CHEMICAL KINETICS TO DYE FOR

Chemical Kinetics is the branch of chemistry which is concerned with the study of the rate of chemical reactions.  The rate of a reaction is a measure of its speed.  Consider the hypothetical reaction

E + 2B ®  2C + D    (1)

The rate of formation of C is

(2)

where [C]_f and [C]_i are the concentrations of C at times t_f and t_i , respectively. The symbol D stands for "change".  The rate of formation of C is the change in the concentration of C over the time interval Dt.  Similarly, the rate of formation of D is

(3)

The rates of consumption of A and B are

	(4)
	(5)

The negative signs in equations (4) and (5) arise from the fact that although the  rates are positive numbers, the   concentrations of the reactants decrease with time, and their changes are negative. From the stoichiometry of reaction (1) we see that the consumption of 1 mole of E results in the consumption of 2 moles of B and the formation of 2 moles of C and 1 mole of D.  B is consumed twice as fast as A, and C is produced twice as fast as D. Thus, the relationships between the rate expressions in equations (2)-(5) is

(6)

The rate of the reaction, Rate_RXN can be expressed either in terms of the rate of disappearance of reactants or the rate of appearance of products:

(7)

In general, the rate of a reaction depends on the concentration of the reactant as follows:
 

Equation (8) is the rate law for the reaction, and it shows that the rate is proportional to the product of the concentrations of the reactants   each  raised to some power x or y. The proportionality constant, k,  is the rate constant and depends only on temperature.   The exponents x and y determine the reaction order with respect to A and B, respectively.  The sum of the exponents is the overall order of the reaction. 

 For example, if x = 1, and y = 2, then the reaction is said to be first order in A,  second order in B, and third order overall. 

The values of the exponents in the rate law must be determined by experiment, and cannot be deduced from the stoichiometry of the reaction.

Rate Laws  involving only one reactant: For the reaction

E ® Products

the rate law is 

If x = 1, the reaction is first order, and

Using the methods of calculus,  this equation yields equation (10), which is an example of an integrated rate law.

(9)

In equation (10),  [E]_o is the initial concentration of E, and [E] is its concentration at time t.  The integrated rate law gives the concentration of reactant as a function of time.  Integrated rate laws for second and zero order reactions are given below.

Order	Rate Law	Integrated  Rate Law
zero			(10)
First			(9)
Second			(11)

The integrated rate laws can be used to determine the order of a reaction.  For example, if a reaction is first order, equation (9) predicts that a plot of ln([E]) versus time is linear with a slope equal to - k. If the reaction is zero order, equation (10) predict that a plot of [E] versus time is linear with a slope equal to -k.  Finally, equation (11) predicts that if the reaction is second order, a plot of 1/[E] versus time is linear with a slope equal to k. This is summarized in the figure below.

Figure 1.

The Method of Isolation  is an experimental technique for determining the order of a reaction.  In this method, one of the reactants is present in large excess relative to the other.  For example, consider the reaction

E + B ® C + D

Suppose that the initial concentrations of E and B are 1.000 x 10^-4 M and 0.2000 M, respectively.  We see that [B] >>[E]. If the reaction goes to completion,  all of E is used up since it is the limiting reactant, and the concentrations of both reactants will have decreased by  1.00 x 10^-4 M.  The final concentration of B at the end of the reaction is 0.2000 - 1.000 x 10^-4 M = 0.1999 M, a  decrease of only 0.05 %.  The concentration of B remains essentially constant during the reaction,  and equation (8) becomes:  

where

 The only variable in equation (12) is the concentration of E, and the order with respect to E can be determined by plotting each of the quantities: [E],  ln([E]), and 1/[E] versus time, as in Figure 1, and determining which plot is linear. If [E] versus time is linear then the order with respect to E is zero, etc. As discussed above, k_o can be obtained from the slope of the linear plot.

The order with respect to B can be determined by using different excess concentrations of B, and observing the effect on k_o.  For example, if doubling the concentration of B doubles k_o then in equation (13), y = 1, and the reaction is first order in B.  On the other hand, if doubling the concentration of B causes k_o to increase by a factor of 4, then y = 2, and the reaction is second order in B.

