Chapter 19
description
Transcript of Chapter 19
1
Chapter 19
Chemical Thermodynamics Entropy, Free Energy and
Equilibrium
2
19.1 Thermodynamics
Thermo: heat Dynamics: power
State Functions: considers only initial and final states
Does not consider pathways or rate
3
19.1 Thermodynamics Study of energy flow and its transformations
(heat and energy flow) Determines direction of reactions
(spontaneous or nonspontaneous under given conditions)
Considers only initial and final states
Organized into three laws: 1st Law 2nd Law 3rd Law
4
19.1 Basic Definitions System Surrounding Open system Closed system Isolated system State of system: defined by values of
composition, pressure, T, V. State Function: defined only by initial and
final condition of the system (Enthalpy, Entropy, Gibbs Free Energy).
Energy change signaled by: accomplishment of work and/or appearance or disappearance of heat.
system surroundings
universe
system surroundings
universe
5
19.1 Reversible and Irreversible Processes
Reversible process: the system can be restored to its original state by exactly reversing the original change. Example: melting ice at its melting point
Irreversible process: we cannot restore the system to its original state by simple reversing the process. Different path has to be used. Example: expansion a gas into vacuum.
6
19.1 First Law of Thermodynamics 1st Law:
Energy can be neither created nor destroyed Energy of the universe is constant
Important concepts from thermochemistry Enthalpy Hess’s law
Purpose of 1st Law Energy bookkeeping
How much energy? Exothermic or endothermic? What type of energy? Δu = q + w q = heat; w = work system does on the
surroundings (-PΔV)
7
19.2 Spontaneous vs Nonspontaneous Spontaneous process
Occurs without outside assistance in the form of energy (occurs naturally) Product-favored at equilibrium May be fast or slow May be influenced by temperature
Spontaneous versus nonspontaneous processes. Expansion of gas: spontaneous. Reverse: not.
8
19.2 Spontaneous vs. NonspontaneousSpontaneous Processes: (exothermic or endothermic?) Gases expand into larger volumes at constant
temperature ________________ H2O(s) melts above 0C ____________ H2O(l) freezes below 0C ____________ NH4NO3 dissolves spontaneously in H2O ____________ Steel (iron) rusts in presence of O2 and H2O ________ Wood burns to form CO2 and H2O __________ CH4 gas burns to form CO2 and H2O __________
Evolution of Heat (Exothermicity) : not enough to predict spontaneity
9
19.2 Spontaneous vs Nonspontaneous
Nonspontaneous process Does not occur unless there is outside
assistance (energy?) Reactants-favored at equilibrium
All processes which are spontaneous in one direction cannot be spontaneous in the reverse direction Spontaneous processes have a definite
direction Spontaneous processes are irreversible. Can
be reversed with considerable input of energy.
10
19.2 Factors That Favor Spontaneity
Spontaneous Processes driven by Enthalpy, H (Joules)
Many, but not all, spontaneous processes tend to be exothermic.
Entropy, S (Joules/K) Measure of the disorder of a system Many, but not all, spontaneous
processes tend to increase disorder of the system
Exothermicity favors spontaneity, but does not guarantee it.
11
19.2 Factors That Favor Spontaneity: Enthalpy
Examples of spontaneous reaction that is not exothermic:
NH4NO3(s) → NH4+ (aq) + NO3
-(aq) ΔH = 25 kJ/mol
Expansion of gas: energy neutral Phase changes: endothermic processes
that occurs spontaneously. Chemical system: H2(g) + I2(g) ↔ 2HI(g)
Equilibrium can be approached from both sides (spontaneous both ways) even though the forward reaction is endothermic and the reverse is exothermic.
12
19.2 Spontaneity: Examples
1. Based on your experience, predict whether the following processes are spontaneous, are spontaneous in reverse direction, or are in equilibrium:
(a) When a piece of metal heated to 150 ºC is added to water at 40 ºC, the water gets hotter.
(b) Water at room temperature decomposes into hydrogen and oxygen gases
(c) Benzene vapor, C6H6(g), at a pressure of 1 atm condenses to liquid benzene at the normal boiling point of benzene, 80.1 ºC.
