Transcript Entropy, Free Energy, and Equilibrium

Entropy, Free Energy,
and Equilibrium
Chapter 18
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Thermochemistry is the study of heat change in chemical
reactions.
The system is the specific part of the universe that is of
interest in the study.
SURROUNDINGS
SYSTEM
open
Exchange: mass & energy
closed
isolated
energy
nothing
6.2
Thermodynamics
State functions are properties that are determined by the state
of the system, regardless of how that condition was achieved.
energy, enthalpy, pressure, volume, temperature , entropy
Potential energy of hiker 1 and hiker 2
is the same even though they took
different paths.
6.7
Enthalpy (H) is used to quantify the heat flow into or out of a
system in a process that occurs at constant pressure.
DH = H (products) – H (reactants)
DH = heat given off or absorbed during a reaction at constant pressure
Hproducts < Hreactants
DH < 0
Hproducts > Hreactants
DH > 0
6.3
Because there is no way to measure the absolute value of
the enthalpy of a substance, must I measure the enthalpy
change for every reaction of interest?
Establish an arbitrary scale with the standard enthalpy of
formation (DH0f ) as a reference point for all enthalpy
expressions.
Standard enthalpy of formation (DH0f) is the heat change
that results when one mole of a compound is formed from
its elements at a pressure of 1 atm.
The standard enthalpy of formation of any element in its
most stable form is zero.
DH0f (O2) = 0
DH0f (C, graphite) = 0
DH0f (O3) = 142 kJ/mol
DH0f (C, diamond) = 1.90 kJ/mol
6.5
0 ) is the enthalpy of
The standard enthalpy of reaction (DHrxn
a reaction carried out at 1 atm.
aA + bB
cC + dD
DH0rxn = [ cDH0f (C) + dDH0f (D) ] - [ aDH0f (A) + bDH0f (B) ]
DH0rxn = S nDH0f (products) - S mDHf0 (reactants)
Hess’s Law: When reactants are converted to products, the
change in enthalpy is the same whether the reaction takes
place in one step or in a series of steps.
(Enthalpy is a state function. It doesn’t matter how you get
there, only where you start and end.)
6.5
Thermodynamics
DE = q + w
DE is the change in internal energy of a system
q is the heat exchange between the system and the surroundings
w is the work done on (or by) the system
w = -PDV when a gas expands against a constant external pressure
6.7
Enthalpy and the First Law of Thermodynamics
DE = q + w
At constant pressure, q = DH and w = -PDV
DE = DH - PDV
DH = DE + PDV
6.7
Spontaneous Physical and Chemical Processes
• An unassisted change in a system
• A system that is unstable or not at equilibrium will strive to
reach equilibrium
spontaneous
Unstable
Stable
nonspontaneous
Will not happen on its own  add work
Le Chatelier’s Principle
18.2
Spontaneous Physical and Chemical Processes
• A waterfall runs downhill
• A lump of sugar dissolves in a cup of coffee
• At 1 atm, water freezes below 0 0C and ice melts above 0 0C
• Heat flows from a hotter object to a colder object
• A gas expands in an evacuated bulb
• Iron exposed to oxygen and water forms rust
spontaneous
nonspontaneous
18.2
spontaneous
nonspontaneous
18.2
Reversible Process
Goes back and forth between states along the same path
Chemical systems at equilibrium are reversible
A + B
 C+D
H2O liquid & ice @ 0°C are in equilibrium
ice  water 1 mole @ 0°C q = DHfus is added
water  ice 1 mole @ 0°C q = DHfus is removed
A
B
1 path
Irreversible Process
One that cannot simply be reversed to restore to the original state
Must take a new path to get back
In a spontaneous process, the path between reactants and
products is irreversible
A
B
Does a decrease in enthalpy mean a reaction proceeds
spontaneously?
Spontaneous reactions
CH4 (g) + 2O2 (g)
CO2 (g) + 2H2O (l) DH0 = -890.4 kJ
H+ (aq) + OH- (aq)
H2O (l) DH0 = -56.2 kJ
H2O (s)
NH4NO3 (s)
H2O (l) DH0 = 6.01 kJ
H2O
NH4+(aq) + NO3- (aq) DH0 = 25 kJ
18.2
Entropy (S) is a measure of the randomness or disorder of a
system.
order
disorder
S
S
DS = Sf - Si
If the change from initial to final results in an increase in randomness
Sf > Si
DS > 0
For any substance, the solid state is more ordered than the
liquid state and the liquid state is more ordered than gas state
Ssolid < Sliquid << Sgas
H2O (s)
H2O (l)
DS > 0
18.2
S°solid < S°liquid << S°gas
S° increases with the
number of atoms
S° increases with
increasing molar mass
NOTE: Elements in
their standard state
do not have zero
entropy.
spontaneous
nonspontaneous
Randomness is directly related to probability.
The more random the system’s state, the more
probable the state.
18.2
Entropy
W=1
W = number of microstates
S = k ln W
DS = Sf - Si
DS = k ln
W=4
Wf
Wi
Wf > Wi then DS > 0
W=6
Wf < Wi then DS < 0
18.3
Processes that
lead to an
increase in
entropy (DS > 0)
18.2
How does the entropy of a system change for each of the
following processes?
(a) Condensing water vapor
Randomness decreases
Entropy decreases (DS < 0)
(b) Forming sucrose crystals from a supersaturated solution
Randomness decreases
Entropy decreases (DS < 0)
(c) Heating hydrogen gas from 600C to 800C
Randomness increases
Entropy increases (DS > 0)
(d) Subliming dry ice
Randomness increases
Entropy increases (DS > 0)
18.2
First Law of Thermodynamics
Energy can be converted from one form to another but
energy cannot be created or destroyed.
Second Law of Thermodynamics
The entropy of the universe increases in a spontaneous
process and remains unchanged in an equilibrium process.
Spontaneous process:
DSuniv = DSsys + DSsurr > 0
Equilibrium process:
DSuniv = DSsys + DSsurr = 0
18.3
Entropy Changes in the System (DSsys)
The standard entropy of reaction (DS0rxn ) is the entropy
change for a reaction carried out at 1 atm and 250C.
aA + bB
DS0rxn =
cC + dD
[ cS0(C) + dS0(D) ] - [ aS0(A) + bS0(B) ]
DS0rxn = S nS0(products) - S mS0(reactants)
What is the standard entropy change for the following
reaction at 250C? 2CO (g) + O2 (g)
2CO2 (g)
S0(CO) = 197.9 J/K•mol
S0(O2) = 205.0 J/K•mol
S0(CO2) = 213.6 J/K•mol
DS0rxn = 2 x S0(CO2) – [2 x S0(CO) + S0 (O2)]
DS0rxn = 427.2 – [395.8 + 205.0] = -173.6 J/K•mol
18.3
Entropy Changes in the System (DSsys)
When gases are produced (or consumed)
•
If a reaction produces more gas molecules than it
consumes, DS0 > 0.
•
If the total number of gas molecules diminishes,
DS0 < 0.
•
If there is no net change in the total number of gas
molecules, then DS0 may be positive or negative
BUT DS0 will be a small number.
What is the sign of the entropy change for the following
reaction? 2Zn (s) + O2 (g)
2ZnO (s)
The total number of gas molecules goes down, DS is negative.
18.3
Entropy Changes in the Surroundings (DSsurr)
Exothermic Process
DSsurr > 0
Endothermic Process
DSsurr < 0
18.3
Third Law of Thermodynamics
The entropy of a perfect crystalline substance is zero at the
absolute zero of temperature.
18.3
Gibbs Free Energy
Enthalpy Changes

