 # Determining the ka of an acid-base indicator

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Determining the ka of an acid-base indicator
Experiment 6

Indicator HIn + H2O ↔ In- + H3O+ Red blue Ka = [H3O+] [In-]/[HIn]
[H3O+] = Ka [HIn]/[In-] (-log [H3O+]) = (-log Ka) + (log [In-]/[HIn]) pH = pKa + log [In-]/[HIn]

Determining Ka Ka = [H3O+] [In-]/[HIn]
Adjust pH slightly and measure the concentration of all three species, independently H3O+ (pH meter) In- and HIn (spectroscopy)

Ka = [H+][In-]/[HIn]

Quantitative Spectroscopy
Beer’s Law Al1 = el1bc e is molar absorptivity (unique for a given compound at l1) b is path length c concentration

Standard Practice Prepare standards of known concentration
Measure absorbance at lmax Plot A vs. concentration Obtain slope Use slope (and intercept) to determine the concentration of the analyte in the unknown

Typical Beer’s Law Plot

Spectroscopy Indicators give fairly broad visible absorption spectra
Blue solution absorbs in the red region Red solution absorbs in the blue region But there is usually some significant overlap

Absorption measurement
Must make measurements at two wavelengths Al1 = el1HInbcHIn + el1InbcIn- Al2 = el2HInbcHIn + el2InbcIn- Must have the slopes of four Beer’s law plots. Then you have two equations with two unknowns.

The four slopes Measure standard solutions of Indicator adjusted to high pH (three pH units above pKa) [In-]/[HIn] = 1000 Measure standard solutions of Indicator adjusted to low pH (three pH units below pKa) [HIn]/[In-] = 1000 These solution will be prepared and measured to produce the four Beer’s Law Plots (each set at both wavelengths)

In the lab Prepare Indicator solution adjusted to the proper pH
Measure its pH and Absorbance at 430 nm and 565 nm Adjust pH with dilute HCl or NaOH by .2 pH units and remeasure Continue until you have five measurements within 1.0 pH units above and below the starting pH

Spreadsheet Use data to produce four Beer’s Law Plots
Determine slopes of Beer’s Law Plots Calculate [H+] from the pH Use slopes to solve the system of two equations for [HIn] and [In-] Solve for Ka, Ka = [H+][In-]/[HIn] Solve for pKa, pKa = -logKa Calculate averages and 95 % CL