Appendix III

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Appendix III

155 APPENDIX III

Determination of the acid dissociation constants of PADA in DTAC The acid dissociation constants of PADA are expressed by the relationships

] [

] ][

[

2 2

1 +

+

= +

L H

H

K _A HL (III.1)

] [

] ][

2 [ +

= +

HL H

K _A L (III.2)

If the Lambert & Beer law applies for a wavelength where the species [HL] only absorb, with a 1 cm path length cell the overall absorbance is given by the equation

] [HL

Abs = ε _HL (III.3)

The mass conservation equations is

] [ ] [ ]

[ H ₂ L ² HL L

C _L =

⁺

+ ⁺ + (III.4)

Introduction of equation (III.1) and (III.2) into (III.4) yields

2 1 2 1

1 ] [ ]

[

] ] [

[

A A A

A L

K K H K H

H K HL C

+ +

= + ₊ ⁺ (III.5)

Substituting equation (III.5) into equation (III.3) and rearranging one obtains

2 1 2 1

1 ] [ ]

[

] [

A A A

A HL

L H K H K K

H K C

Abs

+

= ₊ + ε ₊ ⁺

(III.6)

which corresponds to equation (4.14) of chapter 4.

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Appendix III

156 The acid dissociation constants, K A1 and K A2 , are obtained by a non linear fit of the

experimental data on the basis of equation (III.6).

Appendix III

Appendix III

155 APPENDIX III

Determination of the acid dissociation constants of PADA in DTAC The acid dissociation constants of PADA are expressed by the relationships

] [

] ][

[

2 2

1 +

+

= +

L H

H

K A HL (III.1)

] [

] ][

2 [ +

= +

HL H

K A L (III.2)

If the Lambert & Beer law applies for a wavelength where the species [HL] only absorb, with a 1 cm path length cell the overall absorbance is given by the equation

] [HL

Abs = ε HL (III.3)

The mass conservation equations is

] [ ] [ ]

[ H 2 L 2 HL L

C L =

+ + + (III.4)

Introduction of equation (III.1) and (III.2) into (III.4) yields

2 1 2 1

1

] [ ]

[

] ] [

[

A A A

A L

K K H K H

H K HL C

+ +

= + + + (III.5)

Substituting equation (III.5) into equation (III.3) and rearranging one obtains

2 1 2 1

1

] [ ]

[

] [

A A A

A HL

L H K H K K

H K C

Abs

+

= + + ε + +

(III.6)

which corresponds to equation (4.14) of chapter 4.

Appendix III

156

The acid dissociation constants, K A1 and K A2 , are obtained by a non linear fit of the

experimental data on the basis of equation (III.6).

K _A HL (III.1)

K _A L (III.2)

Abs = ε _HL (III.3)

[ H ₂ L ² HL L

C _L =

+ ⁺ + (III.4)

= + ₊ ⁺ (III.5)

= ₊ + ε ₊ ⁺