DH
Exothermic Endothermic
Entropy Changes

D STOT
Spontaneous
Spontaneous process:
Equilibrium process:
Not Spontaneous
DSuniv = DSsys + DSsurr > 0
DSuniv = DSsys + DSsurr = 0
For a constant-temperature process:
Gibbs free
energy (G)
DG = DHsys -TDSsys
DG < 0
The reaction is spontaneous in the forward direction.
DG > 0
The reaction is nonspontaneous as written. The
reaction is spontaneous in the reverse direction.
DG = 0
The reaction is at equilibrium.
The standard free-energy of reaction (DG0rxn) is the freeenergy change for a reaction when it occurs under standardstate conditions.
aA + bB
cC + dD
0
DGrxn
= [cDG0f (C) + dDG0f (D) ] - [aDG0f (A) + bDG0f (B) ]
0
DGrxn
= S nDG0f (products) - S mDG0f (reactants)
Standard free energy of
formation (DG0f ) is the free-energy
change that occurs when 1 mole
of the compound is formed from its
elements in their standard states.
DG0f of any element in its stable
form is zero.
What is the standard free-energy change for the following
reaction at 25 0C?
2C6H6 (l) + 15O2 (g)
12CO2 (g) + 6H2O (l)
0
DGrxn
= S nDG0f (products) - S mDG0f (reactants)
0
DGrxn
= [12DG0f (CO2) + 6DG0f (H2O)] - [ 2DG0f (C6H6)]
0
DGrxn
= [ 12x–394.4 + 6x–237.2 ] – [ 2x124.5 ] = -6405 kJ
Is the reaction spontaneous at 25 0C?
DG0 = -6405 kJ < 0
spontaneous
18.4
DG = DH - TDS
18.4