A. CHEMICAL EQUILIBRIUM B. THERMODYNAMICS …kadima/CHE322 fall 2006/CHAPTER 6... · a. chemical equilibrium b. thermodynamics and equilibrium ... h. buffer solutions ... che 322

CHE 322 EQUILIBRIUM

CHAPTER 6 / HARVEY

A. CHEMICAL EQUILIBRIUM

B. THERMODYNAMICS AND EQUILIBRIUM

C. MANUPULATING EQUILIBRIUM CONSTANTS

D. EQUILIBRIUM CONSTANTS FOR CHEMICAL REACTIONS

1. Precipitation Reactions 2. Acid-Base Reactions 3. Complexation Reactions 4. Oxidation-Reduction Reactions E. LE CHÂTELIER'S PRINCIPLE

F. LADDER DIAGRAMS

G. SOLVING EQUILIBRIUM PROBLEMS

H. BUFFER SOLUTIONS

I. ACTIVITY EFFECTS

J. SUGGESTED PROBLEMS

6.1, 6.2, 6.4, 6.5, 6.7, 6.12, 6.14, 6.19

APPENDIX 3 AND 4

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CHE 322 EQUILIBRIUM

A. EQUILIBRIUM Gulberg and Waage (1867) A reaction is at equilibrium when the rates of the forward and reverse reactions are equal. It is a dynamic state. aA bB cC dD

rf raterate =ba

ff BAkrate ][][= dc

rr DCkrate ][][=

[ ] [ ][ ] [ ] r

fba

dc

eq kk

BADCK ==

The expression obtained is the correct expression for the equilibrium constant, but the method of derivation has no general validity. Because, reaction rates depend on the mechanism of the reaction! Reaction rates depend on the number of colliding species (molecularity) whereas the equilibrium constant expression depends only on the stoichiometry of the reaction. e.g. S2O8

2− + 3I− → 2 SO42− + I3

−

Rate = kf [S2O8

2−] [I−]

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CHE 322 EQUILIBRIUM

Change in concentrations of reactants and products as the reaction proceeds What can be predicted from knowledge of the equilibrium constant? 1) the tendency of the reaction to occur and in what direction 2) Not whether it is fast enough to be feasible in practice ** Even with a large K, a reaction may proceed from right to left if sufficiently large concentrations of products are initially present

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CHE 322 EQUILIBRIUM

B. THERMODYNAMICS AND EQUILIBRIUM

aA bB cC dD

A chemical system evolves spontaneously towards its lowest energy state. Energy of a chemical system changes during a chemical reaction. What determines the final position of a reaction? 1) Enthalpy 2) Entropy and temperature

TSHG −= (1) At constant pressure and temperature

STHG ∆−∆=∆ (2)

G∆ change in Gibbs free energy H∆ change in enthalpy (net flow of energy as heat) S∆ change in entropy

T temperature in Kelvins

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CHE 322 EQUILIBRIUM

H∆

ST∆

G∆ Forward reaction

Reverse reaction

< 0

> 0

< 0

Spontaneous

< 0

< 0 , ST∆ < H∆

< 0

Spontaneous

< 0

< 0 , ST∆ > H∆

> 0

Spontaneous

< 0

< 0, ST∆ = H∆

0

EQUILIBRIUM

EQUILIBRIUM

> 0

< 0

>0

Spontaneous

> 0

> 0, ST∆ > H∆

< 0

Spontaneous

> 0

> 0, ST∆ < H∆

> 0

Spontaneous

> 0

> 0, ST∆ = H∆

0

EQUILIBRIUM EQUILIBRIUM

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CHE 322 EQUILIBRIUM

Gibbs free energy is a function of concentrations

QRTGG o ln+∆=∆ (3)

[ ] [ ][ ] [ ]ba

dc

BA

DCQ = (4)

oG∆ change in Gibb's free energy under standard -state conditions

Standard-state conditions 298 K 1M solute Pure solid Pure liquid 1 atm partial pressure At equilibrium 0=∆G Therefore KRTGo ln−=∆ (5)

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CHE 322 EQUILIBRIUM

Thermodynamic Equilibrium Constant versus Concentration Equilibrium Constant For very dilute/ ideal solutions (mM), in the absence of interactions between reactants, the equilibrium constant can be calculated using concentrations. Equilibrium constant based on concentration is sometimes referred to as concentration equilibrium constant.

