(adsbygoogle = window.adsbygoogle || []).push({}); 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 = ε_{1a}b[HIn] + ε_{1b}b[In-]

A2 = ε_{2a}b[HIn] + ε_{2b}b[In-]

Aa = ε_{a}b[HIN]

Ab = ε_{b}b[IN-]

Ab/Aa = ε_{b}b[IN-] / ε_{a}b[HIN]

Rearrange:

[In-] / [HIn] = ε_{a}Ab / ε_{b}Aa

A = Aa+Ab

so

[In-] / [HIn] = ε_{a}(A-Aa) / ε_{b}(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 = ε_{1a}b[HIn] + ε_{1b}b[In-]

A2 = ε_{2a}b[HIn] + ε_{2b}b[In-]

which led me to

[In-] / [HIn] = (A1ε_{2a}-A2ε_{1a}) / (A2ε_{1b}- A1ε_{2b})

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

HELP

Thank you.

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# Homework Help: Henderson Hasselbach to absorbance derivation

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