13
19.2 Entropy Direct measure of the randomness or disorder
of the system. Related to probability
describes # of ways the particles in a system can be arranged in a given state (position and/or energy levels)
The most likely state – the most random More possible arrangements, the higher
disorder, higher entropy Ordered state – low probability of occurring Disordered state: high probability of
occurring
14
19.2 Entropy versus Probability Systems tend to move spontaneously
towards increased entropy. Why? Entropy is related to probability
(positional) Disordered states are more probable
than ordered states
S = k (lnW) k (Boltzman’s constant) = 1.38 x 10-23 J/K W = # possible arrangements in system
15
19.2 Spontaneous Processes: Dispersal of Matter
Isothermal (constant temperature) expansion of gas
After opening stopcock the molecules could be in any arrangement shown (4 arrangements)Probability for each arrangement = (1/2)2
25% probability
25% probability
Two molecules present:
16
Gas Container = two bulbed flask
Gas Molecules
Ordered State
19.2 Spontaneous Process: Isothermal Gas Expansion
Consider why gases tend to isothermally expand into larger volumes.
17
Gas Container
S = k ln (W) = k (ln 1) = (1.38 x 10-23 J/K)(0) = 0 J/K
For 3 particles, probability = (1/2)3
For N particles, probability = (1/2)N
Ordered State
19.2 Spontaneous Process: Isothermal Gas Expansion
18
Disordered States
19
Disordered States
20
Disordered States
21
Disordered States
22
Disordered States
23
Disordered States
24
Disordered States
25
More probable that the gas molecules will disperse between two halves than remain on one side
Disordered States
26
Driving force for expansion is entropy (probability); gas molecules have a tendency to spread out
Disordered States
27S = k(ln 7) = (1.38 x 10-23 J/K)(1.95) = 2.7 x 10-23 J/K
Disordered States
28
Stotal = k(ln 23) = k(ln 8) = (1.38 x 10-23 J/K)(1.79) = 2.9 x 10-23 J/K
Total Arrangements
29
19.2 Spontaneous Processes
With 1 mole of molecules, the number of possible arrangements increases dramatically. The probability that the gas molecules will be distributed between the two flasks increases greatly.
Spontaneous processes are those in which the disorder of the system increasesThe isothermal expansion of a gas is spontaneous because of the increase in randomness or “disorder” of the system.
30
19.2 Entropy Entropy, S (J/K) State Function S= (heat change)/T = q/T S = Sfinal – Sinitial
S > 0 represents increased randomness or disorder
Note: The magnitude of change in entropy depends on temperature.
31
19.2 Entropy: example
1. ΔS = q/TThe element mercury, Hg, is a silvery liquid at room temperature. The normal freezing point of mercury is -38.9 ºC, and its molar enthalpy of fusion is ΔHfusion = 2.331 kJ/mol. What is the entropy change when 50.0 g of Hg(l) freezes at the normal freezing point?
(-2.48 J/K)
32
19.2 Patterns of Entropy Change For the same or similar substances:
Ssolid < Sliquid < <Sgas
solidliquid vapor
33
19.2 Patterns of Entropy Change
solidliquid vapor
Rigidly held
particles; few
positions available
to particles
Particles free to flow; more
positions available for
particles
Particles farther apart, occupy
larger volume of space; even more positions available
to particles
34
19.2 Patterns of Entropy Change
solidliquid vapor
most ordere
d
least ordere
dless ordere
d
35
19.2 Patterns of Entropy Change Solution formation usually leads to increased
entropy for the system. Is it true for the surroundings (solvent)?
solute
solvent
solution
particles more disordered
19.2 Patterns of Entropy Change
36
19.2 Patterns of Entropy Change
Describe in words the entropy of the system
37
19.2 Patterns of Entropy ChangeDissolution of NaCl in water:1. The crystal breaks up2. The Na+ and Cl- ions are surrounded by hydrating
water molecules.NaCl(s) → Na+(aq) + Cl-(aq)
3. Each ion is surrounded by several water molecules.
4. NaCl becomes disordered (entropy increases)5. The water molecules become more ordered!
(entropy decreases)6. NaCl dissolves – net entropy increases.
