[This lab was adapted from "A Simplified Method for Finding the pKa of an Acid-Base Indicator by Spectrophotometry", Journal of Chemical Education, Vol. 76, p 395, March 1999.]
The magnitude of an equilibrium constant, Keq, expresses the equilibrium position for a chemical system. Most acid-base indicators can be considered weak acids and their ionization can be represented as: . The equilibrium expression would be:
It is a common practice to quote the pKa (the -log of the Ka) of indicators and weak acids. In this experiment you will take a simplified approach to finding the pKa of an indicator. This approach will not require that the spectroscope be standardized and an absorbance vs. concentration plot obtained as in past labs. The pKa will be the y-intercept of a plot of pH vs. log ; where AHIn is the absorbance of HIn at , AIn is the absorbance of In- at , aHIn is the absorbtivity of HIn, and aIn is the absorbtivity of In- .
Taking the log of equation 1 above gives:
According to the Beer-Lambert Law
Substituting equations (3) and (4) into equation (2) gives:
If we now let equal the absorbance at and respectfully, for solutions where [In]=[HIn]. equations (3) and (4) give:
Dividing equation (6) by equation (7), rearranging , and comparing to equation (5) gives:
Combining equations (8) and (5) gives
It can be seen that a plot of pH vs. will be linear with a slope of one (1) and a y-intercept equal to the pKa of the indicator.
The abosorbance of the indicator at both at and will be measured at five different pH values. A plot of pH vs. will be constructed. The value of k can be calculated by taking and absorbance readings at after the equilibrium has been shifted nearly 100% to the right by the addition of NaOH, and after the equilibrium has been nearly 100% to the left by the addition of HCl.
1.Your instructor will assign an indicator to us. Determine and by taking a sample of the indictor to which a few drops of 1M NaOH has been added, and measuring the absorbance of the solution at wavelengths in the range of 380 nM to 780 nM in 10 nM increments using distilled water as the blank. Construct a plot of absorbance vs wavelength. The wavelength at which maximum absorbance occurs is . In a similar way determine by replacing 1 M NaOH with 1 M HCl.
2. Prepare 250 mL of the indicator solution by consulting the following chart.
3. Transfer 50 mL of the solution to each of five beakers. Measure and record the pH of one of the solutions and adjust the pH of solutions by adding either 1 M NaOH or 1 M HCl to five different pH values in a range given by the following chart.
4. Measure the absorbance of each of the solutions prepared in step 3 above both at and . These wavelengths were determined in step 1.
5. Adjust the pH of one of the samples used in step 4 to 10 or 11 by adding a few drops of 6 M NaOH and measure the absorbance. This will be .
6. Adjust the pH of a second indicator sample in step 4 to 1 or 2 by adding a few drops of 12 M HCl and measure the absorbance. This will be .
7. Compute which will be the value of k in equation (9) above. Construct a plot of pH vs. and determine the pKa . As stated in the discussion above the pKa of your indicator will be the the y-intercept. of this plot.
1. Determine the pKa of your indicator.
2. Consult the article referenced in the discussion. How does your result compare to the accepted pKa? What is the relative error?