Chemical Equilibrium

1
Chemical Equilibrium

• Entropy, SGibb free energy (enthalpy), G
• Spontaneity
• Equilibrium constant
• Chemical reactions

2
Entropy

• In thermodynamics, entropy is an extensive state
  function that accounts for the effects of
  irreversibility in thermodynamic systems
• The concept of entropy is central to the second
  law of thermodynamics, which deals with physical
  processes and whether they occur spontaneously.
• Spontaneous changes occur with an increase in
  entropy.

3
Definition of the entropy

• Quantitatively, entropy, symbolized by S, is
  defined by the differential quantity dS dq / T,
  Joule/K
• where dq is the amount of heat absorbed Joule
  in a reversible process in which the system goes
  from one state to another, and
• T is the absolute temperature K.

4
Relation between entalpy and entropy

• P const. consequently dqp DH
• DS DH / T, Joule/K, and Tconst.
• The dimensions of entropy are energy divided by
  temperature, which is the same as the dimensions
  of Boltzmann constant (k R/NA) and heat
  capacity.
• The DH flows because of the temperature
  differencepositive DH, T(system) lt T(surr)

5
Ice melting example

• Heat dQ from the warmer room surroundings,
  T(surr) 298 K, will spread out to the cooler
  system of ice and water at its constant
  temperature, T(system) 273 K, the melting
  temperature of ice.
• The entropy of the system will change by the
  amount dS1 dQ/273 J/K.
• The total heat for this process is the energy
  required to change water from the solid state to
  the liquid state, and is called the enthalpy of
  fusion ?H of ice fusion at 273 K.

6
Ice melting example cont.

• The total entropy change of the system is DS1
  ?H/273 J/K.
• The entropy of the surroundings will change by
  the amount dS2 -dQ/298 J/K.
• The total entropy change of the surroundings is
  DS2 -DH/298 J/K.
• DS1 DS2 gt 0
• the decrease in the entropy of the surrounding
  room is less than the increase in the entropy of
  the system. Because T1(system) lt T2(surr) and
  DHgt0.

7
Directionality of Heat Transfer

• Heat always transfer from hotter object to cooler
  one.
• ENDOthermic heat transfers from SURROUNDINGS to
  the SYSTEM.

The figure illustrates the melting of
ice.T(system) 273 K. All energy is consumed by
thephase change (s ? l). Only the T(surr) may
decrease. In a very large room, however T(surr.)
is constant (for example 298 K).
8
Spontaneous events

• The total entropy change is positive
• this is always true in spontaneous events in a
  thermodynamic system and
• it shows the predictive importance of entropy
• the final net entropy after such an event is
  always greater than was the initial entropy.
• This is because the spontaneous heat flow
  direction.

9
Spontaneous events

• Ice melts spontaneously if the surroundings
  temperature is larger than 273 K
• Ice does not melts spontaneously if the
  surroundings temperature is smaller than 273 K
• Mixing gases (spontaneous, but no energy change)
• Solving crystals

10
Standard molar entropy

• The dimensions of molar entropy are energy
  divided by temperature and mol J mol-1 K-1.
• T 298 K, PP0 (101.3 kPa), STP
• The standard molar entropy S0 is a function of T,
  at 0 K S0 0 J mol-1 K-1.Page 726, Fig. 20-6.
• See Webbook of chemistry.

11
Standard Molar Entropy as a Function of
Temperature
12
Gibbs free energy

• The Gibbs free energy was developed in the 1870s
  by the American mathematical physicist Willard
  Gibbs.
• The Gibbs free energy is defined as
• G ? H T S where (in SI units)
• G is the Gibbs energy (J)
• H is the enthalpy (J)
• T is the temperature (K)
• S is the entropy (J/K)

13
Importance

• The Gibbs energy is one of the most important
  thermodynamic functions for the characterization
  of a system. It is a factor in determining
  outcomes such as
• the K equilibrium constant for a reversible
  reaction, and
• the DU potential difference volt of an
  electrochemical cell.
• Every system seeks to achieve a minimum of Gibbs
  free energy.