Why is the rate law important?  The rate law of a chemical reaction gives us insight into how the reaction occurs at the molecular level.  It helps us to understand what the molecules are doing as the reaction occurs.  Many reactions occur through a sequence of steps called a reaction mechanism.  Consider the overall reaction

E + 2B ® 2C + D

with the observed rate law:

Rate = k[E][B]

A possible mechanism, consistent with this rate law is:

Each step in the mechanism is a one-step reaction, or elementary reaction, and describes a molecular event. In this mechanism, one molecule of E reacts with one molecule of B to make one molecule each of X and D.  One molecule of X then reacts with one molecule of B to make two molecules of C. For an elementary reaction the order is equal to the molecularity, the number of reactant molecules participating in the elementary reaction.  Reactions (a) and (b) are both bimolecular, and their rates are:

Rate_a = k_a[E][B]
Rate_b = k_b[X][B]

One criterion for a  mechanism is that the sum of the elementary reactions must equal the overall reaction. This mechanism meets that criterion.  A second criterion is that the mechanism be consistent with the observed rate law.  In this case,  the mechanism contains a slow rate-determining step.  This step determines the rate of the overall reaction, and the measured rate must be that of reaction (a). That is,  the rate law should be first order in each of the reactants E and B. The observed rate law is in agreement with this prediction.

The rate law does not prove that this is the correct mechanism.  Other mechanisms can be written which are consistent with the observed rate law.  Additional experimental evidence, such as the detection of the presence of the reaction intermediate, X,  would be needed to prove that the above mechanism is the correct one.  

Purpose 

  In  this experiment you will study the kinetics of the reaction between sodium hypochlorite, NaOCl, and a food dye FD&C Blue #1.  Sodium hypochlorite is the active ingredient in commercial bleaches, such as Clorox and Purex.  The reaction is 

NaOCl + FD&C Blue # 1 ® Colorless products              (14) 

The structure of FD&C Blue #1 is shown below.

The rate law for reaction (15) is

The purpose of the experiment is to determine the order with respect to NaOCl and Blue #1, that is the values of x and y in equation (15).   The Method of Isolation will be used with an excess of NaOCl.  If NaOCl is present in large excess, its concentration is essentially constant, and we define a new constant, k_o,  where k_o =k[NaOCl]^x , and equation (15) then becomes

All of the reactants and products are colorless except Blue #1.  The blue color of a solution of blue # 1 is due to the fact that the dye molecules absorb a portion of the visible spectrum.  That part of the spectrum which is not absorbed is transmitted and gives the solution its blue color. As shown in  Figure 2,   The dye molecules absorb orange light ( wave length of about 630 nm).

The concentration of the dye can be determined by measuring the amount of light absorbed by the reaction mixture as a function of time.  The measurement of light absorption will be accomplished with a colorimeter.  See Figure 3.

Figure 3

In the colorimeter, orange light  from the light source passes through the sample solution and reaches the light detector.  The light detector measures the intensity of the light reaching it.  In this case, the only light absorbing substance in solution is the dye, the amount of light absorbed by the solution is a measure of the dye concentration. The higher the concentration of dye in the solution the lower the intensity of the light striking the detector.  The amount of light absorbed by the solution is measured in terms of absorbance, A.  The absorbance is defined as

A  = -log(I_t/I_o)

where I_o is the intensity of the light reaching the detector when the cell is filled with pure water, and I_t is the intensity observed when the cell contains the reaction mixture at time t.  The absorbance of the solution is directly proportional to the concentration of the dye.  That is

where C  is a constant.   

To determine the order with respect to Blue #1 you will measure the absorbance of the reaction mixutre versus time using a colorimeter interfaced with a computer.  The computer will save the data for later analysis.  Unfortunately, the colorimeter does not measure absorbance directly, but instead measures percent transmission or %T.  It will be necessary to convert  absorbance to %T.   This can be accomplished using the relation:

(18)

Stockroom: Things for each group to borrow and return on the same day.

• Clear cuvet
• Black cuvet
• Black film can

Procedure

1. Part 1, Calibration of Colorimeter:  
   Prepare 20 mL of a 20% bleach solution by mixing 16 mL of deionized water and 4 mL of commercial bleach in a beaker.  You will need this solution in this part and in  Part 3a.
   Click on the Labworks icon, click on Calibrate, click on % Trans A,   Place the black-taped cuvette in the colorimeter, and put the cover over it. On the computer screen, place the cursor in the "set zero box", and, when the reading stabilizes,  press enter . Replace the taped cuvette with one containing the 20 % bleach solution, prepared above, and cover it.  Click in the "set 100% value" box. When the reading stabilizes  press enter.  Click OK.
   