[ ] [ ][ ] [ ]beq

aeq

deq

ceq

CBA

DCK = (6)

Real thermodynamic equilibrium constant

bB

aA

dD

cC

aa

aaK = (7)

[ ]AaA γ= (8)

a activity γ activity coefficient

+−= HapH log Molecular solutes have activity coefficients very near unity up to an ionic strength of 0.1. Activity coefficients of pure liquids and solids are equal to one.

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CHE 322 EQUILIBRIUM

Activity coefficients of ionic solutes For ionic solutes the extended Debye-Huckel equation is used to calculate the activity coefficient

µα

µγ

××+

××=−

A

AA

z

3.31

51.0log

2 (9) at 25°C, 1.0≤µ

∑=i

ii zc 221µ (10)

Az charge of the ion Aα effective diameter of the hydrated ion in nanometers

µ ionic strength of the solution It is handy to recognize the following Type of ionic compound

Ionic strength

−+BA C ++2

2 BA C3

−+ 22 BA C4 ++3

3 BA C6

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CHE 322 EQUILIBRIUM

Relationship between concentration equilibrium constant and thermodynamic equilibrium constant

bB

aA

dD

cC

CKKγγ

γγ=

bB

aA

dD

cC

CKKγγ

γγlogloglog −−=−

bB

aA

dD

cC

C pKpKγγ

γγlog+=

BADCC badcpKpK γγγγ loglogloglog +−++=

)3.31

51.0)((

2222

µµ

αααα +++−−+=

B

B

A

A

D

D

C

CC

zb

za

zd

zcpKpK

Measure CK at different ionic strength and extrapolate to zero to obtain K .

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CHE 322 EQUILIBRIUM

C. MANUPULATING EQUILIBRIUM CONSTANTS

C.1 Reverse reaction's equilibrium constant

12

1K

K =

C.2 Overall equilibrium constant

Ni+2 NH3 Ni(NH3)+2

Ni(NH3)+2 NH3 Ni(NH3)2+2

Ni(NH3)2+2 NH3 Ni(NH3)3

+2

Ni(NH3)3+2 NH3 Ni(NH3)4

+2

4321 KKKKKoverall = If reactions (A + B) = reaction C, the equilibrium constant of reaction C (Kc) is equal to the product of the equilibrium constants for reaction A and B.

C.3 Equilibrium Constants are used for: •Calculation of concentrations of chemical species at equilibrium under conditions where the same information might be difficult to measure or is unobtainable by direct experiment. •Prediction of conditions that will lead to desired results

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CHE 322 EQUILIBRIUM

D. EQUILIBRIUM CONSTANTS FOR CHEMICAL REACTIONS

D.1 PRECIPITATION REACTIONS Metathesis reaction

33 )( NaNOsAgClNaClAgNO +→+

)()()()()()()( 33 aqNOaqNasAgClaqClaqNaaqNOaqAg −+−+−+ ++→+++ Net ionic equation

)()()( sAgClaqClaqAg →+ −+ Solubility product : spK

)()()( aqClaqAgsAgCl −+ +⎯→←

== −+ ]][[ ClAgKsp 10108.1 −× 74.9=sppK

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CHE 322 EQUILIBRIUM

D.2 ACID-BASE REACTIONS

D.2.1 Brønsted and Lowry definition Acid: proton donor Base: proton acceptor

D.2.2 Strong and weak acids and bases Strong acids and bases are completely dissociated in water HCl, HNO3, HCLO4, HI, First proton of H2SO4 NaOH, KOH Weak acids and weak bases Weak acids and weak bases are weak electrolytes, they are partially dissociated in water. CH3COOH H2O CH3COO- H3O+

Conjugated base of the acid

CH3COO- H2O CH3COOH OH-

NH3 H2O NH4

+ OH-

Conjugated acid of the base

NH4+

H2O NH3 H3O+

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CHE 322 EQUILIBRIUM

D.2.3 Acid and base dissociation constants

][]][[

3

33COOHCH

OHCOOCHKa

+−=

][

]][[

3

3−

−=

COOCH

OHCOOHCHKb

wba KOHOHKK ==× −+ ]][[ 3

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CHE 322 EQUILIBRIUM

D.2.4 Dissociation of water H2O(l) H2O(l) H3O+(aq) OH-(aq)

Water is amphiprotic

14100000.1 −×=wK at 24 °C

][][

3+

− =OH

KOH w

14==+ wpKpOHpH

14==+ wba pKpKpK

D.2.5 Other amphiprotic species HCO3

- H2O H2CO3(aq) OH-(aq)

HCO3

-(aq) H2O(l) CO3-2(aq) H3O+(aq)

