Spontaniety Spontaneous reactions are reactions, that once started, continues by itself without further input of energy from the outside. If a reaction is spontaneous under a given set of conditions, then the reverse reaction is considered non-spontaneous.

Identifying Spontaneity Identify whether the reactions below are spontaneous or not: H2O (s)  H2O (l) 2H2 (g) + O2 (g)  2H2O (l) *requires a spark to begin 2H2O (l)  2H2 (g) + O2 (g) *requires consistent electric current

Enthaply and Spontaneity: Almost all exothermic reactions are considered to be spontaneous (at 25 *C and 1 atm). ΔH for a spontaneous reactions tends to be negative. However, some endothermic reactions at specific temperatures may be considered spontaneous, for example the melting of ice at 1 atm above 0 *C: H2O (s)  H2O (l) ΔH = 6.0 kJ Endothermic reactions that are non-spontaneous at room temperature often become spontaneous when the temperature is raised. The Randomness Factor: In general, nature tends to move spontaneously from more ordered to more random states (order to disorder).

Entropy The randomness factor discussed is treated quantitatively as entropy (S). Basically the greater the disorder (more random the distribution of molecules) the greater the entropy. -Entropy, like enthalpy is a state property so that ΔS = Sfinal - Sinitial unit for S = J/mol K

Factors that influence entropy that a system has in a particular state: A liquid has higher entropy than the solid from which it is formed. A gas has a higher entropy than the liquid from which it is formed. Increasing the temperature of a substance increases its entropy. A completely ordered pure crystalline solid has an entropy of 0 K (3rd law of thermodynamics).

Standard molar entropies of elements, compounds, and aqueous ions: Elements have nonzero standard entropies. Standard molar entropies of pure substances are always positive quantities. Aqueous ions may have negative entropy values. As a group, gases tend to have higher entropies than liquids. An increase in the number of moles of a gas also leads to a higher entropy and vice versa. As a molecule becomes more complex, the higher the entropy (more ways for the atoms to move about with respect to one another).

Example 17.1 Predict whether ΔS is positive or negative for each of the following processes: Taking dry ice from a freezer where its temperature is -80°C and allowing it to warm to room temperature Dissolving bromine in hexane Condensing gaseous bromine to liquid bromine

Which of the following reactions results in the largest increase in entropy? (A) CO2(s) CO2(g) (B) H2(g) + Cl2(g)  2HCl(g) (C) KNO3(s)  KNO3(l) (D) C(diamond)  C(graphite)

Calculating Entropy To calculate the standard entropy change, ΔS, use the following relation: ΔS = ∑ ΔS products - ∑ ΔS reactants The 2nd Law of Thermodynamics: In a spontaneous process, there is a net increase in entropy, taking into account both the system and surroundings, ΔS > 0

Example Calculate the entropy change at 25ºC in J/K for 2SO2(g) + O2(g)  2SO3(g) given the following data: SO2(g): 248.1 J/mol-K O2(g): 205.3 J/mol-K SO3(g): 256.6 J/mol-K [2(256.6)] - [2(248.1) + 1(205.3)] = -188.3 J/K

Example 17.2 Calculate ΔS for (1) dissolving one mole of calcium hydroxide in water (2) the combustion of one mole of methane, CH4, to form carbon dioxide and liquid water

Gibbs Free Energy (G) ΔG = ΔH - TΔS Gibbs free energy is a quantity that basically allows us to put the two quantities, enthalpy and entropy, together in such a way as to arrive at a single function whose sign will determine whether the reaction is spontaneous. The basic definition of Gibbs free energy is: ΔG = ΔH - TΔS (The Gibbs-Helmholtz Equation)  G = Gibbs Free Energy (J) H = Enthalpy (J/mol) T = Temperature (K) S = Entropy (J/mol K -- please be aware that the mole in the unit tends to cancel out from the ΔS equation)

Understanding ΔG The Gibb’s free energy equation combines all the information that we have learned thus far. But what does the Gibb’s free energy value tell us about a reaction? It tells us the following: If ΔG is negative, the reaction is spontaneous in the forward direction. If ΔG is equal to zero, the reaction is at equilibrium. If ΔG is positive, then the reaction is nonspontaneous in the forward direction, but the reverse reaction will be spontaneous. For elements at standard state (pure elements at 25ºC and 1 atm are assigned a value of zero).

Example 17.3 For the reaction CaSO4 (s)  Ca2+ (aq) + SO42- (aq) calculate: ΔH° ΔS° ΔG° at 25°C

Gibbs Free Energy of Formation The standard free energy of formation, ΔGf, can also be used to solve for the free energy of a reaction (reference Appendix 1 in text): ΔGf rxn = ∑ ΔGf products - ∑ ΔGf reactants If it is a negative quantity then the compound can be formed spontaneously from the elements, like in the formation of water: H2 (g) + ½ O2 (g)  H2O (l) ΔGf = -237.2 kJ Elements in their elemental state will have a ΔGf = 0

Example 17.4 Using ΔG°f values from Appendix 1, calculate the standard free energy change at 25°C for the reaction CaSO4 (s)  Ca2+ (aq) + SO42- (aq) Using ΔG°f values from Appendix 1, calculate the standard free energy change at 25°C for the dissolution of 1 mole of calcium chloride.

ΔG = ?? ΔG = negative ΔG = positive spontaneous at high temperatures at all temperatures at low temperatures ΔG = positive non-spontaneous Δ S – Δ H – Δ S + Δ H + K=1

Fe2O3 (s) + 3H2 (g)  2Fe (s) + 3H2O (g) Example 17.6 At what temperature does ΔG° become zero for the reaction Fe2O3 (s) + 3H2 (g)  2Fe (s) + 3H2O (g)