CHEMICAL EQUILIBRIUMCHEMICAL EQUILIBRIUM

aA + bB cC + dD

Equilibrium constant

a,b,c,d – stoichiometry coefficients

[A], [B], [C], [D] –concentrations of A, B, C, D

ba

dc

BA

DCK

in standard state:

• For solutes – 1M

• For gases – 1 atm

• For solids and pure liquids: [X] = 1

In these conditions K is dimensionless.

K>1 Forward reaction is

favoured

the dynamic state in which rates of the forward and reverse reactions are identical.

CHEMICAL EQUILIBRIUM

Equilibrium const. for a reverse reaction:Equilibrium const. for a reverse reaction: K1 = 1/K

dc

ba

1DC

BAK

Equilibrium const. for two reactions added:Equilibrium const. for two reactions added: K3 = K1 x K2

[HA]]][A[H

K1

][C][H

][CHK2

][C][H

][CH

[HA]

]][A[H.KK 21

3K[HA][C]

]][CH[A

H+ + C CH+

HA + C CH+ + A-

HA H+ + A-

cC + dD aA + bB

The equilibrium constant is derived from the thermodynamics of a chemical reaction.

ENTHALPY

ΔH - enthalpy change is the heat absorbed or released during reaction

ΔH < 0

Heat liberated

Exothermic reaction

ΔH > 0

Heat absorbed

Endothermic reaction

THERMODYNAMICS

ENTROPY

ΔS – a measure of ‘disorder’ of a substance

ΔS > 0

Products more disordered than reactants

ΔS < 0

Products less disordered than reactants

Gas Liquid SolidDecrease in disorder

Example:

KCl(s) K+(aq) + Cl-(aq)

ΔS0 = +76 J/K mol at 250C

FREE ENERGY

Gibbs free energy: ΔG = ΔH - TΔS

ΔG < 0 The reaction is favoured K>1

ΔG > 0 The reaction is not favoured K<1

Free energy and equilibrium:

/RTΔG0eK KlnRTΔG OR

When a system at equilibrium is disturbed, the direction When a system at equilibrium is disturbed, the direction in which the system proceeds back to equilibrium is in which the system proceeds back to equilibrium is such that the change is partially offset.such that the change is partially offset.

BA

DCK

If reaction is at equilibrium and reactants are added (or products removed),the reaction goes to the right.

If reaction is at equilibrium and products added ( or reactants are removed),the reaction goes to the left.

LE CHATELIER’S PRINCIPLELE CHATELIER’S PRINCIPLE

A + B C + D

According to Le Châtelier:If Q > K reaction will proceed in the reverse

directionIf Q < K reaction will proceed in the forward

direction

Recall:

Q = Reaction quotient

has the same form as equilibrium constant (K), but the solution concentrations do not have to be equilibrium concentrations.

Thus at equilibrium:Q = K

[A] = 0.002M [B] = 0.025M

[C] = 5.0M [D] = 1.0M = 1x105 at 250C

To reach equilibrium:

Q = K

and the reaction must go to the right

spontaneous

A + B C + D BA

DCK

0.0250.002

1.05.0K

Say we add double reactant A, [A] = 0.004M

0.0250.004

1.05.0Q

= 0.5x105 at 250C

Q < K

At equilibrium:

G/RT-eK ΔG = ΔH - TΔS

Independent of T

For endothermic reactions (ΔH > 0):

K increases if T increases.

For exothermic reactions (ΔH < 0):

K decreases if T increases.

S/RH/RT/RTSTH-( eeeK .)

THE EFFECT OF TEMPERATURE ON K

K = KK = Kspsp (solubility product) when the equilibrium (solubility product) when the equilibrium

reaction involves a solid salt dissolving to give its reaction involves a solid salt dissolving to give its constituent ions in solution.constituent ions in solution.

Recall: [Solid] = 1

Saturated solution – in equilibrium with undissolved solid

Thus if an aqueous solution is left in contact with excess solid, the solid will dissolve until Ksp is

satisfied.

Thereafter the amount of undissolved solid remains constant.