2. Part 2, Measurement of percent transmission of the stock blue #1 solution:
   Click on Design and then on EZ Progam.  Under 3 choose Time, and under 4 choose Color A.  Click on Aquire.  Fill the cuvette with the stock blue #1 solution,  place it in the colorimeter, and cover it.  Click on start.  The percent transmission of the solution will appear on the screen.  When the reading stabilizes record it in your notebook.
   

3. Part 3, Measurement of %T versus time for reaction (15):  
   a)  Click on Design, EZ Program,   time, and Color A.  Set the Delay to 10 s.  Click  on Aquire.   You are now ready to make Measurements  of  %T versus time for reaction (14).  Carefully measure 10 mL of the stock blue #1 solution with a graduated cylinder,  and pour it into a 150 mL beaker.  Measure 10.0 mL of of the 20 m% bleach solution, prepared in Part 1,  with a graduated cylinder, and add it to  the dye solution in the beaker.  Quickly stir the mixture, and pour it into a clean, dry cuvette. Hold the cuvette by the top edge to avoid getting finger prints on the light-transmitting walls.  place the cuvette in the colorimeter, cover it, and click on start on the computer screen.   Values of %T versus time, and a corresponding graph will appear on the computer screen. Place the beaker containing the remaining reaction mixture next to the colorimeter, and observe the color change as the reaction progresses.  Stop the data collection when the %T values reach a constant value.  Save the data to your computer disk.  Repeat this measurement once.
   
   b)  Repeat Parts 1 and 3a) using a 10 % bleach solution in place of the 20 % bleach solution.  Prepare 20 mL of this solution by mixing 18 mL of deionized water and 2 mL of commercial bleach in a beaker.    
   
   

Conclusion

Please answer each question below clearly.  Do the calculations in questions 1 through 3 by hand.

1. Convert the %T value of the stock blue #1 solution, measured in Part 2 of the procedure,  to absorbance, using equation (18).  Calculate the constant C, in equation (17) using your absorbance value and the concentration of the solution as found on the bottle label.
   

2. Commercial bleach is a 5%, by mass, aqueous solution of  sodium hypochlorite, NaClO.  What is the molar concentration of NaClO?
   

3. In Part 3a) of the procedure, what are the concentrations of blue #1 and NaClO in the reaction mixture before reaction occurs.  Are we justified in assuming that the concentration of NaClO is much greater than that of blue #1?
   

4. Enter your % T versus time data, and your value of C, into the Excel spreadsheet.  Convert the % T values to absorbance.  In the sample spreadsheet below, "Absorbance at infinity" refers to the constant value of the absorbance obtained once the reaction has gone to completion. This "infinity" value must be subtracted from each of the absorbance values as shown  in column D to obtain a "corrected absorbance".  Convert the "corrected absorbances" to concentration of dye, [E], and  calculate ln[E] and 1/[E]. A sample spreadsheet is shown below.
   
   

   Prepare graphs of each of the quantities [E], ln[E] and 1/[E] versus time.  From your graphs determine the order of the reaction with respect to Blue #1.
   
   

5. For the linear graph obtained in question 4 determine the slope using the add trendline feature of Excel .  Right click on a data point in the graph.  Left click on add trendline.  Pick linear regression.  Click on the "Options" tab.  Choose "Display equation on chart".  The equation of the straight line will be displayed on the graph.  The slope will be equal to -k_o if the reaction is either zero or first order with respect to blue #1, and it will equal k_o if the reaction is second order with respect to blue #1.
   

6. What is the ratio of the value of k_o obtained in part 3a),  to the value obtained in part 3b)?  Round this ratio to the nearest whole number, and use the resulting value to determine x, the order with respect to NaOCl.
   

7. What is the value of the rate constant, k,  in equation (15)?
   
   

8. Rewrite equation (15) with the correct values of x and y.

9. What is a possible rate-determining step in the mechanism of this reaction?