Atkins & de Paula: Elements of Physical Chemistry: 5e Chapter 7: Chemical Equilibrium: The Principles Chapter 7: Chemical Equilibrium: The Principles

End of chapter 7 assignments Discussion questions: 2 Exercises: 1, 2, 3, 4, 5, 6, 7, 10, 11, 15, 18 Use Excel if data needs to be graphed Discussion questions: 2 Exercises: 1, 2, 3, 4, 5, 6, 7, 10, 11, 15, 18 Use Excel if data needs to be graphed

Homework Assignment How many of you have already read all of chapter 7 in the textbook? In the future, read the entire chapter in the textbook before we begin discussing it in class How many of you have already read all of chapter 7 in the textbook? In the future, read the entire chapter in the textbook before we begin discussing it in class

Homework Assignment Connect to the publisher’s website and access all “Living Graphs” Change the parameters and observe the effects on the graph Sarah: these “Living Graphs” are not really living; this is just a hokey name! Connect to the publisher’s website and access all “Living Graphs” Change the parameters and observe the effects on the graph Sarah: these “Living Graphs” are not really living; this is just a hokey name!

Homework Assignments Read Chapter 7. Work through all of the “Illustration” boxes and the “Example” boxes and the “Self-test” boxes in Chapter 7. Work the assigned end-of-chapter exercises by the due date Read Chapter 7. Work through all of the “Illustration” boxes and the “Example” boxes and the “Self-test” boxes in Chapter 7. Work the assigned end-of-chapter exercises by the due date

Principles of chemical equilibrium Central Concepts: Thermodynamics can predict whether a rxn has a tendency to form products, but it says nothing about the rate At constant T and P, a rxn mixture tends to adjust its composition until its Gibbs energy is at a minimum Central Concepts: Thermodynamics can predict whether a rxn has a tendency to form products, but it says nothing about the rate At constant T and P, a rxn mixture tends to adjust its composition until its Gibbs energy is at a minimum

Gibbs Energy vs Progress of Rxn Fig 7.1 (158) (a) does not go (b) equilibrium with amount of reactants ~amount of products (c) goes to completion Fig 7.1 (158) (a) does not go (b) equilibrium with amount of reactants ~amount of products (c) goes to completion

Example Rxns G6P(aq)  F6P(aq) N 2 (g) + 3 H 2 (g)  2 NH 3 (g) Reactions are of this form: aA + bB  cC + dD If  n is small enough, then,  G = (  F6P x  n) – (  G6P x  n) --now divide by  n  r G =  G/  n =  F6P –  G6P G6P(aq)  F6P(aq) N 2 (g) + 3 H 2 (g)  2 NH 3 (g) Reactions are of this form: aA + bB  cC + dD If  n is small enough, then,  G = (  F6P x  n) – (  G6P x  n) --now divide by  n  r G =  G/  n =  F6P –  G6P

The Rxn Gibbs Energy  r G =  G/  n =  F6P –  G6P  r G is the difference of the chemical potentials of the products and reactants at the composition of the rxn mixture We recognize that  r G is the slope of the graph of the (changing) G vs composition of the system (Fig 7.1, p154)  r G =  G/  n =  F6P –  G6P  r G is the difference of the chemical potentials of the products and reactants at the composition of the rxn mixture We recognize that  r G is the slope of the graph of the (changing) G vs composition of the system (Fig 7.1, p154)

Effect of composition on  r G Fig 7.2 (154) The relationship of G to composition of the reactions  r G changes as  n (the composition) changes Fig 7.2 (154) The relationship of G to composition of the reactions  r G changes as  n (the composition) changes

Reaction Gibbs energy Consider this reaction: aA + bB  cC + dD  r G = (c  C + d  D ) – (a  A + b  B ) μ J tμ J + RT ln a J (derived in sec 6.6) Chemical potential (μ) changes as [J] changes The criterion for chemical equilibrium at constant T,P is:  r G = 0 (7.2) Consider this reaction: aA + bB  cC + dD  r G = (c  C + d  D ) – (a  A + b  B ) μ J tμ J + RT ln a J (derived in sec 6.6) Chemical potential (μ) changes as [J] changes The criterion for chemical equilibrium at constant T,P is:  r G = 0 (7.2) 

Meaning of the value of  r G Fig 7.3 (155) When is  r G<0? When is  r G=0? When is  r G>0? What is the signifi- cance of each? Fig 7.3 (155) When is  r G<0? When is  r G=0? When is  r G>0? What is the signifi- cance of each?

