# Homework Help: Henderson Hasselbach to absorbance derivation

1. Feb 20, 2012

### Puchinita5

1. The problem statement, all variables and given/known data
Did a lab where I had to determine the Ka value of an indicator using spectrophotometry.

This is a question I need to answer in my lab report:

Derive the equation

pH = pKa + log([A-Aa]/[Ab-A])

from the equation

pH = pKa + log( [In-]/[HIn])

using Beer's law.

A: measured absorbance at λb at specified pH
Aa: absorbance of acidic form at λb
Ab: absorbance of basic form at λb
λb: wavelength of maximum absorbance for basic form

2. Relevant equations

3. The attempt at a solution

A1 = ε1ab[HIn] + ε1bb[In-]
A2 = ε2ab[HIn] + ε2bb[In-]

Aa = εab[HIN]
Ab = εbb[IN-]

Ab/Aa = εbb[IN-] / εab[HIN]

Rearrange:

[In-] / [HIn] = εaAb / εbAa

A = Aa+Ab

so

[In-] / [HIn] = εa(A-Aa) / εb(A-Ab)

I'm stuck. I have been working on this for hours and cannot figure out how to get to the answer. Mainly, I just don't know how to get the molar absorbtivities to help me because they are all different. I'm so confused. Can someone steer me in the right direction? I also tried solving using the first two equations:

A1 = ε1ab[HIn] + ε1bb[In-]
A2 = ε2ab[HIn] + ε2bb[In-]

which led me to

[In-] / [HIn] = (A1ε2a-A2ε1a ) / (A2ε1b - A1ε2b)

which doesn't help me either because I can't see how to get rid of the molar absorbtivities.

HELP

Thank you.