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Henderson Hasselbach to absorbance derivation

  1. Feb 20, 2012 #1
    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.
     
  2. jcsd
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