14
Importance 2

• If DG is negative, then DG is the maximum amount
  of useful work that a spontaneous reaction can
  perform at constant temperature and pressure.
• If DG is positive, work must be done on the
  system to make the reaction occur (for example
  electrolysis, we shall see later).

15
Equilibrium constant and potential difference

• DG DH T DS Eqs. (20.6) and (20.7)
• DG0 -RT ln K K equilibrium constant
• DG DG0 RT ln Q R8.314 J mol-1 K-1
  Q reaction quotient Q?K then DG ?0
• DG -n F DUn number of mols of electrons, F
  Faraday constant (96485 C/mol), DU potential
  difference V
• DG0 -n F DU0 standard molar Gibbs f.e.

16
Electrochemistry

• Nernst equation
• DG DG0 RT ln Q
• -n F DU -n F DU0 RT ln Q / -n F
• DU DU0 - RT/(n F) ln Q
• DU DU0 0.059/n log Q
• Where Q ? K, spontaneously.
• As K is reached DU 0 then
• DU0 0.059/n log K V

17
Important equations

• DG0 -RT ln K -2.303 RT log K
• K exp(- DG0/(RT))
• Chemical reaction
• aA bB ? cC dD

The thermodynamical equilibrium constantK is
dimensionless, and it is expressed with
dimensionless activity ratios.
18
General Expressions
a A b B . ? c C d D .
19
Activity
The a symbols represent the a ratio of the
equilibrium activity of the reactants and
products to their activity in their standard
state.

• The standard states have been defined to have
  unit activity.
• The units used to express the equilibrium
  activities are the same as those used to express
  the standard states activity. Units in the
  ratios cancel. The a symbol is unitless.
• For pure solids and liquids a1.
• For gases (ideal) aP/P0, where P0 is the
  atmospheric pressure.
• For components of solution (ideal) a molarity
  concentration value as the standard state is 1
  mol/l.

20
The Reaction Quotient, Q Predicting the
Direction of Net Change.

• Equilibrium can be approached various ways.
• Qualitative determination of change of initial
  conditions as equilibrium is approached is needed.

At equilibrium Qc Kc
21
Reaction Quotient
22
The Equilibrium Constant Expression
k1
Forward
CO(g) 2 H2(g) ? CH3OH(g)
Rfwrd k1COH22
k-1
Reverse
CH3OH(g) ? CO(g) 2 H2(g)
Rrvrs k-1CH3OH
At Equilibrium
Rfwrd Rrvrs
k1COH22 k-1CH3OH
Kc
23
Three Approaches to Equilibrium
24
Three Approaches to the Equilibrium
25
Calculating the Equilibrium Constant
V 10 L T 483 K
CH3OH
Qc
Kc
14.5 M-2
COH22
Equilibrium
Initial
?
26
K and the chemical reaction

• K is stricly related to a given reaction equation
  at a given temperature and pressure
• Changing the direction K 1/K
• Sum of reactions K K1K2 (summing DG0 ?
  summing -lnKs)

27
Combining Equilibrium Constant Expressions
N2O(g) ½O2 ? 2 NO(g) Kc ?
N2(g) ½O2 ? N2O(g) Kc(2) 2.71018
N2(g) O2 ? 2 NO(g) Kc(3) 4.710-31
1.710-49
28
Reaction S and G change

• DSrxno SnpSo(products) - SnrSo(reactants)
• DGrxno SnpDGfo(products) - SnrDGfo(reactants)
• Extensive properties
• Reverse Change sign
• Summing the individual steps

29
Using thermodynamical tables
P atm, T298.13 K

• The enthalpy change is positive, 44.0 kJ mol-1.
  The evaporation of water is an endothermic
  procedure
• The Gibbs free energy change DG0 8.5 kJ mol-1
  is positive, consequently the reaction is non
  spontaneous, the water remains liquid at 298.13
  K. The equilibrium vapor pressure is 23.76 mmHg.
  For this pressure the DG0 0 (equilibrium).
• The entropy change is positive during the
  evaporation of the water, DS0 118.9 J mol-1 K-1

30
DG dependence on T K

• Suppose that the temperature dependence of the
  reaction enthalpy and entropy is negligible for
  298 lt T lt 400 K.
• Then the approximate boiling point of water, is
  the temperature where DG0 0 Tboil 44000/
  118.9 370 K. Quite close to 373 K.
• Above this temperature the reaction Gibbs free
  energy will be negative, so the water will be in
  the gas phase.