38
19.3 Entropy and Temperature
(a) A substance at a higher temperature has greater molecular motion, more disorder, and greater entropy than (b) the same substance at a lower temperature.
39
Stan
dard
ent
ropy
, S(J
/K)
Temperature (K)0
20
10
30
40
50
10050 250 300150 200
What kind of changes are represented here?
40
Stan
dard
ent
ropy
, S°(
J/K)
Temperature (K)0
20
10
30
40
50
10050 250 300150 200
Solid
LiquidGas
What is the effect of temperature on entropy?
41
19.3 Entropy in Temperature
42
Substance
S (J/K) Substance
S (J/K)
H2O(l) 69.9 NaCl(s) 72.3H2O(g) 188.8 NaCl(aq) 115.5
I2(s) 116.7 Na2CO3(s) 136.0I2(g) 260.6 CH4(g) 186.3Na(s) 51.5 C2H6(g) 229.5K(s) 64.7 C3H8(g) 269.9Cs(s) 85.2 C4H10(g) 310.0
19.2 Standard Molar Entropies of Selected Substances at 298 K
43
19.2 Patterns of Entropy Change Chemical Reactions
#n gas molecules in product > #n molecules in reactants (Srxn > 0)
Physical Changes: cases where entropy increases Expansion of gas Formation of solutions Temperature changes. If only solids, ions and/or liquids involved, S
increases if total # particles increases.
If ΔS > 0, , randomness increases and entropy increases
44
19.2 Entropy: Examples
2. Predict if ΔS increases, decreases or does not change
(a) Freezing liquid mercury(b) Condensing H2O(vapor)(c) Precipitating AgCl(d) Heating H2(g) from 60.0 ºC to 80 ºC (e) Subliming iodine crystals(f) Rusting iron nail
45
19.3 Entropy - Examples3. Predict which substance has the higher entropy:
a) NO2(g) or N2O4(g)b) I2(g) or l2(s)
4. Predict whether each of the following leads to increase or decrease in entropy of a system If in doubt, explain why.a) The synthesis of ammonia:
N2(g) + 3H2(g) ↔ 2NH3(g)
b) C12H22O11(s) C12H22O11(aq)
c) Evaporation to dryness of a solution of urea, CO(NH2)2 in vapor. CO(NH2)2(aq) → CO(NH2)2(s)
H2O (l)
46
19.3 Second Law of Thermodynamics: System
6. Predict the sign of ΔS0 for each of the following reactions:a) Ca+2(aq) + 2OH-(aq) → Ca(OH)2(s)
b) MgCO3(s) → MgO(s) + CO2(g)
d) H2(g) + Br2(g) → 2HBr
47
19.3 Second Law of Thermodynamics
Expresses the connection between entropy and spontaneity.
In any spontaneous process there is always an increase in the entropy of the Universe. The entropy remains unchanged at equilibrium.
SPONTANEOUS PROCESS:ΔSuniv = Δ Ssys + Δ Ssurr > 0
NONSPONTANEOUS PROCESS:ΔS universe= ΔS syst. + ΔS surr. <0Reversible process is spontaneous
48
19.3 Second Law: Entropy Changes
EQUILIBRIUM PROCESSES (reversible)
♦ΔS universe= ΔS syst. + ΔS surr. =0
♦ΔS syst = ΔS surr
♦ΔS syst = ΔSº final - ΔS0 initial
49
19.3 Entropy Changes in a System (Reactions)
Entropy changes in a system aA + bB → cC + dD Standard entropy change ΔSº (25 ºC, 1atm). Only changes in entropy can be measured. Each element has an entropy value (compare
to enthalpy). Absolute value for each substance can be
determined. For a chemical system:
ΔSº rxn = ΔSº products - ΔS0 reactants
Standard Molar entropy, S0, is the entropy of one mole of a substance in its standard state (298 K)
50
5. Using standard molar entropies, calculate S°rxn for the following reaction at 25°C:
2SO2(g) + O2(g) → 2SO3(g)S° = 248.1 205.1 256.6 (J · K-
1mol-1)
(Ans.: -187.9 J/K)
19.3 Second Law: Example
51
19.3 Entropy of Reactions (System)6. Using thermodynamic tables, calculate the
standard entropy changes for the following reactions at 25 ºC
a) Evaporation of 1.00 mol of liquid ethanol to ethanol vapor.