Variation of  r G with composition For solutes in an ideal solution: a J = [J]/c , the molar concentration of J relative to the standard value c  = 1 mol/dm 3 For perfect gases: a J = p J /p , the partial pressure of J relative to the standard pressure p  = 1 bar For pure solids and liquids, a J = 1 For solutes in an ideal solution: a J = [J]/c , the molar concentration of J relative to the standard value c  = 1 mol/dm 3 For perfect gases: a J = p J /p , the partial pressure of J relative to the standard pressure p  = 1 bar For pure solids and liquids, a J = 1 p155f

Variation of  r G with composition  r G = (c  C + d  D ) – (a  A + b  B ) (7.1c)  r G  = (c  C + d  D ) – (a  A + b  B ) (7.4a)  r G  = {cG m (C)+dG m (D)} – {(aG m (A)+bG m (B)} (7.4b) 7.4a and 7.4b are the same Is there an error in 7.1c in the textbook?  r G = (c  C + d  D ) – (a  A + b  B ) (7.1c)  r G  = (c  C + d  D ) – (a  A + b  B ) (7.4a)  r G  = {cG m (C)+dG m (D)} – {(aG m (A)+bG m (B)} (7.4b) 7.4a and 7.4b are the same Is there an error in 7.1c in the textbook?  

Variation of  r G with composition  r G =  r G  + RT ln a A a B a b a C a D cd Q = a A a B a b a C a D cd ()  r G =  r G  + RT ln Q Since Then

Reactions at equilibrium Again, consider this reaction: aA + bB  cC + dD Q, arbitrary position; K, equilibrium 0 =  r G  + RT ln K and  r G  = –RT ln K Again, consider this reaction: aA + bB  cC + dD Q, arbitrary position; K, equilibrium 0 =  r G  + RT ln K and  r G  = –RT ln K Q = a A a B a b a C a D cd K = a A a B a b a C a D cd equilibrium ( )

Equilibrium constant With these equations….  0 =  r G  + RT ln K  r G  = –RT ln K (7.8) We can use values of  r G  from a data table to predict the equilibrium constant We can measure K of a reaction and calculate  r G  With these equations….  0 =  r G  + RT ln K  r G  = –RT ln K (7.8) We can use values of  r G  from a data table to predict the equilibrium constant We can measure K of a reaction and calculate  r G 

Relationship between  r G  and K Fig 7.4 (157) Remember,  r G  = –RT ln K So, ln K = – (  r G  /RT) If  r G  1; & products predominate at equilibrium And the rxn is thermo- dynamically feasible Fig 7.4 (157) Remember,  r G  = –RT ln K So, ln K = – (  r G  /RT) If  r G  1; & products predominate at equilibrium And the rxn is thermo- dynamically feasible At K > 1,  r G  < 0 At K = 1,  r G  = 0 At K 0

Relationship between  r G  and K On the other hand… If  r G  >0, then K<1 and the reactants predominate at equilibrium… And the reaction is not thermo- dynamically feasible HOWEVER…. Products will predominate over reactants significantly if K  1 (>10 3 ) But even with a K<1 you may have products formed in some rxns On the other hand… If  r G  >0, then K<1 and the reactants predominate at equilibrium… And the reaction is not thermo- dynamically feasible HOWEVER…. Products will predominate over reactants significantly if K  1 (>10 3 ) But even with a K<1 you may have products formed in some rxns

Relationship between  r G  and K For an endothermic rxn to have  r G  0; furthermore, Its temperature must be high enough for its T  r S  to be greater than  r H  The switch from  r G  >0 to  r G  1 This switch takes place at a temperature at which  r H  - T  r S  = 0, OR…. For an endothermic rxn to have  r G  0; furthermore, Its temperature must be high enough for its T  r S  to be greater than  r H  The switch from  r G  >0 to  r G  1 This switch takes place at a temperature at which  r H  - T  r S  = 0, OR…. T = rHrH rSrS

Table 7.1 Thermodynamic criteria of spontaneity  G =  H – T  S

Table 7.1 Thermodynamic criteria of spontaneity  G =  H – T  S 4. If  H is positive and  S is negative,  G will always be positive—regardless of the temperature. These two statements are an attempt to say the same thing.