K AND SOLUBILITY

Example:

Calculate the mass of PbCl2 that dissolves in 100 ml

water. (Ksp = 1.7x10-5 for PbCl2)

Initial:

Final:

(solid)

(solid)

m = 0.45 g

PbCl2(s) Pb2+(aq) + 2Cl-(aq)

Now add 0.03M NaCl to the PbCl2 solution We added 0.03M Cl-

THE COMMON ION EFFECTTHE COMMON ION EFFECT

Initial:

Final:

(solid)

(solid)

PbCl2(s) Pb2+(aq) + 2Cl-(aq)

For this system to be at equilibrium when [Cl-] is added, the [Pb2+] decreases (reverse reaction).

– this is an application of the Le Chatelier’s principle and is called THE COMMON ION EFFECT

The salt will be less soluble if one of its constituent ions is already present in the solution.

The Common Ion Effect - experimentThe Common Ion Effect - experiment

THE NATURE OF WATER AND ITS IONS

H+ does not exist on its own in H2O forms H3O+

H3O+:

In aqueous solution, H3O+ is tightly associated with 3

molecules of H2O through exceptionally strong

hydrogen bonds.

One H2O is held by weaker ion-dipole attraction

Can also form H5O2+ cation H+ shared by 2 water

molecules

H3O2- (OH-.H2O) has been observed in solids

AUTOPROTOLYSIS

Water undergoes self-ionisation autoprotolysis,

since H2O acts as an acid and a base.

H2O + H2O H3O+ + OH-

The extent of autoprotolysis is very small.

For H2O: Kw = [H3O+][OH-] = 1.0 x 10-14 (at 25oC)

pH pH ≈≈ -log[H -log[H++]] Approximate definition of pH

pH + pOH = -log(Kw) = 14.00 at 250C

pH

It is generally assumed that the pH range is 0-14. But we can get pH values outside this range.

e.g. pH = -1 [H+] = 10 M

This is attainable in a strong concentrated acid.

BUT in a real solution all charged ions are:

surrounded by ions with opposite charge – ionic atmosphere

hydrated - surrounded by tightly held water dipoles

ba

dc

BA

DCK Equilibrium constant

[A], [B], [C], [D] –concentrations of A, B, C, D

ACTIVITY

aA + bB cC + dD

Adding an “inert” salt to a sparingly soluble salt increases the solubility of the sparingly soluble salt.

“inert” salt = a salt whose ions do not react with the compound of interestWHY?

Consider:

BaSO4 (Ksp = 1.1x10-10) as the sparingly soluble salt and

KNO3 as the “inert” salt. In solution:

The cation (Ba2+) is surrounded by anions (SO42-, NO3

-)

net positive charge is reduced

The anion (SO42-) is surrounded by cations (Ba2+, K+)

net negative charge is reduced

attraction between oppositely charged ions is decreased.

The net charge in the ionic atmosphere is less than the charge of the ion at the center.

The greater the ionic strength of a solution, the higher the charge in the ionic atmosphere.

Each ion-plus-atmosphere contains less charge and there is less attraction between any particular cation and anion.

The ionic atmosphere decrease the attraction between ions.

Activity of the ion in a solution depends on its hydrated radius not the size of the bare ion.

A measure of the total concentration of ions in solution. The more highly charged an ion, the more it is counted.

i

2iizc

2

1μ

Where ci = concentration of the ith species zi = charge for all ions in solution

IONIC STRENGTH, µ

Example:

Find the ionic strength of 0.010 M Na2SO4 solution.

Effect of ionic strength on solubility

Explain all 4 cases

To account for the effect of ionic strength, concentrations are replaced by activities.