b) The oxidation of one mole pf ethanol vapor (combustion reaction)c) Are the reactions spontaneous under the given conditions.
Answers:a) 122.0 J/K b) 96.09 J/K
52
19.3 Entropy Changes in the System
In a reaction More gas molecules produced: entropy
increases Less gas molecules produced: entropy
decreases No net change of # of gas molecules
produced: entropy changes, but slightly
Liquid, solid products: hard to estimate-needs calculations
53
19.3 Entropy Changes in Surrounding
Entropy of surroundings Increases in an exothermic process Decreases in an endothermic process Change depends on temperature ΔSsurr is then proportional to the change
in enthalpy in the system (negative sign needed to make entropy positive in an exothermic process)
54
19.3 Second Law of Thermodynamics (System)
7. Examples: H2O(s) melts above 0C (endothermic). What
about entropy? Steel (iron) rusts in presence of O2 and H2O
(exothermic). What about entropy? 4Fe(s) + 3O2(g) 2Fe2O3(s)
CH4 gas burns to form CO2 and H2O (exothermic). What about entropy?
CH4(g) + 2O2(g) CO2(g) + 2H2O(g)
Each process increases entropy of the universe.
55
19.3 Entropy of Surrounding
(a)When an exothermic reaction occurs in the system (ΔH < 0), the surroundings gain heat and their entropy increases (Δ Ssurr > 0).
(b) When an endothermic reaction occurs in the system (Δ H > 0), the surroundings lose heat and their entropy decreases (Δ Ssurr < 0).
62
19.3 Second Law of Thermodynamics To determine Suniv for a process, both Ssystem and
Ssurroundings need to be known: Ssystem
related to matter dispersal in system Ssurroundings
determined by heat exchange between system and surroundings and T at which it occurs
Sign of Ssurr depends on whether process in system is endothermic (Ssurr< 0) or exothermic (Ssurr >0)
Magnitude of Ssurr depends on T
Ssurr = -Hsystem/T
63
19.3 Second Law of Thermodynamics Consider transferring the same amount of heat to two
different systems, one at 298K and another at 500K.
More entropy (disorder) is created in the system at lower temp.
At high temperatures the system is already disordered
Tq
S rev
298K 500KQ Q
Kq
Kq
500298
64
19.3 Second Law of Thermodynamics
8. Reaction: N2(g) + 3H2(g) → 2NH3(g)ΔHº = -92.6kJ ΔSsys = -199 J/K at 25 ºC
ΔSsurr = -(-92.6 x1000)J/298K = 311 J/KΔSuniv = -199 J/K + 311 J/K = 112 J/K
Reaction spontaneous at 25 ºC
65
19.3 Third Law of Thermodynamics
Perfect crystal: its internal arrangement is absolutely regular. Nothing is in motion (vibrations, rotations and translations)
The entropy of a pure (perfect) crystal at 0K is 0.
66
Third Law of Thermo
Gives us a starting point, S at 0K is equal to zero.
All others must be >0.
Standard Entropies Sº ( at 298 K and 1 atm) of substances are listed.
Products - reactants to find Sº (a state function)
More complex molecules higher Sº.
