I.Graphical Determination of Reaction Order for Crystal Violet Dye

Chemistry 212 LabFall 2011

Chemical Kinetics I, A Survey:

I.Graphical Determination of Reaction Order for Crystal Violet Dye

II.Determination of the Complete Rate Law

Purpose

For a simple reaction system consisting of an organic dye and aqueous base, determine the order of the reaction with respect to the organic dye. This general method involves monitoring a reaction by visible spectroscopy, and obtaining data sets of percent transmittance versus time. Later processing of these data sets will lead to the unambiguous assignment of reactant order by a graphical method.

Introduction

Kinetics is a large and diverse field of study within chemistry. It is primarily concerned with discovering, and if possible controlling, those factors that govern the rates of reaction. Starting with the relatively simple reaction system A→ B, immediately two ways to determine rate become apparent:

• Determinethe rate at which the reactant, A, is consumed, or

• Determinethe rate at which the product, B, is formed

Such a simple analysis leads to the construction of a general rate expression for this system, mathematically expressing the two general methods outlined above:

This general rate expression can be read in terms of either A or B. For the reactant A: "Rate is equal to minus the change in the concentration of A over the change in time." For the product B: "Rate is equal to the change in the concentration of B over the change in time." This treatment allows the reaction rates to have positive values for [A] and [B], and for the two rates to be expressed in terms of one another.

What this general expression really says mathematically, is something that is intuitively obvious physically: that the rate at which product B forms cannot be any faster than the rate at which reactant A is being consumed to produce it. General rate expressions become more complicated, but keep these same features, when a reaction system under study becomes more complex.

Below isa more complicated general reaction equation, and a corresponding general rate expression for that reaction:

The introduction of reaction coefficients brings one additional term to each reactant and product in the general rate expression.

Relevant Background Information:

The more complicated general rate expression above can still be read the same way as the simple one, and has the same utility. Being able to measure the change in concentration as a function of time for any single reactant or product allows the measurement of the rate of change over time for any of the other reactants or products. In this experiment, the disappearance of the color of one of the reactants can be used, if one so desires, to characterize the rates for all chemical species in the reaction system.

Thus the design of this experiment is to monitor, by visible spectroscopy, this disappearance of color, and convert that information into a general expression for how a particular reactant behaves. One can assume the disappearance of color to be related directly to the consumption of the reactant and an appearance of product. You will also determine the order of reaction with respect to this consumed reactant, which becomes part of what is called the rate law for the reaction.

You will be concerned with how the change in concentration versus time can be turned into a reactant order for a given reactant. Usually reaction orders have integer values, or zero. They can also be fractional, and can even be negative. The reaction under study is one of the type A(color) → B(colorless), and the rate can be conveniently expressed in terms of disappearance of color:

The reaction order, x, can be found in one of two ways. In the first general method, the rate can be found by varying the concentration of A. For example, a 'baseline' concentration of 1 for A, yields a corresponding 'baseline' rate, also of 1. If you were to then double the concentration of A to 2, assuming all other factors remain the same, the rate of reaction could again be measured. The dependence of changing the concentration of A on rate could be measured directly, and the order solved mathematically by:

If the rate were observed to increase by a factor of two, this expression simplifies to:

The reaction order, x, is therefore equal to 1. The reaction can then be said to be, "first-order with respect to A." Convince yourself that if doubling the concentration of A led to no change in the observed rate, that the reaction order x would be 0. Also, if doubling the concentration of A led to a factor of 4 increase in rate, that the reaction order x would be 2.

In the second general method, the use of integrated rate law expressions is used to determine reaction order. The results for zero-, first-, and second-order reactions are presented in the following table.

Zero-Order First-Order Second-Order

Rate Law k[A]0 k[A]1 k[A]2

Integrated Rate Expression[A]t = kt + [A]0 ln[A]t = kt + ln[A]0 1/[A]t = kt + 1/[A]0

Linear graph[A] versus time ln[A] versus time 1/[A] versus time

Slopek kk

Relevant Chemistry and Experimental Details

I. Determination of Reaction Order with respect to Crystal Violet Dye

The reaction of the organic dye crystal violet with aqueous base is a relatively simple one, whose progress can be tracked over time by the disappearance of a purple color:

crystV(aq) + OH(aq) ------> crystVOH(aq)

(purple) (colorless)

A general rate expression for this reaction can be written:

The complete rate law for this system is:

The disappearance of the purple color, indicating the consumption of the crystal violet dye, can be monitored over time with a Spectronic 20 visible spectrometer. This instrument is able to determine how much of a given incident beam of light is being allowed through a sample at a given wavelength. The more color, the less light passing through. As the reaction proceeds, and the color fades, more of the incident light is allowed through. The experimental procedure asks that readings from the spectrometer be taken in percent transmittance, which should be seen to increase as a function of time. This would be indicative of an initially "rich" color fading over time, thus allowing more of the incident light to be 'transmitted' through it. Percent transmittance readings should be converted to absorbance with this equation:

Absorbance = log(%T/100)

Absorbance can be related to concentration (although the exact concentration of the crystal violet dye is neither found nor needed, as is shown shortly) using the Beer-Lambert Law.