 G =  H – T  S 1.If  H is negative and  S is positive, then  G will always be negative regardless of temperature. 2.If  H is negative and  S is negative, then  G will be negative only when T  S is smaller in magnitude than  H. This condition is met when T is small. 3.If both  H and  S are positive, then  G will be negative only when the T  S term is larger than  H. This occurs only when T is large. 4.If  H is positive and  S is negative,  G will always be positive—regardless of the temperature.

 G =  H – T  S Factors Affecting the Sign of  G

Gibbs Free Energy (G) For a constant-temperature process:  G =  H sys – T  S sys The change in Gibbs free energy (  G) 18.4 If  G is negative (  G<0), there is a release of usable energy, and the reaction is spontaneous! If  G is positive (  G>0), the reaction is not spontaneous! G = H – TS All quantities in the above equation refer to the system

For a constant-temperature process:  G =  H sys – T  S sys  G < 0 The reaction is spontaneous in the forward direction.  G > 0 The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction.  G = 0 The reaction is at equilibrium Gibbs Free Energy (G)

aA + bB cC + dD G0G0 rxn d  G 0 (D) f c  G 0 (C) f = [+] – b  G 0 (B) f a  G 0 (A) f [+] G0G0 rxn n  G 0 (products) f =  m  G 0 (reactants) f  – The standard free-energy of reaction (  G 0 ) is the free-energy change for a reaction when it occurs under standard-state conditions. rxn Gibbs Free Energy (G) 7.10 p158

Who will explain this graph to the class?

Relationship between  r G  and K For an endothermic rxn to have  r G  0; furthermore, Its temperature must be high enough for its T  r S  to be greater than  r H  The switch from  r G  >0 to  r G  1 This switch takes place at a temperature at which  r H  - T  r S  = 0, OR…. For an endothermic rxn to have  r G  0; furthermore, Its temperature must be high enough for its T  r S  to be greater than  r H  The switch from  r G  >0 to  r G  1 This switch takes place at a temperature at which  r H  - T  r S  = 0, OR…. T = rHrH rSrS

Reactions at equilibrium Fig 7.5 (162) An endothermic rxn with K>1 must have T high enough so that the result of subtract- ing T  r S  from  r H  is negative Or  r H  –T  r S  < 0 Set  r H  – T  r S  =0 and solve for T Fig 7.5 (162) An endothermic rxn with K>1 must have T high enough so that the result of subtract- ing T  r S  from  r H  is negative Or  r H  –T  r S  < 0 Set  r H  – T  r S  =0 and solve for T T = rHrH rSrS equilibrium  r G  =  r H  – T  r S 

Reactions at equilibrium equilibrium  r G  =  r H  – T  r S 

Table 7.2 Standard Gibbs energies of formation at K* (gases)

Table 7.2 Standard Gibbs energies of formation at K* (liquids & solids)

Standard Gibbs Energy of Formation Fig 7.6 (159) Analogous to altitude above or below sea level Units of kJ/mol Fig 7.6 (159) Analogous to altitude above or below sea level Units of kJ/mol

The equilibrium composition The magnitude of K is a qualitative indicator If K  1 (>10 3 ) then  r G  < –17 25ºC, the rxn has a strong tendency to form products If K  1 ( ºC, the rxn will remain mostly unchanged reactants If K  1 (10 – ), then  r G  is between –17 to ºC, and the rxn will have significant concentrations of both reactants and products The magnitude of K is a qualitative indicator If K  1 (>10 3 ) then  r G  < –17 25ºC, the rxn has a strong tendency to form products If K  1 ( ºC, the rxn will remain mostly unchanged reactants If K  1 (10 – ), then  r G  is between –17 to ºC, and the rxn will have significant concentrations of both reactants and products p.160

Calculating an equilibrium concentration Example 7.1 (p165) Example 7.2 (p166) Example 7.1 (p165) Example 7.2 (p166)

Standard reaction Gibbs energy  r G =  G m (products) –  G m (reactants)  r G =  r H – T  r S  r G =  G m (products) –  G m (reactants)  r G =  r H – T  r S     

7.6 K c and K p aA + bB cC + dD K c = [C] c [D] d [A] a [B] b In most cases K c  K p aA (g) + bB (g) cC (g) + dD (g) K p = K c (RT)  n K p = pCpC d pDpD pApA pBpB a b c K p = K c (RT)  n When does K p = K c ?

Derivation 7.1: K c and K p Atkins uses Work through Derivation 7.1, p.162 K = K c  cRTcRT pp ][  v gas K = K c  T K ][  v gas Substituting values for c , p , and R, we get What is this K ? What is  v gas ?

