Spontaneous Processes Spontaneous: process that does occur under a specific set of conditions Nonspontaneous: process that does not occur under a specific set of conditions

Spontaneous Physical and Chemical Processes A waterfall runs downhill A lump of sugar dissolves in a cup of coffee At 1 atm, water freezes below 0 0C and ice melts above 0 0C Heat flows from a hotter object to a colder object A gas expands in an evacuated bulb Iron exposed to oxygen and water forms rust spontaneous nonspontaneous

Spontaneous vs Nonspontaneous

Spontaneous expansion of a gas stopcock closed 1 atm evacuated stopcock opened 0.5 atm

Spontaneous Processes Often spontaneous processes are exothermic, but not always…. Methane gas burns spontaneously and is exothermic Ice melts spontaneously but this is an endothermic process… There is another quantity!

A spontaneous endothermic chemical reaction. water Ba(OH)2 8H2O(s) + 2NH4NO3(s) Ba2+(aq) + 2NO3-(aq) + 2NH3(aq) + 10H2O(l) . DrH0 = +62.3 kJ/mol

Entropy Entropy (S): Can be thought of as a measure of the disorder of a system In general, greater disorder means greater entropy

Probability- what is the chance that the order of the cards can be restored by reshuffling?

Microstates - How many different arrangements?

Microstates - Possible distributions

Microstates - More possible distributions

Microstates 1868 - Boltzmann - entropy of a system is related to the natural log of the number of microstates (W) S = k ln W k = Boltzmann constant (1.38 x 1023J/K)

Microstates Entropy is a state function just as enthalpy S = Sfinal  Sinitial Rewrite: S = k ln Wfinal  k ln Winitial Wf > Wi then S > 0 entropy increases

Standard Entropy Standard entropy: absolute entropy of a substance at 1 atm (typically at 25C) Complete list in Appendix 2 of text What do you notice about entropy values for elements and compounds? Units: J/K·mol

Entropies

Entropy (S) is a measure of the randomness or disorder of a system. DS = Sf - Si If the change from initial to final results in an increase in randomness Sf > Si DS > 0 For any substance, the solid state is more ordered than the liquid state and the liquid state is more ordered than gas state Ssolid < Sliquid << Sgas H2O (s) H2O (l) DS > 0

Predicting Relative S0 Values of a System

1. Temperature changes The increase in entropy from solid to liquid to gas. S0 increases as the temperature rises.

2. Physical states and phase changes The entropy change accompanying the dissolution of a salt. pure solid solution MIX pure liquid S0 increases as a more ordered phase changes to a less ordered phase.

The small increase in entropy when ethanol dissolves in water. 3. Dissolution of a solid or liquid The small increase in entropy when ethanol dissolves in water. Ethanol Solution of ethanol and water Water S0 of a dissolved solid or liquid is usually greater than the S0 of the pure solute. However, the extent depends upon the nature of the solute and solvent.

4. Dissolution of a gas The large decrease in entropy when a gas dissolves in a liquid. O2 gas O2 gas in H2O A gas becomes more ordered when it dissolves in a liquid or solid.

5. Atomic size or molecular complexity Entropy and vibrational motion. N2O4 NO NO2 In similar substances, increases in mass relate directly to entropy. In allotropic substances, increases in complexity (e.g. bond flexibility) relate directly to entropy.

Processes that lead to an increase in entropy (DS > 0)

The Second and Third Laws of Thermodynamics System: the reaction Surroundings: everything else Both undergo changes in entropy during physical and chemical processes

Second Law of Thermodynamics Entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. Equilibrium process: caused to occur by adding or removing energy from a system that is at equilibrium

Second Law of Thermodynamics Mathematically speaking: Spontaneous process: Suniverse = Ssystem + Ssurroundings > 0 Equilibrium process: Suniverse = Ssystem + Ssurroundings = 0

Entropy Changes in the System Entropy can be calculated from the table of standard values just as enthalpy change was calculated. Srxn = nS products  mS reactants

Entropy Changes in the Surroundings Change in entropy of surroundings is directly proportional to the enthalpy of the system. Ssurroundings   Hsystem Notice: exothermic process corresponds to positive entropy change in surroundings

Entropy Changes in the Surroundings Change in entropy of surroundings is inversely proportional to temperature Ssurroundings  1 / T Combining the two expressions:

Entropy Changes If the entropy change for a system is known to be 187.5 J/Kmol and the enthalpy change for a system is known to be 35.8 kJ/mol, is the reaction spontaneous? Spontaneous if: Suniv= Ssys + Ssurr > 0

Entropy Changes Is the reaction spontaneous? Suniv= 187.5 + 120.0 < 0 so the reaction is non-spontaneous

Third Law of Thermodynamics Entropy of a perfect crystalline substance is zero at absolute zero. Importance of this law: it allows us to calculate absolute entropies for substances

Gibbs Free Energy G = H – T S The Gibbs free energy, expressed in terms of enthalpy and entropy, refers only to the system, yet can be used to predict spontaneity.

Gibbs Free Energy If G < 0,negative, the forward reaction is spontaneous. If G = 0, the reaction is at equilibrium. If G > 0, positive, the forward reaction is nonspontaneous

Predicting Sign of G

Predicting Temperature from Gibbs Equation Set G = 0 (equilibrium condition) 0 = H – T S Rearrange equation to solve for T- watch for units! This equation will also be useful to calculate temperature of a phase change.

Gibbs Free Energy (G) G, the change in the free energy of a system, is a measure of the spontaneity of the process and of the useful energy available from it. DG0system = DH0system - TDS0system G < 0 for a spontaneous process G > 0 for a nonspontaneous process G = 0 for a process at equilibrium DrG0 = S mDG0products - S nDG0reactants

DG0 of any element in its stable form is zero. The standard free-energy of reaction (DrxnG0 ) is the free-energy change for a reaction when it occurs under standard-state conditions. aA + bB cC + dD D G0 rxn dD G0 (D) f cD G0 (C) = [ + ] - bD G0 (B) aD G0 (A) D G0 nD G0 (products) S mD G0 (reactants) Standard free energy of formation (D G0) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states. f m DG0 of any element in its stable form is zero. f m

2C6H6 (l) + 15O2 (g) 12CO2 (g) + 6H2O (l) What is the standard free-energy change for the following reaction at 25 0C? 2C6H6 (l) + 15O2 (g) 12CO2 (g) + 6H2O (l) DG0 rxn nDG0 (products) f = S mDG0 (reactants) - DG0 rxn 6DG0 (H2O) f 12DG0 (CO2) = [ + ] - 2DG0 (C6H6) DG0 rxn = [ 12x–394.4 + 6x–237.2 ] – [ 2x124.5 ] = -6405 kJ Is the reaction spontaneous at 25 0C? DG0 = -6405 kJ < 0 spontaneous

Sample Problem 2.5: Determining the Effect of Temperature on DG0 PROBLEM: An important reaction in the production of sulfuric acid is the oxidation of SO2(g) to SO3(g): 2SO2(g) + O2(g) 2SO3(g) At 298K, DG0 = -141.6kJ; DH0 = -198.4kJ; and DS0 = -187.9J/K (a) Use the data to decide if this reaction is spontaneous at 250C, and predict how DG0 will change with increasing T. (b) Assuming DH0 and DS0 are constant with increasing T, is the reaction spontaneous at 900.0C? PLAN: The sign of DG0 tells us whether the reaction is spontaneous and the signs of DH0 and DS0 will be indicative of the T effect. Use the Gibbs free energy equation for part (b). SOLUTION: (a) The reaction is spontaneous at 250C because DG0 is (-). Since DH0 is (-) but DS0 is also (-), DG0 will become less spontaneous as the temperature increases.

Sample Problem 2.5: Determining the Effect of Temperature on DG0 continued (b) DG0rxn = DH0rxn - T DS0rxn DG0rxn = -198.4kJ - (1173K)(-187.9J/mol*K)(kJ/103J) DG0rxn = 22.0 kJ; the reaction will be nonspontaneous at 900.0C

DG and the Work a System Can Do For a spontaneous process, DG is the maximum work obtainable from the system as the process takes place: DG = workmax For a nonspontaneous process, DG is the minimum work that must be done to the system as the process takes place: DG = workmax An example

Reaction Spontaneity and the Signs of DH0, DS0, and DG0 -TDS0 DG0 Description - + Spontaneous at all T + - Nonspontaneous at all T + - + or - Spontaneous at higher T; nonspontaneous at lower T - + + or - Spontaneous at lower T; nonspontaneous at higher T