atkins & de paula: elements of physical chemistry: 5e chapter 7: chemical equilibrium: the...
Post on 31-Dec-2015
247 Views
Preview:
TRANSCRIPT
Atkins & de Paula: Elements of Physical Chemistry:
5e
Atkins & de Paula: Elements of Physical Chemistry:
5e
Chapter 7: Chemical Equilibrium: The
Principles
Chapter 7: Chemical Equilibrium: The
Principles
End of chapter 7 assignmentsEnd 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 AssignmentHomework 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 AssignmentHomework Assignment
• Connect to the publisher’s website and access all “Living Graphs”
• http://bcs.whfreeman.com/elements4e/
• 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”
• http://bcs.whfreeman.com/elements4e/
• 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 AssignmentsHomework 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
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
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 RxnsExample Rxns
• G6P(aq) F6P(aq)
• N2(g) + 3 H2(g) 2 NH3(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
rG = G/n = F6P – G6P
• G6P(aq) F6P(aq)
• N2(g) + 3 H2(g) 2 NH3(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
rG = G/n = F6P – G6P
The Rxn Gibbs EnergyThe Rxn Gibbs Energy
rG = G/n = F6P – G6P
rG is the difference of the chemical potentials of the products and reactants at the composition of the rxn mixture
• We recognize that rG is the slope of the graph of the (changing) G vs composition of the system (Fig 7.1, p154)
rG = G/n = F6P – G6P
rG is the difference of the chemical potentials of the products and reactants at the composition of the rxn mixture
• We recognize that rG is the slope of the graph of the (changing) G vs composition of the system (Fig 7.1, p154)
Effect of composition on rGEffect of composition on rG
• Fig 7.2 (154)• The relationship
of G to composition of the reactions
rG changes as n (the composition) changes
• Fig 7.2 (154)• The relationship
of G to composition of the reactions
rG changes as n (the composition) changes
Reaction Gibbs energyReaction Gibbs energy
• Consider this reaction:aA + bB cC + dD
rG = (cC + dD) – (aA + bB)
μJtμJ+ RT ln aJ (derived in sec 6.6)
• Chemical potential (μ) changes as [J] changes
• The criterion for chemical equilibrium at constant T,P is: rG = 0 (7.2)
• Consider this reaction:aA + bB cC + dD
rG = (cC + dD) – (aA + bB)
μJtμJ+ RT ln aJ (derived in sec 6.6)
• Chemical potential (μ) changes as [J] changes
• The criterion for chemical equilibrium at constant T,P is: rG = 0 (7.2)
Meaning of the value of rGMeaning of the value of rG
• Fig 7.3 (155)
• When is rG<0?
• When is rG=0?
• When is rG>0?
• What is the signifi-cance of each?
• Fig 7.3 (155)
• When is rG<0?
• When is rG=0?
• When is rG>0?
• What is the signifi-cance of each?
Variation of rG with composition
Variation of rG with composition
For solutes in an ideal solution:
• aJ = [J]/c, the molar concentration of J relative to the standard value c = 1 mol/dm3
For perfect gases:
• aJ = pJ/p, the partial pressure of J relative to the standard pressure p = 1 bar
For pure solids and liquids, aJ = 1
For solutes in an ideal solution:
• aJ = [J]/c, the molar concentration of J relative to the standard value c = 1 mol/dm3
For perfect gases:
• aJ = pJ/p, the partial pressure of J relative to the standard pressure p = 1 bar
For pure solids and liquids, aJ = 1
p155f
Variation of rG with composition
Variation of rG with composition
rG = (cC + dD) – (aA + bB) (7.1c)
rG = (cC + dD) – (aA + bB) (7.4a)
rG = {cGm(C)+dGm(D)} – {(aGm(A)+bGm(B)} (7.4b)
• 7.4a and 7.4b are the same
Is there an error in 7.1c in the textbook?
rG = (cC + dD) – (aA + bB) (7.1c)
rG = (cC + dD) – (aA + bB) (7.4a)
rG = {cGm(C)+dGm(D)} – {(aGm(A)+bGm(B)} (7.4b)
• 7.4a and 7.4b are the same
Is there an error in 7.1c in the textbook?
