Kinetics: Fading of Indicators

Goals

• To design aspects of a procedure for a kinetics study
• To determine the overall rate law for a reaction using the pseudo-order method
• To find the value of the rate constant

The rates of chemical reactions depend in general on several factors. First and most important is the identity and inherent chemical reactivity of the reactants. Second, reaction cannot take place unless the reacting molecules collide with each other. The frequency of such collisions depends upon the concentrations of the reacting species (the number of molecules of each reactant in a fixed volume). Third, reaction rate depends on how energetic the molecular collisions are. Because molecular kinetic energy depends strongly on the temperature through the Maxwell-Boltzmann distribution, reaction rates often vary quite dramatically with temperature.

You may have noticed that the color of a solution titrated to a phenolphthalein end point fades with time. Indicators such as phenolphthalein (P^2-) and bromophenol blue (BP^2-) lose their color in basic solution due to structural changes that occur when excess OH^- attacks the molecules (reactions 1 and 2).

In this experiment, we will study the kinetics of these reactions. The rate expressions 1 and 2 are expected to have the form of equation 3:

[In] is the concentration of indicator, [OH^-] is the concentration of hydroxide ion, k is the rate constant, m is the order with respect to indicator and n is the order with respect to OH^-. To determine the rate law, the unknowns k, m, and n must be found by experiment (remember that in general the exponents are not the same as the coefficients of the balanced equation.)

To perform a rate study, you need a way to monitor the concentration of at least one reactant. For colored species, a convenient way to follow changes is to monitor the absorbance at an absorbed wavelength, since A is directly proportional to the concentration of the colored species via Beer's Law (equation 4):

Here e is the molar absorptivity, l is the pathlength through the cell and C is the concentration of the species of interest. Since molar absorptivity is constant for a given molecule at a specific wavelength and the pathlength is fixed by the cell, absorbance, A, varies only with C, the concentration of absorbing species. Therefore, A may be substituted for concentration in the data analysis. In reactions 1 and 2, the indicator reactants are colored and all other participants are colorless, so the kinetics of both reactions may be followed by watching the absorbance of the indicator reactant decay with time as reaction proceeds.

Reactions 1 and 2 each involve 2 chemically distinct reactants. This is a common situation; most reactions involve more than 2 reactants. A general version of such reactions is in (5):

For such reactions, it is probable that the rate will depend on two or more concentrations; that is, that the rate law will have the form of equation 6.

There are several experimental options for determining the rate law in this situation. First, it might be possible to use the initial rate method, in which the initial concentrations of the reactants are systematically varied and the changes in initial rate are compared to the changes in the initial concentrations. Alternately, the pseudo-order method may be used. In this approach, the concentrations of all reactants other than the one being measured are made at least 10 times greater than the concentration of the measured reactant. Then only the concentration of the measured reactant will change significantly during the course of the reaction; the other reactants have such large concentrations that they essentially do not change as reaction proceeds. Because these concentrations are constant, they may be "lumped in" with the rate constant to give a so-called pseudo-order rate law:

Thus the reaction will behave as if it is n-order in reactant A; the dependence of rate on the other reactants is now incorporated in the rate constant k'. The [A]-time data may now be plotted according to the integrated first- and second-order rate equations (ln[A] versus t for first, 1/[A] versus t for second) to determine whether n is 1 or 2. m and q may be determined by carrying out other pseudo-order studies using different (but still large) concentrations of B, D, etc. For each study, a value of k' will be obtained. The dependence of k' on powers of [B] and [D] can then be discovered by making appropriate plots.

Before coming to class, you should design in detail a procedure for carrying out a kinetics study of either reaction 1 or 2 using the pseudo-order approach. Your notebooks will be checked for this procedure when you arrive. See the Experimental section below for guidelines to use in designing your procedure. The well-prepared student, one who desires to make the instructor very happy, will design the procedure and discuss it with one of the instructors PRIOR TO the laboratory meeting. Such a student can then begin the kinetics study immediately upon arrival in lab.

Focus Questions

1. Graphically analyze each kinetics run; what is the order of the reaction with respect to indicator? What is the pseudo-order rate constant?
2. Graphically analyze the pseudo-order rate constants; what is the order of the reaction with respect to OH^-?
3. What is the value of the true rate constant for your reaction?
4. A pseudo-order rate study requires that the reaction solution be "flooded" with all reactants except one. In this study, which reactant(s) are flooded? Which one is not?

