Spontaneity

·        Changes for which the products are more stable than the reactants are said to be product favored or spontaneous.

·        Changes for which the products are less stable than the reactants are said to be reactant favored or non-spontaneous.

·        Spontaneity can vary based on reaction conditions (T, P, etc.)

·        Spontaneity is favored when:

1.      Heat is released during the change (exothermic)

2.      The change results in an increase in disorder (entropy increases)

·        Second Law of Thermodynamics: in spontaneous changes, the universe tends toward a state of greater disorder.

 

Entropy

·        Entropy is a thermodynamic state function which measures the degree of disorder of the system

·        Solids are more ordered than liquids; liquids are more ordered than gases

·        Mixing together two substances increases the entropy of each.

·        DS universe  = DS system + DS surroundings

·        During a process the entropy of the system can increase or decrease, but the entropy of the universe must increase. (If entropy of system decreases, entropy of surroundings increases.)

·        Third Law of Thermodynamics: the entropy of a pure, perfect crystalline substance is zero at absolute zero (0 K)

·        Absolute entropy values (shown in Appendix 4) take into consideration the temperature of the system (units = J/mol·K); T= 298 K.

·        As temperature increases, so does the disorder of the system

·        Hess’s Law can be used to calculate entropy changes

DS°rxn = å n S° (products) - å n S° (reactants)

·        Calculate DS°rxn for the following reaction.

2 NO (g) + H2 (g) à N2O (g) + H2O (g)

 

Predictions for the sign of DS sys can be made:

1.      Phase changes: melting, vaporization, and sublimation all have DS sys > 0.  Reverse processes have DS sys < 0.

2.      T change: increases in T have DS sys > 0; decrease in T have DS sys < 0.

3.      V change: increases in V have DS sys > 0; decrease in V have DS sys < 0.

4.      Mixing of substances: substance which become more mixed have DS sys > 0; decreases in mixing lead to DS sys < 0. Dissolving is an example of mixing.

5.      Increase in number of particles: increases have DS sys > 0; decreases have DS sys < 0.

6.      Changes in number of moles of gaseous substances: increases have DS sys > 0; decreases have DS sys < 0. 

(ex. 2 H2 (g) + O2 (g) à 2 H2O (g))

 

Free Energy Change (DG)

The relationship between enthalpy and entropy was described by J. Willard Gibbs in terms of a new state function referred to as Gibbs Free Energy (G).   G = H – TS

·        At constant T and P,       DG = DH – TDS

·        A decrease in Gibbs free energy relates to the release of energy

·        The amount of a decrease corresponds to the maximum amount of energy available to do work.

·        The value of DG also indicates degree of spontaneity for a reaction.

DG > 0 … rxn is non-spontaneous (reverse would be spontaneous)

DG = 0 … system is at equilibrium

DG < 0 … rxn is spontaneous (reverse would be non-spontaneous)

 

·        DG becomes more negative as DH becomes more negative (rxn gives off heat) and as DS becomes more positive (disorder increases)

·        Standard states for temperature and pressure for DG are 1 atm and 25° C.

·        Standard molar free energy of formation DG°f – the amount of free energy released when compounds are formed from their elements.  Values are given in Appendix 4.

·        These values can be used to determine free energy changes for reactions at 1 atm & 298 K:

DG°rxn = å n DG°f (products) - å n DG°f (reactants)

·        This allows us to predict whether reactants or products are more stable under standard conditions (for the “standard reaction”).

·        DG will vary with conc., T,  and P. DG° does not because these conditions cannot vary.

·        In the standard reaction, all reactants are assumed to be completely converted to products; in actual reactions an equilibrium is more likely to occur.

·        DG° can be estimated by the following equation: DG° = DH° - TDS°

·        This is an estimate because actual values for DH° and DS° will vary somewhat with temperature

 

Calculate the standard free energy change for the following reaction at 25°C and 1 atm.

3 NO2 (g) + H2O (l) à 2 HNO3 (l) + NO (g)

 

 

 

 

 

 

 

Use standard enthalpy of formation and absolute entropy values to estimate DG°

 

 

 

This method can be used to help estimate the temperature at which a process is at equilibrium.

·        At equilibrium conditions, DG = 0

·        When DG = 0 the equation DG = DH - TDS can be rearranged to produce:

T = DH/DS

 

Estimate the normal condensation point of water at 1 atm.

H2O (g) à H2O (l)

DH =

DS =

T =

 

 

 

Reactions can be grouped into four classes

1.      DH < 0 and DS > 0 … both favorable so rxn is spontaneous.

2.      DH < 0 and DS < 0 … rxn is spontaneous below a certain T.  (DG = DH – TDS)

3.      DH > 0 and DS > 0 … rxn is spontaneous above a certain T.  (DG = DH – TDS)

4.      DH > 0 and DS < 0 … neither favorable so rxn is non-spontaneous.