14168716-Chemical-Kinetics-Labs.pdf

Chemical Kinetics Labs

April 7

2009 Sukhkaran Dhaliwal SCH4U Mr. J. Linzel

Sukhkaran Dhaliwal


2008/2009

Chemical Kinetics Labs Introduction Chemical kinetics, also known as reaction kinetics, is the st udy of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that can describe the characte ristics of a chemical reaction (Pearson, 2004). The rate of reaction is the change in the amount of reactant s or products over a time interval. The rate of reaction in chemistry, is usually expressed in moles/second (mol/s) or molarity/second (mol/L∙s). There are two ways in which the rate can be expressed: average rate of a reaction or instantaneous rate of reaction. The average rate of reaction shows how the concentration or molarity changes over a specific time interval, w hile the instantaneous rate of react ion shows the rate of change at a specific time. Differential calculus can often be used when calculating the instantaneous rate of change. An easier method would be to calculate the slope of the line at the point of tangency. There are many ways in which chemists can measure reaction rates. Various methods include: monitoring mass, pH, conductivity, pressure, colour, and volume. When monitoring mass, the mass of the reactants can be measured over a time interval and if it releases gas, the mass will decrease. In a reaction involving gasses, the pressure of the system can change as the reaction progresses. An example would be the decomposition of hydrogen peroxide. As it decomposes in a closed system, the pressure will increase as oxygen gas is produced. As well as pressure and mass, change in colour can be used to monitor the progress of a reaction. The absorbance of light is directly related to the concentration of the compound, so by observing the change in absorbance, the rate of r eaction is monitored. The speed of a chemical reaction is affected by factors such as the temperature, concentration, volume, surface area, and orientation. These factors are sufficiently explained through collision theory. When the temperature is greater, there is a greater fraction of particles that have more energy than the activation energy, enabling them to collide and react. These particles also have more kinetic energy. By increasing concentration, while keeping volume and pressure constant, there is a greater chance that the particles will collide and react. Decreasing the volume is essentially another form of increasing the concentration. With greater surface area, more collisions can occur; increasing the rate of reaction. Lastly, orientation is the key for a reaction to occur. If particles do not collide with the correct orientation, a reaction will not occur. As well, catalysts have the ability to increase the rate of reaction by lowering the activation energy barrier.

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Generally, the rate of a reaction increases when the concentration of the reactants are increased. The rate of reaction is directly proportional to the concentration of the reactants. This relationship can be expressed in a general equation called the rate law e quation.

The letters A and B represent the concentration of the reactants. The exponents x and y are called the rate law exponents (orders of reaction). They do not change with temperature and must be determined experimentally. Generally, they do not correspond to the stoichiometric coefficients of their reactants. The letter k represents the proportionality constant called the rate constant. The rate constant differs for each reaction at any given temperature. The rate constant has different units depending on what the overall order of the reaction is. The magnitude of the rate constant indicates the speed of a reaction. Therefore a small rate constant indicates a slow reaction, while a large rate constant indicates a fast reaction. The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the rate constant, and therefore, rate of a chemical reaction (IUPAC, 1997). In short, the Arrhenius equation gives "the dependence of the r ate constant k of chemical reactions on the temperature T (in absolute temperature, such as Kelvin or Rankine) and activation energy” as shown below (IUPAC Goldbook, 1997):

Or

The rate constant is represented by the letter k just like the rate law equation. Ea is activation -1

-1

energy and has units of Joules. R is the universal gas constant and is equal to 8.314 J K mol . The variable T represents temperature, usually in Kelvin. The variable A represents the frequency factor and expresses the importance of orientation of the molecules during collisions. The greater the value of A, the more likely a collision will result in a chemical reaction. The letter e is a mathematical constant called Euler’s number. The modified version of the Arrhenius equation was derived by taking the natural logarithms of both sides. This equation resembles the equation of a straight line: y = ( m ) ( x ) + b. If lnk -1