D.2.6 Polyprotic acids H2CO3 H3PO4 H2C2O4

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CHE 322 EQUILIBRIUM

H2CO3(aq) H2O(l) HCO3-(aq) H3O+(aq)

HCO3-(aq) H2O(l) CO3

-2(aq) H3O+(aq)

7

32

331 1045.4

][]][[ −

+−×==

COHOHHCO

Ka

352.61 =apK

11

3

323

2 1069.4][

]][[ −−

+−×==

HCO

OHCOKa

329.102 =apK

321 aaa KKK ff

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CHE 322 EQUILIBRIUM

D.3 COMPLEXATION REACTIONS

D.3.1 Definitions G.N. Lewis definition of acids and bases Acid: electron pair acceptor

in the formation of a covalent bond. Base: electron pair donor Complexation generally refers to reactions where a ligand (a Lewis base) donates an electron pair to a metal ion (a Lewis acid) to form a covalent bond between.

D.3.2 Formation constants (Kf) and dissociation constants (Kd) Stepwise formation constants ( ) iK Cumulative or overall formation constants ( iβ )

ii KKKK ×××= ...321β

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CHE 322 EQUILIBRIUM

D.4 OXIDATION-REDUCTION REACTIONS

D.4.1 Definitions Reaction in which electrons are transferred from one reactant to another. The reducing reagent is oxidized (oxidation state increases) The oxidizing reagent is reduced (oxidation state decreases)

5 C2O4-2(aq) 2 MnO4

-(aq) H+(aq) 10 CO2(g) 2 Mn+2 8H2O(l)16

Oxalate is oxidized [oxidation state of C changes from +3 to +4] Permanganate is reduced (oxidation state of manganese changes from +7 to +2) Oxalate is the reducing agent Permaganate is the oxidizing agent

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CHE 322 EQUILIBRIUM

D.4.2 Equilibrium Constant for Redox reactions? Because electrochemical potentials are easily measured for redox reactions, they are conveniently used to express equilibrium and to calculate equilibrium constants. Free energy for moving a charge under the influence of a potential E is given by:

QEG ×=∆ (1)

nFQ = (2)

nFEG −=∆ (3)

n number of moles of electrons per mole of reatant F Faraday's constant (96,485 C.mol–1) Negative sign????

oo nFEG −=∆ (4)

QRTGG o ln+∆=∆ (5) Substituting (3) and (4) in (5), yields (6)

QRTnFEnFE o ln+−=− (6) Divide (6) by (−nF)

QnFRTEE o ln−= (7)

1131451.8 −−= molJKR

15.298=T QQ log30258.2ln =

mVVF

RT 16.5905916.030258.2 ==×

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CHE 322 EQUILIBRIUM

Qn

EE o log05916.0−= (8)

Standard-State Electrochemical Potential for the Reaction ( oE ) At equlibrium E = 0, therefore

KnFRTEo log= (9)

Therefore, if the standard-state potential of a reaction is known, the equilibrium constant of the reaction can be calculated. Standard-state potentials for chemical reaction can be calculated using available standard state-potentials of the oxidation and reduction half-reactions.

oox

ored

oreac EEE −=

oredE standard-state reduction potential of the reduced reactant

ooxE standard-state reduction potential of the oxidized reactant

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CHE 322 EQUILIBRIUM

What are Standard-State Reduction Potentials? (Appendix 3D)

Standard-state reduction potential of chemical species relative to the reduction potential of the hydronium ion, which by convention is set to 0.000 V. They express the tendency of chemical species to be reduced relative to the hydronium ion.

2 H3O+(aq) 2 e- 2 H2O(l) H2(g)

VE o

HOH 000.023 / =+

If oE > 0.000, species has a greater tendency to be reduced than H+

Strong oxidizing agents have large positive oE (dioxygen, permanganate)

If oE < 0, species has lesser tendency to be reduced than hydrogen and a greater tendency to be oxidized.

Strong reducing agents have large negative oE (Zinc, Sodium)

)(2)(2 2 gHeaqH ⇔+ −+ VE o 000.0=

)(22 sZneZn ⇔+ −+ VE o 763.0−=

OHeHgO 22 244)( ⇔++ −+ VE o 229.1=

+−+ ⇔+ 23 FeeFe VE o 771.0=

−−− ⇔+ IeI 323 VE o 536.0=

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CHE 322 EQUILIBRIUM

Calculate the equilibrium constant of the following reaction

−+−+ +⇔+ 323 232 IFeIFe

) Standard-State reaction potential

12) Equilibrium constant

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