• stop watch
• spectrometer, Spectronic 20 or other
• spectrometer cuvets
• 2 25- or 50-mL mixing beakers
• 1, 2, and 10 mL graduated pipets
• syringe pipet pumps
• 4 M NaOH
• 4 M NaCl
• bromophenol blue stock solution, 0.5 g/L in water
• phenolphthalein stock solution, 1 g/L in ethanol

Record all plans, procedures, and results in your notebook.

In class, you will be assigned one of the indicators to study. General guidelines for the kinetics studies are given below.

• For bromophenol blue:
  • Progress of reaction will be monitored at a wavelength of 590 nm, where bromophenol blue has a l_max.
  • The total volume of reaction solution will be 5 mL for each run.
  • 0.02 mL of stock indicator solution will be used in each reaction solution.
  • At least 5 hydroxide concentrations in the range between 0.1 and 0.8 M should be studied.
  • The sum of the concentrations of NaOH and NaCl must be 0.80 M in all reaction solutions.
  • Distilled water should be used to make up the total volume of each solution to 5 mL.
  • Each kinetics run should be carried out in duplicate.
• For phenolphthalein:
  • Progress of reaction will be monitored at a wavelength of 560 nm, where phenolphthalein has a l_max.
  • The total volume of reaction solution will be 5 mL for each run.
  • 0.01 mL of stock indicator solution will be used in each reaction solution.
  • At least 5 hydroxide concentrations in the range between 0.01 and 0.1 M should be studied.
  • The sum of the concentrations of NaOH and NaCl must be 0.80 M in all reaction solutions.
  • Distilled water should be used to make up the total volume of each solution to 5 mL.
  • Each kinetics run should be carried out in duplicate.

Prior to class, you should have selected 5 hydroxide ion concentrations in the indicated range and should have calculated the volumes of 4 M stock NaOH solution and 4 M stock NaCl solution to use for each run. You should discuss your calculated volumes with the instructor prior to starting the experiment.

A particular kinetics run should be carried out generally as follows. The most crucial aspect of the procedure is to obtain quick and effective mixing of the reactants in a short period of time. This is accomplished in steps 3 and 4 of the procedure, which must be performed smoothly and rapidly.

• Pipet 0.02 mL of indicator stock solution into a clean, dry 25- or 50-mL beaker.
• Into a second clean, dry 25- or 50-mL beaker, pipet
  • x mL of 4 M NaOH stock solution
  • (1.0-x) mL of 4 M NaCl stock solution
  • 4.0 mL of distilled water
• Rapidly and smoothly pour the contents of the second beaker into the first beaker, simultaneously start the stop watch, and swirl the first beaker rapidly twice.
• Smoothly and rapidly pour the reaction solution into a clean, dry cuvet.
• Wipe the outside of the cuvet if necessary to dry and insert, marks aligned, into the Spectronic 20.
• Record an absorbance-time data point at the 20-second mark and as frequently thereafter as needed to collect at least 8 absorbance-time points during the time it takes for the absorbance to fall to at most half of the initially measured value.
• When you are ready to terminate the run remove the cuvet from the spectrometer.
• Clean mixing beakers and cuvet as follows
  • Rinse vigorously with tap water.
  • Rinse with distilled water.
  • Dry completely.
• Wipe down the outsides of all transfer pipets.
• Return to step 1 for the next run.

Clean-up. When you have finished all of your work:

• Dispose of left-over solutions and reaction mixtures as indicated below.
• Clean glassware by recommended procedures, shake off excess water, and place in the drying oven.
• Clean and return all borrowed equipment to the instructor before leaving lab.
• Clean up your work area before leaving lab.

Disposal Methods

Solutions may be washed down the drain with excess water unless otherwise directed by the instructor.

1. "Kinetics of the Fading of Phenolphthalein in Alkaline Solution," by Lois Nicholson. Journal of Chemical Education, 1989, 66, 725-726.

2. "Fading of Bromophenol Blue," by Randall Winans and Charles Allen Brown. Journal of Chemical Education, 1975, 52, 526-527.

Preparation Questions