CHM110H5 Chap.7 Acid Dissociation and Spectrophotometry
Acid Dissociation and Spectrophotometry
What Experiment 4 measures
This chapter covers the CHM110H5 lab where you find the dissociation constant of bromophenol blue with a spectrophotometer. The indicator is a weak acid: its protonated form HIn is yellow and its deprotonated form In⁻ is blue, linked by HIn + H₂O ⇌ In⁻ + H₃O⁺. Its equilibrium constant KIn equals [H₃O⁺][In⁻]/[HIn], and taking logs gives pKIn = pH + log([HIn]/[In⁻]).
Because the two forms have different colours, they absorb light at different wavelengths, and that difference lets you count each form without separating them.
Beer-Lambert as the measuring tool
At low concentration the absorbance follows A = εbc, where ε is the molar absorption coefficient, b the path length and c the concentration.
Absorbance at a chosen wavelength is therefore proportional to the concentration of whichever form absorbs there. You first prepare the indicator in pH 4.0 potassium hydrogen phthalate buffer, record its spectrum across 380 to 650 nm with the KHP buffer as the blank, and read off the two absorption peaks λ1 and λ2. Every later reading is taken at those two wavelengths, never at an arbitrary point on the curve.
A yellow solution absorbs in the violet-blue region and a blue solution absorbs orange light, so expect the acid-form peak at the short-wavelength end of the scan and the base-form peak near the long end.
From three absorbances to pKIn
Partners split the work: one makes SA1 to SA3 by adding KHP and 0.20 M hydrochloric acid, the other makes SB1 to SB3 with KHP and 0.20 M sodium hydroxide, each in 10 mL total with 8 mL of indicator solution.
SA3 is treated as pure acid form and SB3 as pure base form, since a large excess of acid or base pushes the equilibrium completely to one side. All six vials contain the same total indicator and use the same cuvette, so for any mixture the ratio [HIn]/[In⁻] equals (A − AIn⁻)/(AHIn − A). Substituting gives pKIn = pH + log((A − AIn⁻)/(AHIn − A)).
You apply it to SA1, SA2, SB1 and SB2 at both wavelengths, which yields eight estimates to average.
Where marks are lost
Most errors come from the measurement rather than the algebra. Reading away from the absorption peaks shrinks both differences in the ratio, so tiny noise becomes a large error in the log term.
Zeroing with the wrong blank, leaving fingerprints on the cuvette or trapping a bubble changes A for one reading and shifts the result in opposite directions at the two wavelengths. A misread pH shifts every value by the same amount. Reports are also expected to state the indicator concentration in the vials, about 1.19 × 10⁻⁵ M, and a percent error against a literature value.
What this chapter covers
- 01
Bromophenol blue acid and base forms
- 02
Indicator dissociation constant K_In and pK_In
- 03
Beer-Lambert law A = εbc
- 04
Choosing the two absorption maxima
- 05
Absorbance ratio method for [HIn]/[In⁻]
- 06
Blank, cuvette and wavelength errors
Worked example · free
pK_In of bromophenol blue from an acidic mixture
- 1Assign the reference readings at 592 nm: A_HIn = 0.010 (SA3, acid form) and A_In- = 0.920 (SB3, base form); the mixture reading A = 0.367 lies between them, so the ratio is valid.
- 2Numerator A − A_In- = 0.367 − 0.920 = −0.553; denominator A_HIn − A = 0.010 − 0.367 = −0.357.
- 1[HIn]/[In-] = (−0.553)/(−0.357) = 1.549, and log 1.549 = 0.190.
- 1pK_In = pH + log([HIn]/[In-]) = 3.80 + 0.190 = 3.99.
- 1K_In = 10^(−3.99) = 1.02 × 10⁻⁴.
Key terms
- Acid-base indicator
- A weak acid whose protonated and deprotonated forms have different colours, so the colour of its solution reports the pH of the medium.
- Indicator dissociation constant
- K_In, the equilibrium constant [H3O+][In-]/[HIn] for the indicator ionising in water; its negative log, pK_In, is the pH where both forms are equal.
- Beer-Lambert law
- The relation A = εbc linking absorbance to molar absorption coefficient, path length and concentration, valid for dilute solutions.
- Molar absorption coefficient
- The constant ε, in L mol⁻¹ cm⁻¹, describing how strongly one species absorbs at a given wavelength; it differs between the acid and base forms.
- Absorption maximum
- The wavelength where a species absorbs most strongly; Experiment 4 reads every solution at the peak of the acid form and the peak of the base form.
- Blank solution
- The reference solution used to zero the spectrophotometer, here the KHP buffer, so that only the indicator contributes to the measured absorbance.
Acid Dissociation and Spectrophotometry FAQ
Why is the acid-only solution treated as 100 percent HIn?
Adding 2 mL of 0.20 M HCl raises the hydronium concentration far above K_In, so Le Chatelier's principle drives the dissociation back almost completely. The small leftover In⁻ is negligible compared with measurement noise, which makes SA3 a practical reference for the pure yellow form.
Do I need ε or the path length to find pK_In?
No. Every vial has the same total indicator and is read in the same cuvette, so ε, b and c cancel when you take the ratio of absorbance differences. You only need the mixture reading, the two pure-form readings at the same wavelength, and the measured pH.
Why calculate at two wavelengths if one gives an answer?
The two values act as a cross-check. Agreement means your readings are consistent; if a smudge, bubble or pipetting slip affected one vial, the λ1 and λ2 results drift apart, often in opposite directions, which points you to the faulty measurement.
Exam move
Rewrite equations (1) to (7) from memory and derive the absorbance ratio once yourself so the order of subtraction sticks. Then build a small table with columns pH, A, A − A_In⁻, A_HIn − A, log ratio and pK_In, and fill it for four mixtures at both wavelengths using invented numbers. Check that every row gives the same pK_In.
Finally, pick three error sources, add a deliberate 0.02 shift to one reading, and recompute to see which direction the answer moves at each wavelength.
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