Variation of rG with composition
Variation of rG with composition
rG = rG + RT ln rG = rG + RT ln aA aB
a b
aC aDc d
Q = aA aB
a b
aC aDc d
( )
rG = rG + RT ln Q
Since
Then
Reactions at equilibriumReactions at equilibrium
• Again, consider this reaction:aA + bB cC + dD
• Q, arbitrary position; K, equilibrium• 0 = rG + RT ln K and rG = –RT ln K
• Again, consider this reaction:aA + bB cC + dD
• Q, arbitrary position; K, equilibrium• 0 = rG + RT ln K and rG = –RT ln K
Q = aA aB
a b
aC aDc d
K = aA aB
a b
aC aDc d
equilibrium( )
Equilibrium constantEquilibrium constant
• With these equations….0 = rG + RT ln K
rG = –RT ln K (7.8)
• We can use values of rG from a data table to predict the equilibrium constant
• We can measure K of a reaction and calculate rG
• With these equations….0 = rG + RT ln K
rG = –RT ln K (7.8)
• We can use values of rG from a data table to predict the equilibrium constant
• We can measure K of a reaction and calculate rG
Relationship between rG and KRelationship between rG and K
• Fig 7.4 (157)
• Remember, rG = –RT ln K
• So, ln K = –(rG/RT)
• If rG<0, then K>1; & products predominate at equilibrium
• And the rxn is thermo-dynamically feasible
• Fig 7.4 (157)
• Remember, rG = –RT ln K
• So, ln K = –(rG/RT)
• If rG<0, then K>1; & products predominate at equilibrium
• And the rxn is thermo-dynamically feasible At K > 1, rG < 0
At K = 1, rG = 0
At K < 1, rG > 0
Relationship between rG and KRelationship between rG and K
• On the other hand…
• If rG>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 K1 (>103)
• But even with a K<1 you may have products formed in some rxns
• On the other hand…
• If rG>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 K1 (>103)
• But even with a K<1 you may have products formed in some rxns
Relationship between rG and KRelationship between rG and K
• For an endothermic rxn to have rG<0, its rS>0; furthermore,
• Its temperature must be high enough for its TrS to be greater than rH
• The switch from rG>0 to rG<0 corresponds to the switch from K<1 to K>1
• This switch takes place at a temperature at which rH - TrS = 0, OR….
• For an endothermic rxn to have rG<0, its rS>0; furthermore,
• Its temperature must be high enough for its TrS to be greater than rH
• The switch from rG>0 to rG<0 corresponds to the switch from K<1 to K>1
• This switch takes place at a temperature at which rH - TrS = 0, OR….
T = rHrS
Table 7.1 Thermodynamic criteria of spontaneity
Table 7.1 Thermodynamic criteria of spontaneity
G = H – TS
Table 7.1 Thermodynamic criteria of spontaneity
Table 7.1 Thermodynamic criteria of spontaneity
G = H – TS
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.
GG = = HH –– T TSS
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 TS 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 TS 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.
GG = = HH –– TTSS
Factors Affecting the Sign of G
Gibbs Free Energy (Gibbs Free Energy (GG))
For a constant-temperature process:
G = Hsys – TSsys
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 = Hsys – TSsys
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.
18.4
Gibbs Free Energy (Gibbs Free Energy (GG))
aA + bB cC + dD
G0rxn dG0 (D)fcG0 (C)f= [ + ] – bG0 (B)faG0 (A)f[ + ]
G0rxn nG0 (products)f= mG0 (reactants)f–
The standard free-energy of reaction (G0 ) is the free-energy change for a reaction
when it occurs under standard-state conditions.
rxn
Gibbs Free Energy (Gibbs Free Energy (GG))
7.10
p158
Who will explain this graph to the class?
Who will explain this graph to the class?
Relationship between rG and KRelationship between rG and K
• For an endothermic rxn to have rG<0, its rS>0; furthermore,
• Its temperature must be high enough for its TrS to be greater than rH
• The switch from rG>0 to rG<0 corresponds to the switch from K<1 to K>1
• This switch takes place at a temperature at which rH - TrS = 0, OR….
• For an endothermic rxn to have rG<0, its rS>0; furthermore,
• Its temperature must be high enough for its TrS to be greater than rH
• The switch from rG>0 to rG<0 corresponds to the switch from K<1 to K>1
• This switch takes place at a temperature at which rH - TrS = 0, OR….