19.3 Entropy and Third Law
67
19.4 Gibbs Free Energy2nd law: Suniv = Ssys + Ssurr > 0 for spontaneousSuniv = Ssys - Hsys/T > 0Rearrange: multiply both sides by (-T)-TSuniv = -TSsys + Hsys < 0
-TSuniv = Hsys - TSsys < 0
GIBBS FREE ENERGY: G = -TSunivG = Gibbs free energy (J or kJ) = (G = -TSuniv ) G = H – TS < 0
andG = Hsys - TSsys < 0
G° = H°sys - TS° < 0 (if at standard state) for Spontaneous Process
68
19.4 Gibb's Free Energy at any Conditions
G=H-TS Never used this way. At constant temperature
G=Hsys –TSsys
G function eliminates the need to deal with entropy of the surroundings
If G is negative at constant T and P, the process is spontaneous.
We deal only with the SYSTEM.
69
19.4 Gibbs Free Energy Summary of Conditions for Spontaneity
G < 0 reaction is spontaneous in the forward
direction (Suniv > 0)
G > 0 reaction is nonspontaneous in the forward
direction(Suniv < 0)
G = 0 system is at equilibrium
(Suniv = 0)Remember- Spontaneity tells us nothing about rate.
70
19.4 Gibbs Free Energy The Gibbs Free Energy is a measure of the maximum
amount of work, at a given temperature and pressure, that can be done on the surroundings by a system.
Never really achieved because some of the free energy is changed to heat during a change, so it can’t be used to do work.Wmax = G
For a spontaneous process: Maximum amount of energy released by the
system that can do useful work on the surroundings
Energy available from spontaneous process that can be used to drive non-spontaneous process.
For a nonspontaneous process: Minimum amount of work that must be done to
force the process to occur
71
19.4 Gibbs Standard Energy Free Energy
The standard free energies of formation, G°, are the free energy values for the formation of a substance under standard conditions.
The standard free energy of formation for any element in its standard state is zero. (Like enthalpy, but not entropy)
Compare: G = Hsys - TSsys (any conditions) G = H0
sys - TS0sys (standard conditions)
72
19.4 Convention for Standard States
State of Matter Standard StateGas 1 atm pressure
Liquid Pure liquidSolid Pure solidElements Gºf = 0Solution 1 molar
73
19.4 Free Energy in Reactions Gº = standard free energy change. Free energy change that will occur if reactants in their
standard state turn to products in their standard state. Can’t be measured directly, can be calculated from
other measurements. The reaction:
aA + bB → cC + dD
Gºrxn = ΣnGº (products) - ΣmGº (reactants)
or Gº=Hº-TSº
Use adapted Hess’s Law with known reactions.
74
19.4 Gibbs Free Energy: Spontaneity and Coupled Reactions
Conversion of rust to iron 2Fe2O3 4Fe + 3O2 G = 1487 kJ (NS)
To convert iron to rust, G must be provided from spontaneous reaction 2Fe2O3 4Fe + 3O2 G = 1487 kJ (NS) 4Fe + 3O2 2Fe2O3 G = - 1487 kJ (S) 6CO + 3O2 6CO2 G = -1543 kJ
(S)
75
19.4 Gibbs Free Energy: Coupled Reactions
Conversion of rust to iron 2Fe2O3 4Fe + 3O2 G = 1487 kJ (NS)
To convert iron to rust, G must be provided from spontaneous rxn 2Fe2O3 4Fe + 3O2 G = 1487 kJ (NS) 6CO + 3O2 6CO2 G = -1543 kJ (S) 2Fe2O3 + 6CO 4Fe + 6CO2 G = -56 kJ (S)
Reactions are “coupled”
76
19.4 Gibbs free Energy: Example
For a particular reaction, Hrxn = 53 kJ and Srxn = 115 J/K. Is this process spontaneous a) at 25°C, and b) at 250°C? (c) At what temperature does Grxn = 0?
Look at the equation G=H-TS Spontaneity can be predicted from the sign
of H and S.
(ans.: a) G = 18.7 kJ, nonspontaneous; b) –7.1 kJ, spontaneous; c) 460.9 K or 188C)
77
ΔH ΔS -|TΔS| ΔG = ΔH-TΔS Reaction Characteristics
Example
- + - Always negative
Spontaneous at all temperatures
2O3(g) →3O2(g)
+ - +Always positive
Nonspontaneous at all temperatures
3O2(g) →2O3(g)
- - +
Negative at low T; positive at high T
Spontaneous at low T; nonspontaneous at high T. Enthalpy driven
H2O(l) →H2O(s)+
+ + -
Positive at low T; negative at high T
Nonspontaneous at low T; becomes spontaneous at high T. Entropy driven.