CC CA γActivity of C Activity coefficient

And general form of equilibrium constant is:

bB

baA

a

dD

dcC

c

bB

aA

dD

cC

[B][A]

[D][C]

AA

AAK

γγ

γγ

ACTIVITY COEFFICIENTS

Activity coefficient:

• Measure of deviation of behaviour from ideality (ideal = 1)

• Allows for the effect of ionic strength

Thus for the sparingly soluble salt BaSO4, dissolving in

the presence of the “inert” salt KNO3:

Ksp = aBa aSO4 = [Ba2+]Ba [SO42-]SO4

If more BaSO4 dissolves in the presence of KNO3,

[Ba2+] and [SO42-] increases and Ba and SO4 decreases

At low ionic strength:

activity coefficients 1

and K concentration equilibrium

Extended Debye-Hűckel equation relates activity coefficients to ionic strength:

305

μ1

μ0.51zlog

2

at 250C

ACTIVITY COEFFICIENTS OF IONS

= effective hydrated radius of the ion

3. The smaller the hydrated radius of 3. The smaller the hydrated radius of the ion, the more important activity the ion, the more important activity effects become.effects become.

Effect of Ionic Strength, Ion charge and Ion Size on the Activity Coefficient

Activity coefficients for differently charged ions with a constant hydrated

radius of 500pm.

(Over the range of ionic strength (Over the range of ionic strength from 0 to 0.1M)from 0 to 0.1M)

1.1. As ionic strength increases, the As ionic strength increases, the activity coefficient decreases. activity coefficient decreases. 1 as 1 as 0 0

2. As the charge of the ion increases, the departure of its activity coefficient from unity increases. Activity corrections are much more important for an ion with a charge of 3 than one with the charge 1.

Use Use interpolationinterpolation to find values of to find values of for ionic strengths not listed for ionic strengths not listed

Obtain values for Obtain values for from the table: from the table:

How to interpolate - SELF STUDY!!

Linear interpolation:

x

intervalxKnown

y

intervalyUnknown

At high ionic strengths:

activity coefficients of most ions increase

Concentrated salt solutions are not the same as dilute aqueous solutions “different solvents”

H+ in NaClO4 solution of varying ionic strengths

The real definition of pH is:

pH pH ≈≈ -log[H -log[H++]]

Approximate definition of pH

HH][HlogAlogpH γ

NOTE:NOTE:

A pH electrode measures activity of HA pH electrode measures activity of H+ + and NOT and NOT concentrationconcentration

pH AND ACTIVITY COEFFICIENTS

The systematic procedure is to write as many The systematic procedure is to write as many independent algebraic equations as there are unknowns independent algebraic equations as there are unknowns (species) in the problem. This includes all chemical (species) in the problem. This includes all chemical equilibrium conditions + two balances: charge and mass equilibrium conditions + two balances: charge and mass balances.balances.

The systematic procedure is to write as many The systematic procedure is to write as many independent algebraic equations as there are unknowns independent algebraic equations as there are unknowns (species) in the problem. This includes all chemical (species) in the problem. This includes all chemical equilibrium conditions + two balances: charge and mass equilibrium conditions + two balances: charge and mass balances.balances.

Chemical equilibrium provides a basis for most Chemical equilibrium provides a basis for most techniques in analytical chemistry and application of techniques in analytical chemistry and application of chemistry to other disciplines such as like biology, chemistry to other disciplines such as like biology, geology etc.geology etc.

The systematic treatment of equilibrium gives us the tool The systematic treatment of equilibrium gives us the tool to deal with all types of complicated chemical equilibria.to deal with all types of complicated chemical equilibria.

SYSTEMATIC TREATMENT OF EQUILIBRIUM

CHARGE BALANCECHARGE BALANCE

E.g. An aqueous solution of KH2PO4 and KOH contains the following ionic species:

H+, OH-, K+, H2PO4-, HPO4

2-, PO43-

The charge balance is:

The coefficient in front of each species

= the magnitude of the charge on the ion

[H+] + [K+] = [OH-] + [H2PO4-] + 2[HPO4

2-] + 3[PO43-]

Charge neutrality

The sum of positive charges in solution equals the sum of negative charges.

MASS BALANCEMASS BALANCE

Quantity of all species in a solution containing a particular atom must equal the amount of that atom delivered to the solution.

E.g. Mass balance for 0.02 M phosphoric acid in water:

Conservation of matter.

0.02 M = [H3PO4] + [H2PO4-] + [HPO4

2-] + [PO43-]

SYSTEMATIC TREATMENT OF EQUILIBRIUM:

Step 1. Write the pertinent reactions.

