In previous chapters we have studied: Why does a change occur in the first place? Methane burns but not the reverse CH 4 + 2O 2 CO 2 + 2H 2 O

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1 Chapter 19. Spontaneous Change: Entropy and Free Energy In previous chapters we have studied: How fast does the change occur How is rate affected by concentration and temperature How much product will be present Why does a change occur in the first place? Chemical Thermodynamics What are the Driving Forces? Methane burns but not the reverse CH 4 + 2O 2 CO 2 + 2H 2 O Steel chain rusts, but a rusty one will not become shiny A cube of sugar dissolves in a cup of coffee after a few seconds of stirring, but not the reverse How can we tell if a reaction will proceed or not? Some chemical and physical changes take place by themselves, given enough time. A spontaneous chemical reaction is one that, given sufficient time, will achieve chemical equilibrium, with an equilibrium constant greater than 1, by reacting from left to right. 1

2 Cu(s) + Cl 2 (g) CuCl 2 (s) spontaneous 2H 2 (g) + O 2 (g) 2H 2 O(g) spontaneous reaction but occurs only if you ignite the mixture O 3 (g) O(g) + O 2 (g) nonspontaneous This does not mean that it does not occur at all. It means that, when equilibrium is achieved, not many O 3 molecules have broken down into products. That is [O][O2] K = = < 1 [O ] 3 at 25 C Chemical Thermodynamics Spontaneity Thermodynamics lets us predict whether a process will occur given enough time. Spontaneous process: occurs by itself without ongoing input of energy from outside system Freezing of water at 1 atm and 5 C Burning or falling may need a little push to get started, but will continue without external aid Nonspontaneous process: does not occur unless we make it happen; system must be supplied with continuous input of energy A book rises only if something else supplies energy Spontaneous does not mean instantaneous and has nothing to do with the rate. Given enough time it will occur by itself Chemical reaction proceeding toward equilibrium is an example of a spontaneous change. If a change is spontaneous in one direction, it is not spontaneous in the other. 2

3 Mechanical Systems System and Surroundings Some spontaneous processes occur with loss of energy. System portion of the universe we wish to study. Surroundings everything else. Universe = System + Surroundings change in the direction which lowers their energy position of equilibrium is when the energy available is minimized (energy has different forms: thermal, potential, kinetic) Example: In the chemistry lab, system is usually a flask, beaker, etc and the surrounds are the rest of the laboratory. Chemical Systems Exothermic The enthalpy (H) is a measure of the total energy of a system (that part of the universe we are considering the rest is called the surroundings ). Can we use the enthalpy to predict the direction of chemical change? Some scientists though that the sign of ΔH determined spontaneity. Physical: CaCl 2 (s) Ca 2+ (aq) + 2Cl - (aq) Chemical: 8Al(s) + 3Fe 3 O 4 (s) 4Al 2 O 3 (s) + 9Fe(l) H reactants products The enthalpy (energy) of the chemical system is lowered. 3

4 Endothermic Enthalpy Physical: H 2 O(s) H 2 O(l) H 2 O(g) NH 4 Cl(s) NH 4+ (aq) + Cl - (aq) Chemical: Ba(OH) 2 8H 2 O(s) + 2NH 4 NO 3 (s) Ba(NO 3 ) 2 (aq) + 2NH 3 (g) + 10H 2 O(l) H reactants products Some spontaneous chemical reactions are endothermic (enthalpy increases). ΔH cannot be used to predict if a reaction or process will go. The reason is that it represents the total energy of the system. We need to examine the available energy (the energy available to do useful work). The unavailable energy per degree kelvin is known as the entropy (S) of a system. Identifying Spontaneous Processes Direction of Chemical Change Predict whether the following are spontaneous? 1.When a piece of metal heated to 150 C is added to water at 40 C, water gets hotter. 2.Water at room temperature decomposes into H 2 (g) and O 2 (g). 3.Reaction of sodium metal and chlorine gas to form sodium chloride. 4.Reaction of nitrogen atoms to form N 2 molecules at 25 C and 1 atm. G = H TS G available energy, Gibbs energy H total energy, enthalpy S unavailable energy per Kelvin, entropy T temperature How can we tell the direction of a spontaneous change when it is not as obvious? The direction of chemical change is the direction which lowers the Gibbs energy. 4

