*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

_{H}

_{Q}## (I.4)

*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

^{-}