115 -Appendix I-
APPENDIX I
Determination of the acid dissociation constants of PADA in micellar system
The acid dissociation constants of PADA (Figure 3.1) are expressed by the relationships ] L H [ ] H ][ HL [ K 2 2 1 A + + + = (I.1) ] HL [ ] H ][ L [ KA2 + + = (I.2)
Multiplication of equations (I.1) and (I.2) gives,
] L H [ ] H ][ L [ K K 2 2 2 2 A 1 A + + = × (I.3)
If the Lamber&Beer law applies for a wavelength where the adsorbing species of the ligand are L, HL and H2L, and for a 1 cm path leght cell, the overall
absorbance is given by equation (I.4)
L HL 2 L 2 H 2 2L ] [HL ] [L] H [ A= + ε + + + ε + + ε (I.4)
The mass conservation equation is
] L [ ] HL [ ] L H [ CL = 2 2+ + + + (I.5)
From equation I.5 one obtains [L] = CL-[H2L2+]-[HL+] which, introduced in
116 -Appendix I- ) ]( HL [ ) ]( L H [ C A L HL L 2 L 2 H 2 2 L L = ε −ε + ε −ε ε − + + + + (I.6) Define; L LC A A= −ε ∆ (I.7) L 2 L 2 H 1 =ε −ε ε ∆ + (I.8) L HL 2 =ε −ε ε ∆ + (I.9)
Introduction of equation (I.7),(I.8) and(I.9) in equation (I.6) yields
] HL [ ] L H [ A=∆ε1 2 2+ +∆ε2 + ∆ (I.10)
Introduction of equations (I.1) and (I.2) in to equation (I.10) and rearrenging yields equation (I.11)
2 A 1 A 1 A 2 2 1 1 A 2 L [H ] K [H ] K K ] H [ ] H [ K C A + + ε ∆ + ε ∆ = ∆ + + + + (I.11)