31
Free Energy Change and Equilibrium
32
Water DG vs T curve (approx.)
Note KeqaH2O(g) / aH2O(l)
33
Water DG vs T curve (approx.)
Note KeqaH2O(l) / aH2O(g)
34
Criteria for Spontaneous Change
Every chemical reaction consists of both a
forward and a reverse reaction. The direction of
spontaneous change is the direction in which the
free energy decreases.
35
Significance of the Magnitude of ?G
DG
K
36
Spontaneous reactionsDG(T) DH TDS (see page
723)
T
T
37
K as function of temperature

• DG0 -RT ln K DH0 - TDS0
• Suppose that the temperature dependence of the
  reaction enthalpy and entropy is negligible

This is the vant Hoff equation.By measuring K
(T) we can obtain DH0
38
vant Hoff equation (first Nobel prize in
chemistry1901).

• A plot of the natural logarithm of K the
  equilibrium constant measured for a certain
  equilibrium versus 1/T the reciprocal temperature
  gives a straight line, the slope of which is the
  negative of DH the enthalpy change divided by R
  the gas constant and the intercept of which is
  equal to DS the entropy change divided by R the
  gas constant.

39
Temperature Dependence of Keq
40
Coupled Reactions

• In order to drive a non-spontaneous reactions we
  changed the conditions (i.e. temperature or
  electrolysis)
• Another method is to couple two reactions.
• One with a positive ?G and one with a negative
  ?G.
• Overall spontaneous process.

41
Smelting Copper Ore
Cu2O(s) C(s) ? 2 Cu(s) CO(g)
-50 kJ
Spontaneous reaction!
42
Focus On Coupled Reactions in Biological Systems
ADP3- HPO42- H ? ATP4- H2O
?G -9.2 kJ mol-1
But H3O 10-7 M not 1.0 M.
?G -9.2 kJ mol-1 41.6 kJ mol-1
32.4 kJ mol-1 ?G'
The biological standard state
43
Focus On Coupled Reactions in Biological Systems
44
Gas Phase equilibrium 1

• H2O(g) C(graphite) ? H2(g) CO(g)

If all terms are partial pressures, K KP Kx
(molar fractions, as partial pressure molar
fraction)
45
Gas Phase equilibrium 2

• Express PA with aA mol/l

Where Dngas is the difference in the
stoichiometric coefficients of gaseous products
and reactants. Here Dngas is 1 2-1
46
Production of some important N containing
compounds

• CH4 H2O ? H2 CO2
• 3H2 air(N2) ? 2NH3 (Haber Bosch)
• NH3 air(O2) H2O ? HNO3
• CO2 NH3 ? urea
• NH3 HNO3 ? NH4NO3
• NH3 H2SO4 ? (NH4)2SO4
• See Page 592

47
Le Chateliers priciple

• System in equilibrium is subjected to a changein
  temperature,pressure,or concentration of a
  reacting species,
• the system reacts in a way that partially offsets
  the change while reaching a new state of
  equilibrium. (page 581)

48
Le Châtelliers Principle
Kc 2.8102 at 1000K
Q gt Kc
49
Effect of Condition Changes

• Adding a gaseous reactant or product changes
  Pgas.
• Adding an inert gas changes the total pressure.
• Relative partial pressures are unchanged.
• Changing the volume of the system causes a change
  in the equilibrium position.

50
Effect of change in volume
CcDd
nC
c
nD
d
Kc

V(ab)-(cd)
AaBb
nA
nB
b
a
V-?n

Kn

• When the volume of an equilibrium mixture of
  gases is reduced, a net change occurs in the
  direction that produces fewer moles of gas. When
  the volume is increased, a net change occurs in
  the direction that produces more moles of gas.

