KINETICS OF CHEMICAL REACTIONS

INTRODUCTION

Kinetics

Kinetics is the study of reaction rates and the dependence of reaction rates on such factors as temperature, kind of solvent, presence of catalysts, and the concentration of reagents. A thorough investigation of the effect of these factors on a given reaction provides information from which the mechanism of the reaction can be deduced, i.e., how the reactants combine or interact to form the products.

Consider the reaction:

A + B products

The reaction will occur when two requirements are met:

1. The molecules collide with the proper orientation. If the molecules only graze one another, or if the wrong ends of the molecules collide, reaction will not occur.

2. The reacting molecules must possess sufficient energy to react.

Each of these requirements is discussed below.

Collisions

Consider a situation in which one molecule of A collides with one molecule of B to form the product, AB, in a one-step mechanism.

A + B AB (1)

The rate of this process may be expressed as change of concentration of any of the species involved in the reaction: A, B and AB.

Rate = = =

The rate is also proportional to the product of the concentrations of A and of B at any given time:

rate = k[A] [B]

The proportionality constant, k, known as the rate constant, is dependent on the temperature of the reaction. It is related to the fraction of collisions between A and B which produce AB, effective collisions. The minimum amount of energy that must be available for a collision to lead to reaction is called the activation energy. If two molecules collide with less than this minimum energy, there will be no chemical change. Increasing the temperature leads to more energetic collisions and an increase in k.

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The reaction rate is also dependent on concentration of reactants, since a higher concentration increases the likelihood of collisions (both effective and ineffective) between reactant molecules. If the concentration of A (see Eq. (1)) is doubled, molecules of A are twice as likely to collide with molecules of B, and the reaction rate will double.

Now consider a reaction with the 1-step mechanism:

2A + B products (2)

This equation shows that two molecules of A combine with one molecule of B. When the concentration of A is doubled, a collision with B is four times as likely. The rate of this mechanism is:

Rate = = - = -

= k[A]2[B]

This equation is the rate law for reaction (2). Note that this rate is proportional to the square of the concentration of A. The exponent to which the concentration of each reactant is raised is the order of the reaction. The sum of the exponents is the overall order of the reaction. For example, Eq. (2) is second-order in A, first-order in B, and overall third-order.

For a general reaction,

nA + mB products

the rate law is:

Rate = = k[A]o [B]p

Note: The exponents in the rate law do not correspond to the coefficients in the stoichiometric equation. The rate law is obtained from the mechanism of a reaction, not from the balanced stoichiometric equation.

The stoichiometric equation for a reaction does not necessarily describe how the reaction occurs. Many reactions occur in a series of steps. The sum of these steps is the mechanism of the overall reaction. For example, the reaction:

2H2(g) + 2NO(g) N2(g) + 2H2O(g)

occurs in a series of steps. The experimentally determined rate law is:

Rate = = k[H2][NO]2

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Chemists study the dependence of the reaction rates on concentration of species in the reaction, derive the rate law, and then propose a consistent reaction mechanism, a series of steps which predict the overall stoichiometry and the concentration dependence of the overall reaction.

Reaction Rates and Energy

The rate constant, k, is related to the fraction of molecules with sufficient energy to react. Consider an energy diagram (or reaction profile) for a typical exothermic reaction. Although the reactants have higher potential energy than the products (the reaction is exothermic), the reactants must initially gain in energy in order to form products. This required energy is the activation energy, Ea. The more molecules with this energy, the greater the reaction rate. The relationship between the rate constant and the activation energy is given by:

k = (3)

where:

A = the Arrhenius factor, a constant for the reaction which is related to collision frequency and orientation

R = gas constant (8.314 J/mol K)

T = absolute temperature (K)

e = base of natural logarithms

INTERPRETATION OF KINETIC DATA – GRAPHICAL TECHNIQUES

Determination of Reaction Order

Using the methods of calculus, rate laws can be integrated to put them in a form in which the data can conveniently be treated graphically. The results of integration of various rate laws are given in Table 1.

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E

reaction coordinate

reactant

product

Ea

Table 1

Rate Law Units of k Order Integrated Form

rate = k M sec1 0 [A] = kt + [A]0

rate = k[A] sec1 1 ln[A] = kt + ln[A]0

rate = k[A]2 M 1sec1 2 = kt +

where: t = time in seconds and [A]0 is the initial concentration of reactant A.

