Question

3. The spectrophotometric analysis done in this activity is measuring the absorbance of the base form (blue form) of the indicator. The blue form absorbs light best at 615 nm (10-h(A) light; thus, the K, value was calculated using the equation K. = Ar-A for sorbance values measured at 615 nm. The derivation for why this equation is equal to the K is included in your Background Section--Spectrophotometric Method. (H,OA derive Starting from the equilibrium constant expression for a weak acid K, IHA . the equation that would have to be used to determine the K value based on pH and absorbance measures if 440 nm light were used. Measuring the absorbance at 440 nm would be measuring the absorbance of the acid form (yellow form) of the indicator (assume any absorbance of the blue form at 440 nm can be ignored). NOTE:"Derive" means show every step in the mathemati- cal derivation of the equation. See pages 78-80 for the derivation of the equation when 615 nm light is used.

Answer 1

It is important to point out that in this case, the reference value of absorbance at 440 nm must be taken from a spectrum of the pure acid form, so this A_ref will not be the same as in the given equation for the blue (basic) form.

A_ref represents the absorbance of the indicator when it is fully in its basic form, so it is proportional to the total concentration of the indicator. Let's say: A_ref = k.c_total, where k is a constant that relates the absorbance with the concentration of the basic form.

Now, when measuring at a different pH, we will measure an absorbance that is proportional to the concentration only of the acid form, so now we will have A = k.c_acid (since the same species is absorbing, k is the same as before).

The expression for the Ka is:

$Ka=\frac{[H_{3}O^{+}][A^{-}]}{[HA]}$

The concentration of H₃O⁺ is given by 10 elevated to -pH, as in the previous equation. We also know that the concentration of HA is proportional to A, and for the concentration of the basic form A^- we can propose:

$Ka=\frac{10^{-pH}\cdot (A_{ref}-A)}{A}=\frac{10^{-pH}\cdot (k\cdot c_{total}-k\cdot c_{acid})}{k\cdot c_{acid}}$

This is equal to:

$Ka=\frac{10^{-pH}\cdot k\cdot ( c_{total}-c_{acid})}{k\cdot c_{acid}}=\frac{10^{-pH}\cdot ( c_{total}-c_{acid})}{c_{acid}}$

And c_total - c_acid is the concentration of the basic species, which is what we need to complete our Ka expression:

$Ka=\frac{10^{-pH}\cdot k\cdot c_{basic}}{k\cdot c_{acid}}=\frac{[H_{3}O^{+}][A^{-}]}{[AH]}$