5 Criterion for Spontaneity For ΔG to be negative: ΔG = ΔH TΔS A process is spontaneous in the direction in which the Gibbs energy decreases: i.e. ΔG is negative. At constant temperature, ΔG < 0 for a spontaneous process ΔG > 0 for a nonspontaneous process ΔG = 0 for a process at equilibrium ΔH negative negative positive ΔS positive negative but ΔH more negative than (-TΔS) (lower T) positive but (-TΔS) more negative than ΔH (higher T) Spontaneity Spontaneity melting of ice endothermic highly organised structure becomes less wellordered octane combustion 2C 8 H 18 (g) + 25O 2 (g) 16CO 2 (g) + 18H 2 O(g) exothermic 27 molecules in the gas phase are converted to 34 molecules Clearly two factors should be considered when trying to predict spontaneity: a decrease in energy or enthalpy an increase in disorder or entropy Sometimes these effects reinforce one another, but at other times they oppose one another. The final outcome is determined by their relative magnitudes. 5

6 Spontaneous Process Disorder and Entropy Matter changes from a more ordered to a less ordered state. A change in order is a change in the number of ways of arranging the particles, and is a key factor in determining the direction of a spontaneous process. There is a natural tendency for a system to become disordered For parts of a system to have more ways of being arranged. Creating order requires work Disorder increases when a process results in more ways for the atoms, ions, or molecules in the system to be arranged. The number of ways to arrange a deck of playing cards Entropy The driving force for a spontaneous process is an increase in the entropy of the universe. Entropy, S, can be viewed as a measure of randomness, or disorder. Number of microstates of system is number of ways it can disperse its thermal energy among various modes of motion of all its particles units of J K -1 mol -1 6

7 Third Law of Thermodynamics Absolute Entropies A perfect crystal has zero entropy at a temperature of absolute zero S sys = 0 at 0 K Perfect means that all the particles are aligned flawlessly in the crystal structure with no defects of any kind. At absolute zero, all particles in the crystal have their minimum energy, and there is only one way they can be arranged. Because S is explicitly known (= 0) at 0 K, S values at other temperatures can be calculated. Elements in their standard states have an entropy greater than zero, i.e. S > 0. The entropy of any pure substance can be measured at a given temperature. The absolute entropy of one mole of a substance in its standard state is called the standard molar entropy, S. Standard Molar Entropies S solid < S liquid << S gas Standard molar entropy (S ): J K -1 mol -1 (Appendix D) Predicting relative values of S Affected by temperature, physical state, dissolution, and atomic or molecular complexity. 1. Temperature changes: S increases as temp rises 2. Physical states and phase changes: -when a more ordered phase changes to a less ordered one, ΔS +ve -S increases as the substance changes from a solid to a liquid to a gas: S solid < S liquid << S gas 7

8 Standard Molar Entropies Entropy and vibrational motion 3. Dissolution of a solid or liquid: the entropy of a dissolved solid or liquid solute is greater than the entropy of the pure solute -Type of solute and solvent affect overall entropy change. 4. Dissolution of a gas: a gas is so disordered to begin with that it becomes more ordered when it dissolves in a liquid -Entropy of a solution of a gas in a liquid is always less than entropy of pure gas. NO NO 2 N 2 O 4 5. Atomic size or molecular complexity: S (KCl) < S (CaCl 2 ) < S (GaCl 3 ) Examples Entropy changes for reversible phase transitions 1. Choose the member with the higher entropy: (a) 1 mol of SO 2(g) or 1 mol of SO 3(g) (b) 1 mol of CO 2(s) or 1 mol of CO 2(g) (c) 1 mol of KBr (s) or 1 mol of KBr (aq) (d) Seawater in midwinter (2 C) or midsummer (23 C) 2. Predict whether ΔS is positive or negative for the following: (a) H 2 O(l) H 2 O(g) (b) Ag + (aq) + Cl - (aq) AgCl(s) (c) 4Fe(s) + 3O 2 (g) 2Fe 2 O 3 (s) (d) N 2 (g) + O 2 (g) 2NO(g) ΔS = = heat transferred temp at which change occurs q T 8