is plotted against T , a straight line should result with a slope of -Ea/R and a y-intercept of ln A. A reaction mechanism is a series of steps that make up an overall reaction. Each step, called an elementary step, involves a single molecular event, such as a simple collision between atoms, molecules, or ions. This step cannot be broken down into further, simpler steps. Molecules that are formed in an elementary reaction and consumed in a subsequent elementary r eaction are called reaction intermediates (Webb, 2002). The term molecularity refers to the number of reactant particles that are involved in an elementary reaction. They can be either unimolecular (one), bimolecular (two), or termolecular (three). The molecularity of the slowest step of the reaction mechanism is equal to the orders of reaction. The slowest step of the reaction mechanism is also called the rate determining step. This is because a reaction can o nly be as fast as its slowest step, so it has bearing on the order of reaction.

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Determining the Rate Expression and Activation Energy for the Decomposition of Hydrogen Peroxide

Data Collection

Table of Volumes and Concentrations Trial

Volume H2O2 (mL)

[H2O2] Before Mixing

Volume KI (mL)

[KI] Before Mixing

1

4

0.88

1

0.50

2

4

0.88

1

0.25

3

4

0.44

1

0.50

4

4

0.88

1

0.50

Table 1 – Table of Volumes and Concentrations for H 2O2 and KI

The only values calculated in this table were t he concentrations of the H2O2 before mixing.

Table of Temperatures and Initial Rates Trial

Reactants

Temperature (°C)

Initial Rate (kPa/s)

1

4 mL 3.0% H2O2 + 1 mL 0.5 M KI

20.10

0.3440

2

4 mL 3.0% H2O2 + 1 mL 0.25 M KI

20.10

0.1744

3

4 mL 1.5% H2O2 + 1 mL 0.5 M KI

20.10

0.0449

4

4 mL 3.0% H2O2 + 1 mL 0.5 M KI

29.90

0.5480

Table 2 – Table of Temperatures and Initial Rates

The temperature and initial rate for the reactions were determined using Logger Pro. The temperature reading was given during the course of the reaction and the initial rate was determined by creating a

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linear fit for the initial increase in kPa and time. From that data, the slope was equal to the initial rate (kPa/s).

Table of Rates, Concentrations, and Rate Constants Trial

Initial Rate (mol/L s)

[H2O2] After Mixing

[KI] After Mixing

Rate Constant k

1

1.41x10-4

0.704

0.10

4.04x10-3 M-3s-1

2

7.15x10-5

0.704

0.05

4.09x10-3 M-3s-1

3

1.84x10-5

0.352

0.10

4.22x10-3 M-3s-1

4

2.25x10-4

0.704

0.10

6.45x10-3 M-3s-1

Table 3 – Table of Rates, Concentrations, and Rate Constants

The initial rate as mol/L∙s was calculated by rearranging the ideal gas law. The concentrations of the reactants were calculated from basic molarity and solution principles. The rate constant (k ) was calculated by first determining the order of the reactants, then using these values with the rate expression to isolate for k. All full calculations are shown in “Data Analysis.”

Pressure vs. Time for Trial 1 180 160 140 ) a 120 P k ( 100 e r u 80 s s e r P 60

40 20 0 1

11

21

31

41

51

61

71

81

91 101 111 121 131 141 151 161 171 181 191 201

Time (s) Figure 1 – Pressure vs. Time Graph for Trial 1

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Pressure vs. Time for Trial 2 140 120 ) 100 a P k ( 80 e r u s 60 s e r P 40

20 0 1

11

21

31

41

51

61

71

81

91 101 111 121 131 141 151 161 171 181 191 201


Pressure vs. Time for Trial 3 112 110 108 ) a P k ( e r u s s e r P

106 104 102 100 98 96 94 92 1

11

21

31

41

51

61

71

81

91 101 111 121 131 141 151 161 171 181 191 201


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Pressure vs. Time for Trial 4 180 160 140

) a 120 P k ( 100 e r u 80 s s e r 60 P

40 20 0 1

11

21

31

41

51

61

71

81

91

101 111 121 131 141 151 161


Data Analysis To calculate the orders of reaction for H 2O2 and KI, the method of analyzing initial rates was used. By changing the concentrations of each, Logger Pro was used to see the change in the rate of reaction (kPa/s), which was eventually converted to mol/L∙s. By comparing how the reaction rates changed to differing concentrations of the reactants, the orders of reaction were calculated. Conversion of kPa/s to mol/L∙s:

Sample Calculation:

Calculating Order of KI:

Calculating Order of H2O2:

1.972

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Sukhkaran Dhaliwal


The variable “y” represents the order of reaction for KI. It can be observed that the value for y is close enough to 1, so therefore rounded to a whole number. The order of reaction for KI is 1.