Step 2. Write the charge balance equation.

Step 3. Write the mass balance equations.

Step 4. Write the equilibrium constant for each chemical reaction.

Step 5. Count the equations and unknowns.

Step 6. Solve for all the unknowns.

E.g.: The ionization of water

H2O H+ + OH- Kw = 1.0x10-14 at 250C

Find the concentrations of H+ and OH- in pure water

For pure water the ionic strength approaches 0 and we can write eq.3 as:

Step 1. Pertinent reaction – only one above.

Step 2. Charge balance: (1)

Step 3. Mass balance: (2)

Step 4. Equilibrium constants – the only one

(3)

Step 5. Count equations and unknowns – 2 eq. and 2 unknowns

Step 6. Solve.

E.g.: The solubility of Hg2Cl2

Step 6. Solve. Using eqn 2 we can write eqn 3 as:

Find the concentration of Hg22+ in a saturated solution of

Hg2Cl2

Step 2. Charge balance: (1)

Step 3. Mass balance:

(2)

Step 4. Equilibrium constants: (3)

(4)

Step 5. Count equations and unknowns – 4 eqs. and 4 unknowns

Step 1. Pertinent reactions Hg2Cl2 Hg22+ + 2Cl- Ksp

H2O H+ + OH- Kw

Coupled equilibria – the product of one reaction is reactant in the next reaction

Problem:

The mineral fluorite, CaF2,

has a cubic crystal structure and often cleaves to form nearly perfect octahedra.

Find the solubility of CaF2 in water.

THE DEPENDENCE OF SOLUBILITY ON pH

Step 1. Pertinent reaction

Step 2. Charge balance

(1)

Step 3. Mass balance

Some fluoride ions react to give HF.

(2)

CaF2 dissolves:

CaF2(s) Ca2+ + 2F- Ksp = 3.9x10-11

For every aqueous solution:

H2O H+ + OH- Kw = 1x10-14

The F- ions reacts with water to give HF:

F- + H2O HF + OH- Kb = 1.5x10-11

Also

Step 4. Equilibrium constants

(3)

(4)

(5)

Step 5. Count equations and unknowns

5 eqs. and 5 unknowns:

Step 6. Solve

CaF2(s) Ca2+ + 2F- Ksp

F- + H2O HF + OH- Kb

H2O H+ + OH- Kw

Using this expression in eqn 3:

Ksp = [Ca2+][F-]2 = [Ca2+](0.80[Ca2+])2

To simplify the problem let us solve it for a fixed pH = 3

That means: [H+] = and [OH-] =

Then from eqn 4:

Kb = [HF][OH-]/[F-]

[HF]/[F-] = Kb/[OH-] = 1.5x10-11/1.0x10-11 = 1.5

Thus [HF] = 1.5[F-]

Substitute [HF] in the eqn 2:

[F-] + [HF] = 2[Ca2+]

And [F-] = 0.80[Ca2+]

Thus [Ca2+] = (Ksp/0.802)1/3 = 3.9x10-4M

[F-] + 1.5[F-] = 2[Ca2+]

Now find:

[F-] = 3.1x10-4 M

[HF] = 4.7x10-4 M

pH dependence of the conc. of Ca2+, F- and HF in a saturated solution.

NOTE: To fix the pH of a solution an ionic compound is added. Thus the charge balance equation as written not longer holds.

Also [OH-] = [H+] + [HF]

No longer holds

Found [Ca] in acid rain that has washed off marble stone (largely CaCO3) increases as the [H+] of acid rain increases.

Applications of coupled equilibria in the modeling of environmental problems

CaCO3(s) + 2H+(aq)

Ca2+(aq) + CO2(g) + H2O(l)

SO2(g) + H2O(l) H2SO3(aq)

oxidation H2SO4(aq)

Total [Al] as a function of pH in 1000 Norwegian lakes.

Al is usually “locked” into insoluble minerals e.g. kaolinite and bauxite. But due to acid rain, soluble forms of Al are introduced into the environment. (Similarly with other minerals containing Hg, Pb etc.)