Use of the Beer-Lambert Law -- Exploiting the Absorbance/Concentration Relationship

The Beer-Lambert Law is a simple relationship between the amount of incident light a given analyte absorbs as a function of the concentration of that analyte:

A = 0 b c

The terms 0 (extinction coefficient) and b (path length) are constant under the conditions of this experiment, allowing the further simplification

absorbance(is directly proportional to) concentration

Without this simplification, it would be necessary to determine the actual concentrations of crystal violet dye at every time measurement. Since the absorbance is directly proportional to the concentration of crystal violet dye, the data sets collected will actually be of absorbance versus time information. You will assume this proportionality is true, and that your measured absorbances will be treated as if they were actually concentrations of crystal violet dye. It does not change any of the attributes of the integrated rate laws to use absorbances in place of concentrations under the conditions of this experiment.

Additional Treatments of Experimental Data: Complete Rate Law and Activation Energy

Determination of the Complete Rate Law

Once the order of reaction with respect to crystal violet dye has been determined, it is possible to find the complete rate law by also determining the order of reaction with respect to aqueous hydroxide, OH. The method used takes advantage of two facts:

• the rate constant, k, is unchanged if the temperature is unchanged

• the concentration of crystal violet dye is constant under the experimental conditions

The rate law can accordingly be simplified to a form such as this:

original rate law:Rate = k [crystV]x [OH]y

modified rate law:Rate = k' [crystV]xwhere k' = k [OH]y

The new symbol k' assumes the crystal violet dye concentration, and the rate constant, are in fact constant. It should now be possible, by varying the hydroxide ion concentration, to determine the exponent y, the order of reaction with respect to hydroxide. It is a consequence of using the modified rate law that now, the actual rate constant, k, is dependent on hydroxide ion concentration. The slope of the graph prepared that reveals the reaction order with respect to crystal violet dye is in fact this term k', and not the actual rate constant, k. Therefore it is necessary to determine the reaction order with respect to crystal violet dye before attempting to determine the order with respect to hydroxide ion concentration. This simplification cannot be made and used without knowing the exponent x.

If, therefore, a series of experiments were run in which the hydroxide concentrations were varied, a dependence of this variance on the rate would be obtained directly, and would reveal itself as hydroxide ion-dependent values for k'. If two such experiments with varying hydroxide ion concentrations were run (denoted by "[OH]1y" and "[OH]2y") the order with respect to hydroxide ion could be found with the following relationships.

k1' k [OH]1y

----= ------

k2' k [OH]2y

which can be simplified to (k1' / k2' ) = ([OH]1 / [OH]2)y. This method has the additional benefit if being able to provide a value for the actual rate constant, k, with just a little extra math. It is not necessary to know the rate constant to construct the complete rate law, only the exponents.

Since this method uses actual experimental numbers, and does not rely on a fitted straight line, it is important to point out that while most reaction orders are whole numbers, it is unlikely actual data will lead directly to a whole number result. When considering which order to assign a given reactant by this method, select the nearest whole number for the reaction order. An answer of 1.124, for example, is best rounded back to 1, and so on.

Experimental Procedure

Collection of %T versus Time Data, Constant Temperature

Data sets are to be collected individually, and for two different concentrations, of aqueous sodium hydroxide solution with crystal violet dye. Standard concentrations might include 0.025 MNaOH, and 0.0125 MNaOH. Be sure to check the reagent bottles in your laboratory section for the exact concentrations available.

Begin by turning on a Spectronic 20 and letting it warm up for at least 15 minutes. Be sure the wavelength indicator is set to 540 nm, and do not adjust it again for the remainder of the experiment. When the instrument has warmed up, use a clean small test tube from your drawer, filled 2/3 with the first NaOH solution you plan to use, as a blank to set 0% and 100% transmittance.

You will be taking a %T reading every minute for at least 15 minutes, so it may be convenient to wait until the room clock's second hand approaches 12 before beginning the following procedure. Add one single drop of the crystal violet dye solution, invert to mix the contents of the test tube, and carefully place the tube into the instrument. When the drop hits the surface is your "time zero", and one minute later you will begin taking readings of %T. Leave the sample tube in the instrument throughout the data collection process. Obtain readings of %T every minute for at least 15 minutes. Record %T values to one decimal place, as this allows you to convert to absorbance and retain three significant figures.

When you have taken your 15th and final reading, remove the sample tube from the instrument and prepare to re-zero the instrument with a new NaOH blank in another test tube. Then repeat the entire 15-minute data collection a second time.

Remember, everyone will be required to measure a full 15-minute data set on two different NaOH samples of differing concentration. The real work of this experiment comes in the data analysis, only some of which you will be required to do in the laboratory.

When you and your partner have finished collecting data, turn off the instrument, discard your samples down the drain, and carefully clean the test tubes you used. Enter whatever data is required into the 212 database before you leave for the day.

Ater consulting the table of reaction orders and their attributes, the order of the crystal violet dye should make itself apparent if, after collecting the absorbance and time data, three graphical plots are prepared:

• One graph of absorbance vs. time

• One graph of ln(absorbance) vs. time

• One graph of 1/absorbance vs. time

Only one of these should be a straight line. This is therefore a direct, graphical determination of the order of reaction with respect to crystal violet dye.

Data Tables -- Percent Transmittance versus Time, Constant Temperature

Concentration of NaOH Solution______

Concentration of Crystal Violet Dye Solution______

Room Temperature______

(assumed to be reaction temperature)

Trial #1Trial #2

Time(min)%TTime(min)%T

1 ______1 ______

2 ______2 ______

3 ______3 ______

4 ______4 ______

5 ______5 ______

6 ______6 ______

7 ______7 ______

8 ______8 ______

9 ______9 ______

10 ______10 ______

11 ______11 ______

12 ______12 ______

13 ______13 ______

14 ______14 ______

15 ______15 ______