Kinetics Of Nucleophilic Substitutions

The study of kinetics involves the observation of the reaction rates and the factors that promote or slow down those rates. In addition to providing knowledge about the process reaction’s reactant to product translation, but it is also helpful in increasing efficiency in the manufacturing world as kinetics provides information about how long a reaction will take and if it occurs at all. Hence, it is crucial even from a financial aspect that kinetics is studied.1

This experiment exhibits the kinetics of a nucleophilic substitution reaction. The purpose of this experiment is to investigate the kinetics of the hydrolysis of t-butyl chloride which solvolyzes by an SN1 mechanism because t-butyl chloride is a tertiary halide (alkyl halide). SN1 mechanism means a first order reaction with substitution by a nucleophilic solvent. The overall reaction is as follows: t-butyl chloride + H2O -> (CH3)3COH + HCl. The mechanism involves a first rate-determining slow step which ionizes t-butyl chloride and produces a chloride anion and carbocation. This is rate determining step because the rate of reaction depends on the alkyl halide and not on the nucleophilic solvent. The ionization is as follows: t-butyl chloride -> (CH3)3C+ + Cl-. Thus, the rate of reaction (rate of disappearance of concentration of t-butyl chloride) corresponds to the concentration of t-butyl chloride. The second step involves the nucleophile and is fast and as follows: (CH3)3C+ + Cl- + H2O -> (CH3)3COH + HCl. These reactions, at specific known temperature, will help the experimenter obtain the exact time it takes for the reaction to occur which in turn will help calculate the rate constant, k. Using the Arrhenius equation, the rate constant k will help calculate the activation energy.2

This experiment demonstrates the correlation between variation in concentration (both t-butyl and hydroxide), temperature, solvent polarity, and substrate structure with the rate of reaction of the hydrolysis of t-butyl chloride as well as exhibits the kinetic order of the reaction. The reactions are taken to increasing levels of completion (10%, 20%, and 30% completion) to make sure that the rate constant K is steady at the same temperature and reactant concentration. The activation energy the reaction requires in order to proceed is also examined in this experiment.

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Experimental:

For experiment run #2 of “III. Study of Solvent Polarity”, in order to make a 60:40 (Water:Acetone) sample, 4mL of t-butyl chloride was mixed with 0.4 mL of 0.1 M NaOH and 5.6mL H2O. The reason was because 5.6 mL of water + 0.4 mL of NaOH= 6 mL and 6 mL/ 10mL total volume of solution = 60% water; 4 mL of t-Butyl chloride = 4 mL and 4 mL/ 10 mL total volume of solution= 40% acetone.

The experimental procedure carried out for this lab followed the steps listed in the lab manual. Refer to Organic Chemistry Lab Manual Fall 2010 – Winter 2011 pages 21-22.

Results:

Note: All the solutions turned a bit lime-green before turning yellow. The time measured for reaction to occur corresponds to the time it took the solution to turn yellow in colour.

Study of Reaction Order

Variation of Hydroxide Concentration

RUN

% Completion

Time (seconds)

k (s-1)

1

10

49

2.15 x 10-3

2

20

94

2.37 x 10-3

3

30

151

2.36 x 10-3

Note: Refer to Appendix for calculation of rate constant k

Variation of t-Butyl Chloride Concentration

RUN

[t-Butyl Chloride] in stock solution

[t-Butyl Chloride] in reaction solution

Time (s)

K (s-1)

Rate of Reaction

(M/s)

Reaction order of t-butyl chloride

1

0.2 M

0.06 M

27

1.90

x 10-3

1.11 x 10-4

1storder

PART A, RUN 1

0.1 M

0.03 M

49

2.15

x 10 -3

6.12 x 10-5

1storder

2

0.1 M

0.015 M

64

1.65

x 10-3

2.34 x 10-5

1storder

Note: Refer to appendix for calculation of [t-butyl chloride] in reaction solution, rate constant k, rate of reaction, and reaction order of t-butyl chloride.

Study of Temperature Variation (Room Temperature: 19.5°C)

RUN

Temperature

Time (seconds)

1a

Room temp. – 10o =(9.5oC)

121

1b

Room temp. – 10o =(9.5oC)

123

Part A, Run 1

Room temp. = (19.5oC)

49

2a

Room temp. + 10o= (29.5oC)

20

2b

Room temp. + 10o=(29.5oC)

20

Study of Solvent Polarity

RUN

Water: Acetone

TIME (seconds)

1

80: 20

22

Part A, Run 1

70: 30

49

2

60: 40

134

Study of Structural Variations in the Substrate

RUN

Substrate

Time (seconds)

1

Isopropyl Chloride

No reaction (Waited for 7 minutes and nothing happened. The reaction mixture was even heated on a steam bath)

Calculating Activation Energy (Ea):

Note: The data of the Runs are from the Study of Temperature Variations.

Run

k (s-1)

Average k (s-1)

-log k

T (°C)

1/T (°C-1)

1a

8.71 x 10-4

8.64 x 10-4

3.06

9.5

0.1053

1b

8.57 x 10-4

Part A, Run 1

2.15 x 10-3

2.15 x 10-3

2.67

19.5

0.0513

2a

5.27 x 10-3

5.27 x 10-3

2.28

29.5

0.0339

2b

5.27 x 10-3

Note: -log k column was plotted on the y-axis and 1/T was plotted on the x-axis of Figure 1

Figure 1: This figure represents the graph of 1/Temperature against -log K, which is used to determine the activation energy of the reaction. A line of best fit is shown to show the equation of the line, which is y=10.049x + 2.0321. The error of the graph is represented by R2. The slope of 10.049 is equal to Ea/2.3R. Hence, the activation energy (Ea) of the reaction is equal to 45.76cal/mole with an error of ± 4.19cal/mole.

Reaction Mechanism:

Discussion:

The first part of the experiment composed of study of reaction order. During part A of this experiment, when the hydroxide concentration was varied (which corresponded to a different amount of completion of reaction), it was observed that the k values were all very close (around 2.36×10-3 s-1). Since the rate constant, k, is an integral part of the rate of reaction, the similar k values indicate that the NaOH concentration in the solution has no effect on the rate of reaction. This is because the nucelophile is not involved in the first step (rate determining) and only reacts to the substrate which occurs during the second (fast) step.3 This shows that the reaction is zero order when looking at the concentration of the nucleophile. It makes sense since the rate determining steps are the slow steps and in this reaction, the first ionization step is the slow step, thus making it the rate determining one. Meanwhile, the second step is fast and so it is not the rate determining one. