[Mere]

I need help with this complex problem.

An indicator (HIn) has a pKa of 5.319
Absorptivity (A) of 8.00 x 10^(-5) M of total indicator in a 1.00 cm cell is measured in acidic and alkaline solutions.

Wavelength --- A (pH = 1.0) --- A (pH = 13.0)
450 nm -------- 0.658 ------------ 0.076 -----
595 nm -------- 0.032 ------------ 0.361 -----

A buffer solution was made with 1.00 x 10^(-4) M of total indicator. Absorbance data is shown below for a 1.00 cm cell. Calculate the pH of the buffer solution.

Absorptivity at 450 nm = 0.508
Absorptivity at 595 nm = 0.212


I believe these equations may be relevant:

HIn ---> H + In, pKa = 5.319

Beer's Law:
A = (ε)(b)(c)
 
ε - molar absorptivity
b - cell length
c - concentration

A(In-) + A(HIn) = A(total) = b Σ(ε)(c) = b(ε1)[In-] + b(ε2)[HIn]
 
pH = pKa + log ([In-]/[HIn])


I have no idea what assumptions i should make.

I tried calculating ε at each specific wavelength and then tried to create two equations with two unknowns (no luck).

How does one relate absorptivity to pH?

[Borek]

At pH 1 and 13 you may assume there is only one form of the indicator present.