Coupled reactions Box 7.1 (164) Weights as analogy to rxns A rxn with a large  r G can force another rxn with a smaller  r G to run in its nonspontan-eous direction Enzymes couple biochemical rxns Box 7.1 (164) Weights as analogy to rxns A rxn with a large  r G can force another rxn with a smaller  r G to run in its nonspontan-eous direction Enzymes couple biochemical rxns

Coupled reactions Biological standard state (pH = 7) Typical symbols for standard state: ¤ ´  ° Read the last paragraph in Box 7.1 on p164 regarding ATP and the “high energy” bond Biological standard state (pH = 7) Typical symbols for standard state: ¤ ´  ° Read the last paragraph in Box 7.1 on p164 regarding ATP and the “high energy” bond + ¤

Equilibrium response to conditions What effect will a change in temperature, in pressure, or the presence of a catalyst have on the equilibrium position? Presence of a catalyst? None. Why?  r G  is unchanged, so K is not changed How about a change in temperature? Or a change in pressure? Let’s see… What effect will a change in temperature, in pressure, or the presence of a catalyst have on the equilibrium position? Presence of a catalyst? None. Why?  r G  is unchanged, so K is not changed How about a change in temperature? Or a change in pressure? Let’s see…

The effect of temperature Fig 7.7 (163)  r G of a rxn that results in fewer moles of gas increases with increasing T  r G of a rxn with no net change…  r G of a rxn that produces more moles of gas decreases with increasing T Fig 7.7 (163)  r G of a rxn that results in fewer moles of gas increases with increasing T  r G of a rxn with no net change…  r G of a rxn that produces more moles of gas decreases with increasing T

Equilibrium response to conditions Le Chatelier’s principle suggests When a system at equilibrium is compressed, the composition of a gas-phase equilibrium adjusts so as to reduce the number of molecules in the gas phase p.172

The effect of pressure Fig 7.9 (174) A change in pressure does not change the value of K, but it does have other consequences (composition) As p  0, x HI  1 What is [I 2 ]? Fig 7.9 (174) A change in pressure does not change the value of K, but it does have other consequences (composition) As p  0, x HI  1 What is [I 2 ]? H 2 (g) + I 2 (s)  2 HI(g)

Key Ideas

The End …of this chapter…”

Spare parts to copy and paste μ J tμ J +RT ln a J Chemical potential (μ) changes as [J] changes μ J tμ J +RT ln a J Chemical potential (μ) changes as [J] changes 

Box 7.1 pp.172f O 2 binding in hemoglobin and myoglobin… …In resting tissue and in lung tissue O 2 binding in hemoglobin and myoglobin… …In resting tissue and in lung tissue

Chemical Potential Review pp , Partial molar properties (e.g. partial molar volume) Read p.129, last two paragraphs Read handout, “Chemical Potential” by Philip A. Candela Chemical potential (  ) is usually described as the “partial molar Gibbs function” or “partial molar Gibbs energy” Review pp , Partial molar properties (e.g. partial molar volume) Read p.129, last two paragraphs Read handout, “Chemical Potential” by Philip A. Candela Chemical potential (  ) is usually described as the “partial molar Gibbs function” or “partial molar Gibbs energy”

Chemical Potential The quantity G/n is so important that it is given a special symbol (  ) and its own name (chemical potential) As the symbols G/n above indicate, chemical potential is the Gibbs free energy per mole of substance The chemical potential is an indication of the potential of a substance to be chemically active (p.130) The quantity G/n is so important that it is given a special symbol (  ) and its own name (chemical potential) As the symbols G/n above indicate, chemical potential is the Gibbs free energy per mole of substance The chemical potential is an indication of the potential of a substance to be chemically active (p.130)

Excursus: Chemical Potential The standard chemical potential of a gas (μ J ), is identical to its standard molar Gibbs energy (G m ) at 1 bar The greater the partial pressure of a gas, the greater its chemical potential The standard chemical potential of a gas (μ J ), is identical to its standard molar Gibbs energy (G m ) at 1 bar The greater the partial pressure of a gas, the greater its chemical potential 

Excursus: Chemical Potential Common expressions of chemical potential: μ J tμ J + RT ln a J μ J tμ J + RT ln μ J tμ J + RT ln p Common expressions of chemical potential: μ J tμ J + RT ln a J μ J tμ J + RT ln μ J tμ J + RT ln p   p p    p = 1 bar