Chemical EquilibriaTadeusz Górecki Ionic Equilibria Page 9 General interpretation of activity: 1. Ions in dilute solutions: activity is equal to the product of the concentration (M

Tadeusz Górecki Ionic Equilibria

Page 1

Chemical Equilibria

OHAcOHHAc 32


Page 2

Addition of HAc to a mixture of NaOH and ammonia:

AcHHAc

34 NHHNH

OHOHH 2

Reaction of copper sulphate with ammonia:

Overall: 2

4332 )(4 NHCuNHCu

233

2 CuNHNHCu

2233

23 )()( NHCuNHNHCu

2333

223 )()( NHCuNHNHCu

2433

233 )()( NHCuNHNHCu

2533

243 )()( NHCuNHNHCu

More accurately:

....))(()( 225233

262 OHOHNHCuNHOHCu

Other possible species and reactions:

CuOH 2

22 )(OHCu

43 NHHNH

OHHOH2


Page 3

Equilibrium constant

Chemical potential:

Total free energy:

At equilibrium

)()(

)( 1

,,

molkJmoln

kJGi

nPTiij

i

iii nnnnTPG ),...,,,,( 21

0 Gdn

dG

r


Page 4

Most common REFERENCE STATES:

• pure liquid state

• infinite dilution state

• elements in their naturally occurring state

STANDARD CONDITIONS:

temperature, pressure and concentration

Reference state and standard conditions together define the

STANDARD STATE

Chemical potential of i in a liquid solution:

xRTf

fRT iliquidpurei

liquidpurei

iliquidpurei lnln 00

iii

ref

i axf

f (activity of the compound)

Activities are relative measures (they depend on the choice of the

reference state)

DCBA

Equilibrium constant:

BA

DC

BA

DC

BA

DC

aa

aaK

][][

][][


Page 5

Assuming that activity coefficients are equal to one:

]][[

]][[

BA

DCK

For acetic acid: AcHHAc

][

]][[

HA

AcHKa

When activity coefficients are not neglected:

0

0

][

][][

HAc

AcHKa

0

AK is independent of the composition of the solution


Page 6

Activity coefficients

extended Debye-Hueckel theory:

IBa

IzzA

1log

- geometric mean activity coefficient of the two ions forming the

electrolyte. For simple 1:1 salts (e.g. NaCl) 2/1

A - constant dependent on temperature and the dielectric constant of

the solvent

in water C25at 51.010825.12/36

TA

z - charge of the ion

I - ionic strength

i

ii zCI 2

2

1

Ci - concentration of every ion present in the solution

zi - charge of ion i

a - adjustable parameter, measured in Å, corresponding to the

effective size of the hydrated ion

B - function of temperature and dielectric constant:

in water C25at 33.03.502/1

TB

Activity coefficient for a single ion:

IBa

IAzz

1log 2


Page 7


Page 8

How well does it work?

Davies equation:

I

I

IzzA 2.0

1log

for single ion:

I

I

IAzz 2.0

1log 2


Page 9

General interpretation of activity:

1. Ions in dilute solutions: activity is equal to the product of the

concentration (M or m) and the activity coefficient:

AAA ][

2. Uncharged molecules (e.g. CO2, H2S, NH3):

bI0log

b depends on the molecule and temperature (typically between 0 and

0.2).

3. Solvent in a dilute solution: activity is approximately equal to the

mole fraction of the solvent (e.g. for 0.1 M NaCl x = 55.5/55.6 =

0.9982).

4. Pure solids and liquids: activity is exactly 1.

5. Gases in equilibrium with the solution: activity is partial pressure of

the gas in atm. At high pressures, a fugacity coefficient is required.

6. Mixtures of liquids: activity of a given compound is approximately

equal to its mole fraction.


Page 10

Examples of equilibrium constants

Autodissociation of water: OHHOH2

Thermodynamic equilibrium constant:

}{

}}{{

2

0

OH

OHHK

{H2O} is 1 for pure water, but 0.98 for 1 M NaCl

In general:

0

0 ][][

OHH

Kw

0 - activity coefficient of water

Concentration constant:

]][[ OHHKw

00

ww KK

Dissociation constant of a weak acid

polyprotic acid (e.g. H3PO4):

HPOHPOH 4243 ][

]][[

43

421

POH

POHHKa

HHPOPOH 2

442 ][

]][[

42

24

2

POH

HPOHKa

HPOHPO 3

4

2

4 ][

]][[24

34

3

HPO

POHKa


Page 11

Weak base:

OHNHOHNH 423

][

]][[

3

4

NH

OHNHKb

we can also write

HNHNH 34

][

]][[

4

3

NH

NHHKa

bwa KKK /

Stepwise formation constant for complexes:

CdClClCd 2

]][[

][21

ClCd

CdClK

2CdClClCdCl

]][[

][ 2

2

ClCdCl

CdClK

32 CdClClCdCl ]][[

][

2

3

3

ClCdCl

CdClK

2

43 CdClClCdCl ]][[

][

3

24

4

ClCdCl

CdClK

Activities can be easily introduced, e.g.:


Page 12

][][

][

2

21ClCd

CdClK

Overall formation constant:

CdClClCd 2

]][[

][21

ClCd

CdCl

11 K

2

2 2 CdClClCd

22

2

2]][[

][

ClCd

CdCl

212 KK

3

2 3 CdClClCd 32

3

3]][[

][

ClCd

CdCl

3213 KKK

2

4

2 4 CdClClCd 42

2

4

4]][[

][

ClCd

CdCl

43214 KKKK

Instability constant:

ClCdCdCl 422

4

][

]][[2

4

42

CdCl

ClCdK inst 4/1 instK


Page 13

Solubility product

ClAgsAgCl )(

}}{{0

ClAgK s

In terms of concentration:

]][[0

ClAgK s

For a divalent cation:

OHMgsOHMg 2)()( 2

2

22

0 ]][[ OHMgK s

AgCl equilibria in the presence of excess Cl-:

ClAgsAgCl )( ]][[0

ClAgK s

.)()( aqAgClsAgCl .)]([1 aqAgClK s

we can also write complex formation reaction:

.)(aqAgClClAg

]][[

.)]([1

ClAg

aqAgCl

hence 011 .)]([ ss KaqAgClK


Page 14

2)( AgClClsAgCl ][

][ 22

Cl

AgClK s

or

22 AgClClAg 2

22

]][[

][

ClAg

AgCl

hence 02

2

2][

][ss K

Cl

AgClK

2

32)( AgClClsAgCl 032

2

3

3][

][ss K

Cl

AgClK

3

43)( AgClClsAgCl 043

3

4

4][

][ss K

Cl

AgClK

.)(aqAgCl - dissolved (but not dissociated) AgCl


Page 15

Temperature dependence of K

000 ln STHKRTG

R - gas constant (8.314 kJ/mol) 0 denotes standard state

015

2

00

)1006.4(303.2

logHJ

RT

H

dT

Kd

Assumption when estimating K at a different temperature: 0H is

constant


Page 16

Mass balance

For acid HA:

][][ AHACHA

When more sources of A- are present (e.g. HA, NaA and CaA2):

...][][][2][2

CaAAHACCCA CaANaAHAT

Poorly soluble salts in water at saturation (e.g. BaSO4):

Mass balance on barium:

SBa ][ 2 (S – molar solubility)

Mass balance on sulphate:

SHSOSO ][][ 4

2

4

hence:

][][][ 4

2

4

2 HSOSOBa

Formation of precipitate (AgCl):

...][.)]([][)]([][ 2 AgClaqAgClAgsAgClAg T

...][2.)]([][)]([][ 2 AgClaqAgClClsAgClCl T

To eliminate [AgCl(s)] (unknown):

...][][][][][ 2 AgClClAgClAg TT

Charge balance

For HAc:

][][][ OHAcH

If a species has more than one charge, its concentration is multiplied by the

number of charges:


Page 17

][][3][2][][ 3

4

2

442

OHPOHPOPOHH

Proton condition (proton balance equation, PBE)

# protons consumed = # protons released

Water can consume a proton to form H3O+ or release a proton to form OH

-,

thus PBE for water is:

][][ OHH

PBE for water is involved in all PBEs for aqueous solutions.

PBE for a monoprotic acid:

][][][ OHAcH

PBE for a strong base:

][][][ OHKH

PBE for a weak base:

][][][ 4 OHNHH

PBE for strong electrolytes:

NaCl:

][][ OHH

NH4Cl:

][][][ 3 OHNHH


Page 18

NaAc:

][][][ OHHAcH

NH4Ac:

][][][][ 3 OHNHHAcH

Polyprotic acids and bases: the concentration terms in PBE must be multiplied

by the number of protons consumed or released in the formation of the species

from the starting material.

Examples:

H2S

][][2][][ 2 OHSHSH

NaHS:

][][][][ 22

OHSSHH

Na2S:

][][][2][ 2 OHHSSHH

Mixtures of electrolytes: the contributions of all the components are added.

Examples:

solution of HAc and HCOOH:

][][][][ COOHAcOHH

mixture of HOBz and NaOBz:

][][][][ OBzOHHOBzH

_____________________________________________________


Page 19

PBE for NaAc:

][][][ OHHAcH

Charge balance:

][][][][ OHAcNaH

Mass balance:

][][][ HAcAcNa

Substitution of mass balance into charge balance:

][][][][][ OHAcHAcAcH

Which is equivalent to PBE.

PBE can always be obtained by combining mass and charge balances.

========================================================

Solving an equilibrium problem

1. Establish the nature of all the species present in the solution.

2. Find the equilibrium constants relating the concentrations of the various

species.

3. Find enough other relations so that there are as many independent equations

as variables.

4. Solve the equations, using approximations where possible.

5. Check the provisional answer by substitution in the full original set of exact

equations. If the discrepancies are too high (> 5%), try more complicated

approximations.

6. Calculate the ionic strength and adjust the equation constants to correspond.

Repeat until the answers do not change.

7. Check all the final answers by substitution in the full set of exact equations.

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Chemical EquilibriaTadeusz Górecki Ionic Equilibria Page 9 General interpretation of activity: 1. Ions in dilute solutions: activity is equal to the product of the concentration (M