9 Melting of ice at normal boiling point Calculating the Change in Entropy of a Rxn H 2 O(s, 1 atm) H 2 O(l, 1 atm) o q ΔS = T ΔH = T fusion mp kj mol = K 1 = 22.0 J K mol What is ΔS when one mole of water freezes? 1 Chemists are especially interested in learning to predict and calculate change in entropy as a reaction occurs. Calculations are similar for enthalpy changes: calculated from enthalpies of formation of reactants & products. ΔH rxn = Σn p ΔH f (products) Σn r ΔH f (reactants) calculated from standard molar entropies of reactants & products. ΔS rxn = Σn p S (products) Σn r S (reactants) Example Example Calculate ΔS for the reaction SiCl 4 (g) + 2Mg(s) 2MgCl 2 (s) + Si(s) Substance: SiCl 4 (g) Mg(s) MgCl 2 (s) Si(s) S /J K -1 mol -1 : A J K -1 B J K -1 C J K -1 D J K -1 E J K -1 Calculate ΔS for the reaction 2Cl 2 (g) + SO 2 (g) SOCl 2 (g) + Cl 2 O(g) Substance: Cl 2 (g) SO 2 (g) SOCl 2 (g) Cl 2 O(g) S /J K -1 mol -1 : A J K -1 B J K -1 C J K -1 D J K -1 E J K -1 9

10 Gibbs Energy Example If a process is nonspontaneous in one direction (ΔG > 0), it is spontaneous in the opposite direction (ΔG < 0) Standard Gibbs Energy Change (ΔG o ) ΔG o = ΔH o TΔS o Used frequently to find any one of these variables when given other two Calculate ΔG rxn at 25 C for the decomposition of potassium chlorate, one of the common oxidizing agents in explosives, fireworks, and match heads. 4KClO 3(s) 3KClO 4(s) + KCl (s) ΔH o f KClO kj mol J K -1 mol -1 KClO kj mol J K -1 mol -1 KCl kj mol J K -1 mol -1 S o Example Calculating Change in Entropy/Enthalpy of Rxn ΔH rxn = Σn p ΔH f (products) Σn r ΔH f (reactants) Determine the standard Gibbs energy change at 298 K for the reaction: 2NO (g) + O 2(g) 2NO 2(g) ΔS rxn = Σn p S (products) Σn r S (reactants) Can also calculate ΔG o rxn using standard Gibbs energy of formation (ΔG o f ) ΔG = standard Gibbs energy change that occurs if reactants in their standard state are converted to products in their standard state. ΔG rxn = Σn p ΔG f (products) Σn r ΔG f (reactants) Use ΔG f values to calculate ΔG rxn for previous examples. 10

11 Gibbs energy of formation ΔG o f: Gibbs energy change that accompanies the formation of exactly 1 mole of the pure substance from free elements in their most stable states under standard state conditions. C(s) + O 2 (g) CO 2 (g) ΔG o f = kj mol -1 All elements in their standard states have ΔG o f =0. Gibbs Energy and Equilibrium ΔG = RT ln K Allows us to calculate standard Gibbs energy change of reaction (ΔG ) from its equilibrium constant, or vice versa. As ΔG becomes more positive, K becomes smaller reaction reaches equilibrium with less product and more reactant As ΔG becomes more negative, K becomes larger reaction reaches equilibrium with more product and less reactant K > 1 (lnk > 0) ΔG rxn < 0 K < 1 (lnk < 0) ΔG rxn > 0 K = 1 (lnk = 0) ΔG rxn = 0 A B The Relationship Between ΔG and K at 25 C ΔG 0 (kj) K Significance x x x10-9 2x10-2 7x x10 1 6x10 8 3x x10 35 Essentially no forward reaction; reverse reaction goes to completion Forward and reverse reactions proceed to same extent FORWARD REACTION Forward reaction goes to completion; essentially no reverse reaction REVERSE REACTION 11

12 Examples Example 1. Determine the value of the equilibrium constant at K for the reaction C 2 H 6 (g) H 2 (g) + C 2 H 4 (g) ΔG 298 = kj 2. Determine the value of K at 100 C for I 2 (g) + Cl 2 (g) 2ICl(g) Calculate ΔG (kj mol -1 ) for following process: AgCl(s) Ag + (aq) + Cl - (aq) K sp = 1.6 x at 25 C For this rxn, ΔH 298 = kj & ΔS 298 = 11.3 J K -1 (Assume that ΔH 298 and ΔS 298 do not vary with T.) Gibbs Energy and Cell Potential ΔG rxn = nfe cell 12

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