T = rHrS
Reactions at equilibriumReactions at equilibrium
• Fig 7.5 (162)• An endothermic
rxn with K>1 must have T high enough so that the result of subtract-ing TrS from rH is negative
• Or rH–TrS < 0
• Set rH–TrS=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 TrS from rH is negative
• Or rH–TrS < 0
• Set rH–TrS=0 and solve for T
T = rHrS
equilibrium
rG = rH – TrS
Reactions at equilibriumReactions at equilibrium
equilibrium
rG = rH – TrS
Table 7.2 Table 7.2 Standard Gibbs energies of Standard Gibbs energies of formation at 298.15 K* (gases)formation at 298.15 K* (gases)
Table 7.2 Table 7.2 Standard Gibbs energies of Standard Gibbs energies of formation at 298.15 K* (gases)formation at 298.15 K* (gases)
Table 7.2 Standard Gibbs energies of formation at 298.15 K* (liquids & solids)
Table 7.2 Standard Gibbs energies of formation at 298.15 K* (liquids & solids)
Standard Gibbs Energy of Formation
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 compositionThe equilibrium composition
• The magnitude of K is a qualitative indicator
• If K 1 (>103) then rG < –17 kJ/mol @ 25ºC, the rxn has a strong tendency to form products
• If K 1 (<10–3) then rG > +17 kJ/mol @ 25ºC, the rxn will remain mostly unchanged reactants
• If K 1 (10–3-103), then rG is between –17 to +17 kJ/mol @ 25ºC, and the rxn will have significant concentrations of both reactants and products
• The magnitude of K is a qualitative indicator
• If K 1 (>103) then rG < –17 kJ/mol @ 25ºC, the rxn has a strong tendency to form products
• If K 1 (<10–3) then rG > +17 kJ/mol @ 25ºC, the rxn will remain mostly unchanged reactants
• If K 1 (10–3-103), then rG is between –17 to +17 kJ/mol @ 25ºC, and the rxn will have significant concentrations of both reactants and products p.160
Calculating an equilibrium concentration
Calculating an equilibrium concentration
•Example 7.1 (p165)
•Example 7.2 (p166)
•Example 7.1 (p165)
•Example 7.2 (p166)
Standard reaction Gibbs energyStandard reaction Gibbs energy
rG = Gm(products) – Gm(reactants)
rG = rH – TrS
rG = Gm(products) – Gm(reactants)
rG = rH – TrS
7.6 Kc and Kp 7.6 Kc and Kp
aA + bB cC + dD
Kc = [C]c[D]d
[A]a[B]b
In most cases
Kc Kp
aA (g) + bB (g) cC (g) + dD (g)
Kp = Kc(RT)n
Kp = pC
dpD
pA pBa b
c
Kp = Kc(RT)n
When does Kp = Kc ?
Derivation 7.1: Kc and Kp Derivation 7.1: Kc and Kp
Atkins uses
Work through Derivation 7.1, p.162
K = Kc cRT
p ][vgas
K = Kc T
12.07K ][vgas
Substituting values for c, p, and R, we get
What is this K?
What is vgas?
Coupled reactionsCoupled reactions
• Box 7.1 (164)• Weights as analogy
to rxns• A rxn with a large
rG can force another rxn with a smaller rG 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
rG can force another rxn with a smaller rG to run in its nonspontan-eous direction
• Enzymes couple biochemical rxns
Coupled reactionsCoupled 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
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?
rG 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?
rG is unchanged, so K is not changed
• How about a change in temperature? • Or a change in pressure? Let’s see…
The effect of temperatureThe effect of temperature
• Fig 7.7 (163) rG of a rxn that
results in fewer moles of gas increases with increasing T
rG of a rxn with no net change…
rG of a rxn that produces more moles of gas decreases with increasing T
• Fig 7.7 (163) rG of a rxn that
results in fewer moles of gas increases with increasing T
rG of a rxn with no net change…
rG of a rxn that produces more moles of gas decreases with increasing T
Equilibrium response to conditions
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
• 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 pressureThe 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 p0, xHI1
• What is [I2]?
• Fig 7.9 (174)• A change in
pressure does not change the value of K, but it does have other consequences (composition)
• As p0, xHI1
• What is [I2]?
H2(g) + I2(s) 2 HI(g)
Key Key IdeasIdeas
Key Key IdeasIdeas
The EndThe End…of this chapter…”…of this chapter…”
Spare parts to copy and pasteSpare parts to copy and paste
• μJtμJ+RT ln aJ
• Chemical potential (μ) changes as [J] changes
• μJtμJ+RT ln aJ
• Chemical potential (μ) changes as [J] changes
Box 7.1 pp.172fBox 7.1 pp.172f
• O2 binding in hemoglobin and myoglobin…
• …In resting tissue and in lung tissue
• O2 binding in hemoglobin and myoglobin…
• …In resting tissue and in lung tissue
Chemical PotentialChemical Potential
• Review pp.128-130, 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.128-130, 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 PotentialChemical 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 PotentialExcursus: Chemical Potential
• The standard chemical potential of a gas (μJ), is identical to its standard molar Gibbs energy (Gm) at 1 bar
• The greater the partial pressure of a gas, the greater its chemical potential
• The standard chemical potential of a gas (μJ), is identical to its standard molar Gibbs energy (Gm) at 1 bar
• The greater the partial pressure of a gas, the greater its chemical potential
Excursus: Chemical PotentialExcursus: Chemical Potential
• Common expressions of chemical potential:
μJtμJ+ RT ln aJ
μJtμJ+ RT ln
μJtμJ+ RT ln p
• Common expressions of chemical potential:
μJtμJ+ RT ln aJ
μJtμJ+ RT ln
μJtμJ+ RT ln p
p
p
p = 1 bar
top related