H2O(s) → H2O(l)
19.4 Gibbs Free Energy and SpontaneityEffect of Temperature on the Spontaneity of
Reactions
1
2
3
4
78Free energy change as a function
of temperature.
19.4 Gibbs Free Energy and Spontaneity
79
19.4 Gibbs Free Energy and Temperature
Spontaneous Processes H2O(s) melts above 0C (endothermic)
H > 0 (endo process), S > 0 ENTROPY DRIVEN
Steel (iron) rusts in presence of O2 and H2O at 25 C (exothermic) 4Fe(s) + 3O2(g) 2Fe2O3(s) H < 0 (Exo) , S < 0 (entropy decreases) ENTHALPY DRIVEN
G < 0 for each process T determines sign of G: G = H -TS
80
19.4 Gibbs Free Energy: Example (p. 748)
9. Predict which of the four cases in Table (slide #78) you expect to apply to the following reactions:a) C6H12O6 (s) + 6O2(g) → 6CO2(g) + 6H2O(g) ΔH = -2540 kJ
b) Cl2(g) → 2Cl(g)
10. Calculate ΔG0 at 298 K for the reaction 4HCl(g) + O2(g) → 2Cl2(g) + 2H2O(g) ΔH0 = 114.4 kJ
a) using Gibbs free Energy equationb) from standard free energies of formation.
( -76.0 kJ)
81
19.4 Gibbs free Energy: Example
11. For the reaction SO2(g) + 2H2S(g) →3S(s) + 2H2O(g)
Calculate the temperature at which ΔG0 = 0Values of ΔH0, kJ/mol ΔS0 (kJ/(K mol) SO2 -296.8 0.2481H2S -20.6 0.2057S 0.0 0.0318H2O -241.8 +0.1887
Answer: 780K
82
19.4 Temperature and Chemical Reactions – Problem Set
14. Calculate the temperature at which the reaction: CaCO3(s) → CaO(s) + CO2(g) becomes spontaneous.ΔS º = 160.5 J/K; ΔH º = 177.8 kJ
Answer: 835 ºC
83
19.4 Phase Transitions: Temperature and Chemical Reactions
15. At its normal boiling point, the enthalpy of vaporization of pentadecane, CH3(CH2)13CH3, is 49.45 kJ/mol. What should be its approximate normal boiling point temperature be? ΔS0 of vaporization is 87 J mol-1 K-1
(570 K)
84
19.5 Free Energy and Equilibrium
ΔG and ΔGº are not the same. ΔG = ΔH – T ΔS
ΔGº = ΔH º – T ΔS º ΔGº is only at standard conditions
(values obtained from Tables)ΔGº = Gº(products) - ΔGº
(reactants)
ΔG any conditions (no Tables of values available)
85
19.5 Free Energy and Equilibrium
Predicament: we start a reaction with all reactants in standard state (1 atm, 25ºC, 1M solution). Is the standard state preserved as the reaction progresses?
It can be shown mathematically that at non-standard conditions:
ΔG = ΔGº +RTlnQ
]tan[[products] quotient reaction ,
tsreacQ
86
The total free energy of a reaction mixture as a function of the progress of the reaction. Beginning with either pure reactants or pure products, the free energy decreases (ΔG is negative) as the system moves toward equilibrium. The graph is drawn assuming that the pure reactants and pure products are in their standard states and that Δ G° for the reaction is negative so the equilibrium composition is rich in products.
