssurr for a reaction under conditions of constant temperature (K) and pressure: • ∆Ssurr = -∆H / T

9. Entropy and Chemical Reactions • Gaseous reactions: • Calculate change in the number of moles of gas, ∆ngas on going from reactants to products. • ∆ngas is positive = entropy is positive • 2NaHCO3 (s) → Na2 CO3 (s) + CO2 (g) + H2O(g) • Gaseous products > Gaseous reactants • Change in Entropy = ∆S = positive

10. Another factor that affects the sign of ∆S is degree of complexity of molecules. • H2 (g) → 2H(g) • Decrease in complexity and increase in number of particles = increase in entropy

11. Third Law of Thermodynamics • “At absolute zero the entropy of a perfectly ordered pure crystalline substance is zero.”

12. Since pure crystal is zero all other must be > 0. • StandardEntropy of 1 mol of substance, So is measured at 298 K (25o C) and 1 atm. • Units are J/K mol. • Values published in Appendix 4 of textbook.

13. Calculating Entropy Change in a Reaction • Entropy is an extensive property (a function of the number of moles) • Generally, the more complex the molecule, the higher the standard entropy value