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Determination of the first acid dissociation constant of the hydroxyquinoline

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Appendix I

151 APPENDIX I

Determination of the first acid dissociation constant of the hydroxyquinoline

The dissociation constant of a weak acid with a pK

A

between 4 and 10 can not be determined spectrophotometrically by direct addition of a strong base to the weak acid because the hydrogen concentration at the equilibrium is very low and therefore not easily evaluated. Therefore it has been indirectly measured by a protonic exchange reaction with a weak acid which must have a pK

A

value similar to the one of our acid.

The exchange reaction between HQ and acetic acid (HA) can be expressed by the relationship

HQ + HA H

2

Q

+

+ A

-

(I.1)

whose equilibrium constant is

1 2

] [ ] [

] [ ] [

A HA

K K HA HQ

A Q

K H =

×

=

+

×

(I.2)

where K

HA

is the acid dissociation constant of HA and K

A1

the first acid dissociation constant of H

2

Q

+

expressed by

] [

] [ ] [

2

1 +

+

×

= H Q

HQ

K

A

H (I.3)

If the Lambert & Beer law applies, for a wavelenght where the two species [HQ]

and [H

2

Q]

+

only absorb and for a 1 cm path lenght cell, the overall absorbance is given by the equation

] [

]

[

2

2

+

+

+

= HQ H Q

Abs ε

HQ

ε

HQ

(I.4)

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Appendix I

152

The following mass balances also apply

] [

]

[ +

2 +

= HQ H Q

C

HQ

(I.5)

] [ ] [ A HA

C

A

=

+ (I.6)

If we now define

HQ HQ

C Abs

Abs = − ε

∆ (I.7)

Q HQ

H

ε

ε

ε = −

+

2

(I.8)

Introduction of equation (I.5) into (I.3) yields

] [

2 +

=

Abs ε H Q (I.9)

Introduction of equation (I.5) and (I.9)into (I.2) yields

] [

] [ 1 1

HA A K

Abs

C

HQ

∆ ×

∆ +

∆ = ε ε (I.10)

which corresponds to equation (4.5) of chapter 4.

A plot of C

HQ

/∆Abs vs. [A

-

]/[HA] = (C

A

-C

HCl

)/C

HCl

is a straight line whose slope

and intercept are equal to 1/K∆ε and 1/∆ε respectively. Therefore, K is obtained as

the intercept/slope ratio and subsequently K

A1

is obtained as K

HA

/K ratio.

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