Each of the integrated forms fits the general equation of a straight line, y = mx + b. The parameters which can be used in the graph of the straight line are summarized in Table 2.

Table 2

Order x y slope (m) y-intercept (b)

0 t [A] k [A]0

1 t ln[A] k ln[A]0

2 t k

If the concentration of A is measured as a function of time, the order of the reaction with respect to A can be determined graphically. Three graphs are drawn: [A] vs. time, ln[A] vs. time, and 1/[A] vs. time. The graph which gives a straight line demonstrates the order of the reaction. (See Table 2).

The following graphs (Fig. 1) show the different plots of kinetic data for a single reaction. That 1/[A] vs. time is a straight line indicates that the reaction is second-order in A. The slope of the line is equal to the rate constant for this reaction.

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paste in graph

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Determination of Activation Energy, Ea

The Arrhenius equation, k = can be expressed in the “straight line” form by taking the natural logarithm (ln) of both sides:

ln k = + ln A

A graph of ln k vs. the inverse of Kelvin temperature is a straight line with slope of Ea/R.

If two values of k are known for two different temperatures:

ln =

it is possible to solve for the activation energy, Ea.

OBJECTIVES

1. To become familiar with the Spectronic 20 spectrophotometer.

2. To obtain and interpret kinetic data.

BEFORE COMING TO LAB1. Set up your lab notebook with Title, Introduction and Data sections.

2. Read sections 12.1-12.5 and 12.7 in Zumdahl.

3. Using the %T data shown below, fill in a table with the values for A, ln[A] and 1/[A] for each time point. Then, graph that set of data on the sheets of graph paper at the end of the experiment and answer the associated questions. Place graphs and answers in your Introduction. Use one piece of graph paper per plot. Use the whole sheet.

In this experiment we will be measuring the change in the color of a reacting species with a Spectronic 20 spectrophotometer. The concentration of the reacting species is directly proportional to its absorbance, A. When using analog spectrometers, it is more accurate to read the % transmittance scale on the spectrophotometer. The conversion equation is:

A = log (4)

Convert the following sets of data from % transmittance to absorbance, A. We

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will assume that this is equal to [A]. Then calculate ln[A] and 1/[A]. Write these in a table, then plot [A] vs. t, ln[A] vs. t and 1/[A] vs. t, and use the plots to answer the following questions.

t(s) % transmittance [A] ln[A] 1/[A] 0 39.8 60 63.1120 79.4180 89.1240 94.4

a. What is the order of the reaction (i.e., which plot is linear)?

b. What is the rate constant, k, for this reaction? (Remember, the slope of a

line is given by .)

PROCEDURE

The reaction that will be studied involves the disappearance of the color of a phenolphthalein solution. We will study the kinetics of the reaction shown below.

(pink) (colorless)

We can write the overall reaction as:

P2 + OH POH3 and the rate equation as:

rate = k [P2]m [OH]n

where [P2] is the concentration of unreacted phenolphthalein, [OH ] is the concen-tration of the hydroxide ions, k is the overall rate constant, m is the order of the reaction with respect to phenolphthalein and n is the order of the reaction with respect to OH.

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+ OH -

O-

COO-

O

O-

HO COO-

O-

To determine the rate equation, the unknowns, k, m, and n must be found.

In order to carry out this experiment, you will need a method to measure the concentration of at least one reactant. Since phenolphthalein is highly colored, a convenient way to follow the change in concentration, [P2]/t, is to monitor the absorbance of the solution using a spectrophotometer. The absorbance of the solution, A, is directly proportional to the concentration of the absorbing species as given by Beer's Law:

A = lC

where 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 given wavelength and the pathlength is fixed by the cell, absorbance, A, will only vary with concentration, C. Therefore, A may be substituted for concentration in the data analysis. We will be measuring the absorption of P2- at 550 nm. Instructions in the use of the Spectronic 20 spectrophotometer appear in Appendix 1.

Note: For each stage of the experiment, use the WASH, RINSE, FILL technique to clean cuvette and minimize sample contamination.

A. DETERMINATION OF THE ORDER OF THE REACTION WITH RESPECT TO [P2]

In this part of the experiment, the rate of disappearance of P2- in the presence of an excess of [OH-] will be recorded as a function of reaction time. One method used to simplify the determination of the order of a reaction with respect to one of the species is to set up conditions so that the other reactant is present in large excess. Therefore, during the reaction, the concentration of that species remains essentially constant.