ΔGrxn < 0
ΔGrxn > 0
87
Spontaneous Spontaneous Reaction Reaction Products Products favoredfavored
equilibrium
position
Pure reactants
Pure products
extent of reaction
Greactants
Gproducts
Grxn < 0
89
19.5 Free Energy and the Equilibrium Constant
At equilibrium:
eq
eq
KRTG
KRTG
ln
ln0
From the above we can conclude:If G < 0, then K > 1 Product favoredIf G = 0, then K = 1 EquilibriumIf G > 0, then K < 1 Reactants favored
K = e-(ΔGº /RT)
Kc used for solutions and molarities, Kp used for gases
Useful equation to determine small
Keq
90
19.5 Temperature Dependence of K
Gº= -RTlnK = Hº - TSº
ln(K) = Hº/R(1/T)+ Sº/R
A straight line of lnK vs 1/T Slope?
Y-intercept?
19.5 Free Energy and Chemical Equilibrium
91
19.5 Reaction Path and ΔGº
ΔGº = -RTln K
Value of ΔGº Sign of K Path of reaction
Negative, <0 K>0 Products are favored
Positive, >0 K<0 Reactants are favored
zero, =0 K = 1 Equilibrium
92
19.5 Keq: Problem Set – 19.6 (p. 755)
16. Determine the value of Keq at 25 ºC for the reaction:2NO2(g) ↔ N2O4(g).
Note: calculate ΔG0 from tables Use ΔG0 = -RTln Kp
( 6.9)
93
19.5 Keq: Problem Set 19.7 (p. 755)
17. Using the solubility product of of silver iodide at 25 ºC (8.5 x 10-17), calculate ΔGº for the process:AgI(s) ↔ Ag+(aq) + I-(aq)
Answer:18. Estimate the value of ΔS0
298 for the dissociation of copper (II) oxide.CuO(s) ↔ 2Cu2O(s) + O2(g) ΔH0
298 = 283 kJ
( 0.203 kJ K-1
94
19.5 Gibbs and Equilibrium: Example
19. Calculate Grxn for the reaction below:2A(aq) + B(aq) C(aq) + D(g)
if G°rxn = 9.9 x 103 J/mol and (a) [A] = 0.8 M, [B] = 0.5 M, [C] = 0.05 M, and PD = 0.05
atm, and (b) (b) [A] = 0.1 M, [B] = 1 M, [C] = 0.5 M, and PD = 0.5
atm. (c) Is the reaction spontaneous under these conditions?
(ans.: a) –2121 J, spontaneous; b) 17875 J, nonspontaneous)
95
Example 5
20. Calculate G°rxn for the ionization of acetic
acid, HC2H3O2 (Ka = 1.8 x 10-5) at 25°C. Is
this reaction spontaneous under standard
state conditions? (ans.: 27 kJ)
19.5 Gibbs and Equilibrium: Example
96
21. Calculate G° for the neutralization of a
strong acid with a strong base at 25°C. Isthis process spontaneous under theseconditions?For the reaction below, K = 1.0 x 1014.
H+ + OH- H2O
(ans.: -80 kJ)
19.5 Gibbs and Equilibrium: Example
97
22. Calculate Keq for a reaction at (a) 25°C and (b) 250°C if H°rxn = 42.0 kJ and S°rxn = 125 J/K. At which temperature is this process product favored?
(ans.: a) 0.15; b) 216; 250C)
19.5 Gibbs and Equilibrium: Example
98
19.5 Summary
First Law of Thermodynamics: ΔU = Δq + Δw
Second Law: ΔSuniv = ΔS sys + ΔSsurr
ΔS sys= ΔH/TΔG = ΔH – T ΔSΔG = ΔGº +RTlnK
ΔGº = -RTlnK
99
19.5 Gibbs Free Energy Many biological reactions essential for life
are nonspontaneous Spontaneous reactions used to “drive”
the nonspontaneous biological reactions Example: photosynthesis
6CO2 + 6H2O C6H12O6 + 6O2 G > 0
What spontaneous reactions drive photosynthesis?
100
19.5 Entropy and Life Processes
If the 2nd law is valid, how is the existence of highly-ordered, sophisticated life forms possible? growth of a complex life form
represents an increase in order (less randomness) lower entropy
101
19.5 Entropy and Life Processes
CO2H2Oheat
Organisms “pay” for their increased order by increasing Ssurr.
Over lifetime, Suniv > 0.
103