2008/2009

The variable “x” represents the order of reaction for H 2O2. It can be observed that the value for x is close enough to 3, so therefore rounded to a whole number. The order of reaction for H2O2 is 3.

From the above calculations it can be concluded that the rate expression for the catalyzed decomposition of hydrogen peroxide is:

Rate = k[H2O2]3[KI] To calculate the rate constant “k”, the orders of reaction first had to be calculated (shown above). After the orders were calculated, that would mean that there would be only one unknown variable in the rate expression, which would be the rate constant. By rearranging the rate expression for the catalyzed decomposition of hydrogen peroxide, the rate constant could be determined for all trials. Since there were three trials at the same temperature, the rate constant will be averaged out, while the last trial was at a higher temperature, will not be taken into account for the averaging of the rate constant. The calculations should show that the rate constant for the first three trials is somewhat similar, while the last trial will be different.

Trial 1

Trial 2

Trial 3

Trial 4

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Average of “k” at 294.25 Kelvin

Now that all the variables and values in the rate law expression have been calculated, it is viable that the activation energy ( E a ) for the reaction be calculated. By using an alternative derivation of the Arrhenius equation, the activation energy can be easily solved for.

Solving for the activation energy

Rearrange for E a

The activation energy for the catalyzed decomposition of hydrogen peroxide was 33.79 kJ.

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From the experimental data collected, information such as the order of reaction, value of the rate constant, rate of reaction, and activation energy could be calculated. The rate expression for the catalyzed reaction of hydrogen peroxide was: 3

Rate = k [H2O2] [KI] -3

-3 -1

The rate constant, k , was averaged to be 4.22x10 M s for 293.25 Kelvin. The rate constant calculated for trials one, two, and three were fairly close to one another showing that experiment was carried out effectively. As expected, the rate constant increased when the reaction occurred at a higher -3

-3 -1

temperature. It was calculated to be 6.45x10 M s for 303.05 Kelvin. This essentially means that more effective collisions occurred at the higher temperature. With this data, it can be formulated that the larger the rate constant, the faster the rate of reaction will be. The order of reaction for the hydrogen peroxide was three and the order of reaction for potassium iodide was one. The overall order of reaction was four. These values were calculated by comparing the initial rates of reaction for differing concentrations. After a ratio was set up, the natural logarithm was taken for both sides to isolate for the unknown value for the order. This was completed twice: one for the differing concentration of hydrogen peroxide and the other for the differing concentration of potassium iodide. It was always compared to the base results (trial one). The following mechanism has been proposed for the catalyzed decomposition of hydrogen peroxide: -

-

H2O2 + I → IO H2O -

-

H2O2 + IO → I + H2O + O2

The first reaction in the mechanism is the rate determining step (slowest reaction). This is quite -

easy to determine because the second reaction’s reactants are H2O2 and IO . This would mean that hydrogen peroxide would be the only substance in the rate expression to have an order that is equal to -

or greater than one. Since IO is not a reactant, this would mean that the order of reaction for KI would be zero, which is not the case. With this being said, the first reaction in the mechanism is indefinitely -

the rate determining step because H2O2 and I are both reactant, which means they have to have an order equal to or greater than one. The activation energy for the catalyzed decomposition was calculated to be 33.79 kJ. A modified version of the Arrhenius equation was used to calculate the activation energy. If the hydrogen peroxide was to decompose without the presence of a catalyst, the activation energy wo uld have been higher, but with potassium iodide acting as the catalyst in the reaction; it was able to lower the activation energy barrier.

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Sukhkaran Dhaliwal


2008/2009

Determining the Rate and Order of a reaction Using colorimetry Data Collection

Table of Reactants, Concentrations, and Initial Rates Trial

Reactants

[FeCl3] After Mixing

[KI] After Mixing

Initial Rate (s-1)

1

1.5 mL 0.0500 M FeCl3 + 1.5 mL 0.0500 M KI

0.0250

0.0250

0.163

2

1.5 mL 0.0500 M FeCl3 + 1.5 mL 0.0250 M KI

0.0250

0.0125

0.040

3

1.5 mL 0.0250 M FeCl3 + 1.5 mL 0.0500 M KI

0.0125

0.0250

0.083

Table 1 – Table of Reactants, Concentrations, and Initial Rates

The only values calculated in this table were t he concentrations of iron (III) and potassium iodide after mixing. Basic molarity and solutions chemistry was used to determine the values. The initial rate was determined from the graphs obtained from Logger Pro. The values represent the initial rate of change (slope) of the graphs.

Absorbance vs. Time for Trial 1 1.8 1.6 1.4

e c 1.2 n a 1 b r o 0.8 s b 0.6 A

0.4 0.2 0 0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

Time (s) Figure 1 – Absorbance vs. Time Graph for Trial 1 11 | P a g e

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Absorbance vs. Time for Trial 2 1.2 1 e c 0.8 n a b r 0.6 o s b 0.4 A

0.2 0 0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

Time (s) Figure 2 – Absorbance vs. Time Graph for Trial 2

Absorbance vs. Time for Trial 3 1.2 1 e c 0.8 n a b r 0.6 o s b 0.4 A

0.2 0 0

5

10

15

20

25

30

35

40

45

Time (s) Figure 3 – Absorbance vs. Time Graph for Trial 3

Data Analysis To calculate the orders of reaction for FeCl 3 and KI, the method of analyzing initial rates was used. By changing the concentrations of each, Logger Pro was used to see the change in the rate of reaction (s -1). A colorimeter was used to measure absorbance, which is defined as a logarithmic measure of the amount of light that is absorbed when passing through a substance. It does not have any units. By comparing how the reaction rates changed to changing the concentrations of the reactants, the orders of reaction were calculated.

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Before calculating the orders of reaction, the concentrations of iron (III) chloride and potassium iodide were calculated. It cannot be done in one step, but rather requires two sets of calculations. To calculate the concentration of iron (III) chloride, the dilution was treated as if potassium iodide was water. To calculate the concentration of potassium iodide, the dilution was treated as if iron (III) chloride was water.

[FeCl3] Calculation Trial 1

[KI] Calculation Trial 1





Calculating Order of FeCl3:

Calculating Order of KI:

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The variable “y” represents the order of reaction for KI. It can be observed that the value for y is close enough to 1, so therefore rounded to a whole number. The order of reaction for FeCl3 is 1.

2008/2009

The variable “y” represents the order of reaction for KI. It can be observed that the value for y is close enough to 2, so therefore rounded to a whole number. The order of reaction for KI is 2.

The data collected from the colorimeter, which measured the absorbance of the solution, was used to calculate the order of reaction for iron (III) chloride and potassium iodide. The rate expression for the reaction is as follows: 2

Rate = k [FeCl3][KI]

The order of reaction for iron (III) chloride was one and the or der of reaction for potassium iodide was two. The overall order of reaction was three. Though the rate of reaction did not have units of mol/L∙s, the order could still be calculated. To calculate the order, it wouldn’t have mattered if the -1

units were mol/L∙s or s because the ratio between the two rates being compared would still be the same after it was converted (if it could have been converted). It was impossible to calculate the rate constant, k , for obvious reasons. Though the rate was in -1

s , this could not have been used to determine the rate constant. The rate of reaction would have to be in mol/L∙s, otherwise the rate constant would have incorrect units and values. To calculate the rate constant, another experiment would have to be conducted using Beer’s Law. This experiment would then allow the conversion from absorbance to a specific molar concentration. With the data from this experiment, calculating the rate constant would be possible. It is not possible with either the rate expression or the Arrhenius equation.

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14168716-Chemical-Kinetics-Labs.pdf

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