51
Effect of Temperature on Equilibrium

• Raising the temperature of an equilibrium mixture
  shifts the equilibrium condition in the direction
  of the endothermic reaction.
• Lowering the temperature causes a shift in the
  direction of the exothermic reaction.

52
Effect of a Catalyst on Equilibrium

• A catalyist changes the mechanism of a reaction
  to one with a lower activation energy.
• A catalyst has no effect on the condition of
  equilibrium.
• But does affect the rate at which equilibrium is
  attained.

53
Le Chateliers priciple example

• 3H2 N2 ? 2NH3 DH0 -92.22 kJ/mol
• 4 mol of gases react and 2 mol NH3 is produced.
• Increasing the pressure ? smaller volume ? favors
  the reaction.
• Exothermic ? lower T ? favors the reaction.
• Lot of air ? more conversion
• Optimum conditions high P, low T (but slow)

54
Synthesis of Ammonia
The optimum conditions are only for the
equilibrium position and do not take into account
the rate at which equilibrium is attained.
55
Aqueous solution equilibrium

• Solubility of PbI2(s) in water
• PbI2(s) ? Pb2(aq) 2 I-(aq)
• See table 16 at the website

56
Acids and BasesSelf-ionization of Water

• Arrhenius H2O ? H(aq) OH-(aq)
• In Bronsted-Lowry theory H2O H2O ? H3O(aq)
  OH-(aq) Kw 10-14
• acid1 base2 acid2 base1
• The hydronium ion is solvated.
• HCl H2O ? H3O(aq) Cl-(aq) KHCl 1000
  Strong acid, goes to completion

57
pH and pOH

• pH - logaH3O - logH3O
• pOH - logaOH- - logOH-
• pH pOH 14 in water at 25ºC
• If pH is smaller than 7 (large H3O) the
  solution is acidic.
• If pH is larger than 7 (small H3O) the
  solution is basic.
• pH 7, neutral (pure water pH).

58
Weak acids (Kc ltlt 1)

• Acetic acid CH3COOH H2O ? H3O(aq)
  CH3COO-(aq) Ka 1.74 10-5, -logKa pKa 4.76
  (at 25ºC)
• Ka H3OA-/HA is called the acid
  ionization equilibrium constant.
• Smaller the acid ionization constant, weaker the
  acid is.
• The acetic acid is stronger acid than water, and
  weaker than HCl.
• See table 15 at the website

59
Weak bases (Kc ltlt 1)

• ammonia NH3 H2O ? NH4(aq) OH-(aq) Kb
  1.74 10-5, -logKb pKb 4.76 (at 25ºC)
• Kb is called the base ionization constant.
• Smaller the ionization constant, weaker the base
  is.
• See table 15 at the website

60
pH of weak acids and bases

• If the molar concentration is largeC gt Kc 100,
  or -logC pC lt pKc 2,and pKc ltlt 14, then the
  water and the acid dissociations can be
  neglected.
• H(aq)Ac-/HAc Kc
• H(aq)Ac- KcHAc KcC x x, xH(aq)
• pH (pKa pC)/2
• pOH (pKb pC)/2

61
Polyprotic acids

• Carbonic (K1, K2) H2CO3, HCO3- , CO32-
• Hydrosulfuric H2S
• Phosphorous H3PO3
• Phosphoric acid (triprotic) H3PO4
• Sulfurous H2SO3
• Sulfuric (K2) H2SO4
• See table 15 at the website

62
Hydrolysis

• Salts of strong acids and strong bases (e.g.
  NaCl) do not hydrolyze, pH 7 (neutral).
• Salts of strong acids and weak bases (e.g. NH4Cl)
  hydrolyze, pH lt 7 (acidic).
• Salts of weak acids and strong bases (e.g. NaAc)
  hydrolyze, pH gt 7 (basic).
• Salts of weak acids and weak bases (e.g. NH4Ac)
  hydrolyze, pH depends on pKs.

63
Lewis acids and bases

• Donation and acceptance of unshared pairs of
  electrons
• A Lewis acid is defined as an electron-pair
  acceptor
• A Lewis base is defined as an electron-pair donor
  
• See page 634
• Website