In our experiment we will add an excess of OH -. Under these conditions, the rate equation can be rewritten as:

Rate = k /[P2-]m

Where k/ = k[OH-]. Measuring the change in concentration of phenolphthalein with time under these conditions will allow you to determine the order of the reaction with respect to phenolphthalein, m. The experiment can then be repeated at a different concentration of OH- and a value determined for n, the order of the reaction with respect to [OH-].

1. Be sure to read and follow the Operating Procedure for the spectrophotometer as given in Appendix I of the Lab Manual.

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2. Turn on the spectrophotometer, set the wavelength at 550 nm, and allow it to warm up for at least 10 minutes prior to use.

3. Make sure the computer is on, and type in “Chem105” for both the username and password (use a capital “C” and the rest lowercase letters) in the login screen, and click “OK”.

4. Double click on the “Kinetics 1” icon on the computer desktop to open the program.

5. Click on “Experiment” in the menu bar and select “Calibrate” from the drop-down menu. Select “CH1: Colorimeter(%T)”.

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6. In the sensor settings window, click on “Calibrate Now”.

7. With the spectrophotometer in transmittance mode, set the transmittance to 0.0, and then enter that value in the “Reading 1” box. Click “Keep”.

8. Pour about 10 mL of the 0.3 M NaOH solution into a small beaker. Using the 10 mL pipet, transfer 4 mL of the solution to your cuvette. Wipe the outside of the cuvette with a Kimwipe and insert it into the sample holder, with the lines on the cuvette and sample holder lined up. Close the cover.

9. Set the transmittance to 100.0 on the spectrophotometer and enter the actual value (i.e. 99.8) read by the spectrophotometer. Click “Keep” and then click “Done”.

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10. Remove the cuvette from the spectrophotometer and add 1 drop of phenolphthalein, P2-. Invert the stoppered cuvette several times to mix, wipe the outside of the cuvette with a Kimwipe, and insert it into the sample holder, with the lines on the cuvette and sample holder lined up. Close the cover. This should all be done as quickly as possible! You want to measure the rate at the very beginning of the reaction.

11. Click “Collect” and observe the data (the data will automatically stop being collected after 350 seconds).

12. After the data has been collected, take a look at the absorbance (A) vs. time

curve. To see the results more clearly, click “Auto-Scale” on the toolbar. You can also change the y-axis from absorbance to ln(A) or (1/A). To do this, left-click on the “Absorbance” on the y-axis and select the variable you want.

13. Observe each of the three curves (absorbance vs. time, natural log vs. time, and inverse vs. time). A straight line fit can be obtained by clicking “Analyze” in the menu bar and selecting “Linear Fit” (be sure to note the slope).

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14. After deciding which graph is the most linear, print this graph by clicking on “File”

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in the menu bar and click “Print Graph” from the drop down menu.

15. Name your graph so you can identify it as your own, click “OK”, then click “OK” again.

16. Analysis of this data will allow you to determine the order of the reaction with respect to [P2-] (See discussion above about plotting the integrated form of the rate laws to determine order of reaction.). See ANALYSIS section for details.

B. DETERMINATION OF THE ORDER OF THE REACTION WITH RESPECT TO [OH-]

1. Click on data in the menu bar and select “Clear All Data” from the drop down menu.

2. Pour about 5 mL of 0.3 M NaCl in another small beaker. Pipet 2.0 mL of the 0.3 M NaOH and 2.0 mL of the 0.3 M NaCl into a clean cuvette. Check that the spectrophotometer is still calibrated. The [OH]- is half as great as in the first experiment, but the ionic strength of the solutions is the same due to the addition of the NaCl solution. Wipe the outside of the cuvette with a Kimwipe. Add 1 drop of phenolphthalein, P2-. Invert the stoppered cuvette several times to mix, and then place it in the spectrophotometer, aligning the marks on the spectrophotometer and the cuvette (Remember to be quick!). Close the cover.

3. Begin collecting data by following the same procedure as used in Steps 11-15 of Part A. When finished, print one graph (you should know which graph to print from Part A) with a linear fit line and slope as before.

C. EFFECT OF TEMPERATURE

1. Close out of the Kinetics 1 program by clicking “File” in the menu bar and clicking on “Exit” from the drop down menu. Click on “No” in the dialogue box asking if you want to save your data.

