Purpose

To determine the rate law and rate constant for a given reaction through measuring its concentration at different times.

Expected Learning Outcomes

• Convert between units and adapt experimental procedures.
• Use a Gilson pipette to measure volumes.
• Determine the concentrations of solutions at different times using spectrophotometric methods.
• Use graphical methods to determine the rate law and rate constant for a reaction.

Textbook Reference

Tro, Chemistry: Structures and Properties, Ch. 14.5.

Introduction

Rate Laws and Integrated Rate Laws

In a given reaction

[latex]\ce{A} \to \ce{B}[/latex]

As the reaction proceeds the number of molecules (and hence concentration) of reactants will decrease, while the number of molecules (and hence concentration) of products will increase.

In general, the rate of reaction will vary as a function of the concentration of reactants, and hence the rate of reaction (typically) will decrease throughout a reaction.  As you can see from the plot above, as the reaction proceeds and the reactant (NH₃) concentration decreases, the slope of the graph decreases in magnitude, reflecting a decrease in the rate.  The dependence of the reaction rate on concentration is given by the rate law, which would be of the form

[latex]\mbox{rate} = k[\ce{A}]^m[\ce{B}]^n \cdots[/latex]

where k is the rate constant and n is the rate order which can be a positive or negative integer or simple fraction.  The rate law should not vary by concentration

For many reactions of the form

[latex]\ce{A}\to \textrm{products}[/latex]

the rate law would be [latex]\textrm{rate} = k[\ce{A}]^n[/latex], where the rate order n would be 0 (zeroth order), 1 (first order) or 2 (second order). For these cases, one can show that the concentration of reactant as a function of time is given by their respective integerated rate laws

Rate laws may depend on all reactants, catalysts and inhibitors; intermediates are generally not part of it. However, there is a trick we can use to simplify the problem. Assuming that there is no dependence on species other than reactants, If we make all other relevant compounds’ concentrations much higher than the reactant of interest ([latex]\ce{A}[/latex] in the examples here), then the other compounds’ concentrations will not change significantly over the course of the reaction and the concentration terms would form part of the effective rate constant:

Therefore, by plotting relevant plots and determining which of these will give the best straight line plot as shown in the table, you can determine the rate order with respect to the limiting reagent.  By comparing the effective rate constants, we will be able to determine the rate order with respect to the excess reagent just like we did with the method of initial rates.^[1]

The Reaction Being Studied

In this experiment, we are studying the reaction of allura red (FD&C 40 red food coloring dye) with sodium hypochlorite (bleach).

[latex]\textrm{allura red} + \ce{NaClO} \to \textrm{products}[/latex]

This reaction will destroy the chromophore in allura red and hence we can study this reaction by measuring the absorbance over the course of the reaction.

As you may recall from the experiment Absorption Spectrum of Allura Red last semester, according to Beer’s Law, the absorbance of a solution A is related to its concentration c by Beer’s Law

[latex]A = \varepsilon bc[/latex]

where [latex]\varepsilon[/latex] is the molar absorption coefficient^[2] (in M^-1 cm^-1, which depends on the compound absorbing light and the wavelength) and b (in cm) is the pathlength (or the thickness of the sample; in a standard cuvette this is 1 cm).

In CHEM-C 125, you determined the wavelength at which allura red absorbs the most and the molar absorption coefficient.^[3]  In this experiment, you will measure the absorbance of the reacting mixture as a function of time.  You will be able to substitute this back into Beer’s Law to find the concentration at each time.

In general, the rate law for this reaction will be

[latex]\mbox{rate} = k[\ce{OCl-}]^m[\textrm{allura red}]^n[/latex]

where m and n are the rate orders with respect to hypochlorite and allura red respectively. In this reaction, as the concentration of sodium hypochlorite is much higher than that of allura red, as mentioned above the concentration-time relationship will relate only to the concentration of allura red.  Therefore, for an initial concentration of hypochlorite of [latex][\ce{OCl-}]_0[/latex], the observed rate law would be

[latex]\textrm{rate} = k_{\textrm{eff}} [\mbox{allura red}]^n[/latex]

where [latex]k_{\textrm{eff}} = k[\ce{OCl-}]_0[/latex].

We therefore expect the different trials to follow zeroth, first, or second order kinetics with respect to the concentration of allura red. However, the rate constants may be different. As a result, by comparing the values of [latex]k_{\mbox{obs}}[/latex] for different trials, you can determine the complete rate law and the rate constant for this reaction.

Procedure

Preparing the Stock Solution of Sodium Hypochlorite

You will be provided with a 6% by mass aqueous solution of sodium hypochlorite.^[4]. From this, you will prepare 10 mL of a 250 mM sodium hypochlorite solution.  You will have a 1000 μL Gilson pipette and the graduated cylinders in your drawer.

Calculations

You may want to attempt these before class.

1. Calculate, based on what you have learnt about concentration units in CHEM-C 106, find the molarity of ClO^– in the 6% by mass solution.  The density of the solution is 1.11 g/cm³
2. Hence, determine how best to make this solution.  You will need to do a dilution calculation to figure out the volume of 6% by mass sodium hypochlorite solution needed.

Lab Work

3. Prepare the 250 mM sodium hypochlorite solution as described.  Be sure to document all steps taken to make this solution; you will be required to write this procedure up similar to how you would write up a formal report.

Preparing the SpectroVis Plus

4. From your laboratory notebook, find the absorption wavelength used and molar absorption coefficient found for allura red in the Absorption Spectrum of Allura Red experiment.  You will need this to analyze the data for this experiment.
5. Prepare a 25 mM solution of sodium hypochlorite in a small test tube by dispensing appropriate volumes of the stock sodium hypochlorite solution and deionized water.  This will be the blank solution.  Place this cuvette in the SpectroVis Plus.
6. On your device, launch Vernier Spectral Analysis. Following the directions provided in the Appendix, begin an absorbance vs time (kinetics) experiment, using the blank cuvette prepared above to calibrate the SpectroVis plus.
7. Enter the wavelength you previously used for creating the Beer’s Law plot of allura red.

Obtaining Kinetics Data

For this experiment, you will study the kinetics with the following mixtures.  You will mix the solutions in a test tube and then dispense an aliquot to measure in the SpectroVis Plus.

You will repeat each set of conditions at least two times.  For each set of conditions:

8. Measure out the deionized water and allura red required for the reaction in a small test tube.^[5] Place the small test tube in the SpectroVis plus.  Be sure to record the concentration of allura red from the bottle.
9. Measure out the sodium hypochlorite solution you prepared in a Gilson pipet.

10. Add the sodium hypochlorite solution into the test tube.  At that instant, click or tap “Collect” on the computer/device and mix the solution by pipetting the liquid up and down.
    • Try and not have the pipet reach near the bottom where the light beam passes).
11. Collect the data for two minutes.
12. Export the data as a CSV file (which can be read in Microsoft Excel or any other spreadsheet program).
    • Be sure that you use a descriptive file name for your data, and that both lab partners have access to copies of the data (e.g. email a copy to your lab partner).

At the end of this experiment, you should have results from four trials: two for each of the conditions listed above.

Waste Disposal

Dispose of all of the waste from this experiment down the drain with plenty of water.

Data Analysis

For each timepoint, by rearranging Beer’s Law, we can show that the remaining concentration of allura red at time t is

\begin{equation}
[\mbox{allura red}]_t = \frac{A_t}{\varepsilon b}
\end{equation}

and given the absorbance at a given time t, path length (1 cm), and the molar absorptivity you found previously, you can find the molarity of allura red at any given time.  From this, calculate ln[allura red] and 1/[allura red] as well.

Make the following plots:^[7]

• Zeroth-order plot: [allura red] vs time
• First-order plot: ln[allura red] vs time
• Second-order plot: 1/[allura red] vs time

Plot all solutions on the same axes (so there would be three graphs).  Your zeroth order graph should look something like this:

To do this, start by plotting the data series for one trial.  Then, for the other solutions, go to Chart Design – Select Data and add additional data series – one for each trial.  For each trial, the effective rate constant [latex]k_{\textrm{eff}}[/latex] would be the absolute value of the slope of that plot.  Average the trials for each condition to find [latex]k_{\textrm{eff}}[/latex] for that given condition.

As mentioned above, in this experiment, the slope is equal to [latex]k_{\textrm{eff}} = k [\ce{OCl-}]^m[/latex], and therefore if the rate order with respect to [OCl^–] is not zero then the k values would be different.  Compare the k values to determine the rate order with respect to [OCl^–] using the method of initial states.  Remember that [OCl^–] under condition 1 is twice that under condition 2.

Based on the slope values and the concentrations of [OCl^–], determine the actual rate constant k based on the average result of all four trials.