2. Double click on the “Kinetics 2” icon on the computer desktop.

3. Pipet 4 mL of 0.3 M NaOH into a clean cuvette.

4. Recalibrate the spectrophotometer by following the same procedure as used in Steps 5-9 of Part A. Use the cuvette prepared in the previous step.

5. Allow the cuvette to sit in a beaker containing tap water and ice for about 10 minutes.

6. After about 10 minutes, remove the cuvette from the ice bath, wipe the outside

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with a Kimwipe, and add 1 drop of phenolphthalein. Invert the stoppered cuvette several times to mix, and then place it in the spectrophotometer, aligning the marks on the spectrophotometer and the cuvette (Quickly!). Close the cover.

7. Click on “Collect”, and study the Absorbance reading in the lower left-hand corner of the screen. As soon as the absorbance reading steadies out (this should take only a few seconds), click “Keep”.

8. Return the cuvette to the ice bath, and continue taking a reading in the same fashion every minute for five minutes (i.e. click “Keep” at about 60, 120, 180, 240, and 300 seconds) always replacing the cuvette in the ice bath between readings and wiping the outside with a Kimwipe before placing it in the spectrophotometer.

9. After taking the last (sixth) reading, click “Stop”. Analyze your data and print out one graph as in Steps 12-15 of Part A.

10. Be sure to record the temperature of the ice bath and room temperature. You will use these to estimate the activation energy of this reaction.

ANALYSIS

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1. Order of the reaction with respect to phenolphthalein

a. Plot the experimental results as:

i. [P2] vs. tii. ln [P2] vs. tiii. 1/[P2] vs. t

Plots must appear in your lab write-up, along with the data tables. Use the graph paper provided in the Lab Manual. Do one plot per page and use the entire page for the plot. Since absorbance is directly proportional to concentration, we will actually use the absorbance, A, instead of [P2].

b. Determine a value for m, the order of the reaction with respect to P2, from the graphs of the data.

First determine which of the three plots best fits a straight line. If the plot of [P2] vs. t gives a straight line, the reaction is zero order with respect to P2. If the plot of ln[P2] vs. t gives a straight line, the reaction is first order with respect to P2. If the plot of 1/[P2] vs. t gives a straight line, the reaction is second order with respect to P2. Use the plot that gives a straight line for the rest of the experiments in which the effect of [OH -] and temperature are explored (parts 2 and 3 below).

The slope of the linear plot is related to k’, the apparent rate constant. Determine the slope of your line. This will give you a value for k’ (see p. 4-4). Remember, k ’ = k[OH]. Solve for the true rate constant, k.

k = k ’/ [OH] = k ’/ 0.3 M

2. Order of the reaction with respect to hydroxide

The order of the reaction with respect to [P2] will be unchanged. It was deter-mined in part 1.b. of the experiment. Now we will vary [OH] to determine the order of the reaction with respect to [OH]. This will be done mathematically by comparing the apparent rate constants at different concentrations of OH.

a. Plot the data from the second experiment at [OH] = 0.15 M, using the same integrated rate equation that you determined in part A. The slope of this line can be used to calculate k’‘, the apparent rate constant with [OH] = 0.15 M.

b. Comparing k’ and k’‘ allows you to determine n, the order of the reac-tion with respect to [OH],

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=

Solve for n. It will be the order of the reaction with respect to OH (an integer).

n = _______________

c. Write out the experimentally determined rate law by substituting values of k, m and n into the general equation:

rate = k [P2]m [OH]n

3. Effect of Temperature on the rate of the reaction

a. Determine kL from the data obtained from the low Temperature experi-ment (part C). Again, you will plot your data at low temperature using the integrated rate equation you used in parts 1 and 2. The slope will be related to kL’, the observed rate constant at a low temperature. Since

kL' = kL[OH]

solve for kL. This will be different from k, since rate constants change with temperature. It should be smaller than k.

kL = b. Using the Arrhenius equation, use the two rate constants for the two

temperatures to estimate the activation energy, Ea, for this reaction.

=

where T = room temperature and TL = ice bath temperature. Remember to use absolute temperature (K). Express your answer in kJ.

Ea = _________ kJ

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graph paper

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graph paper

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graph paper

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graph paper

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graph paper

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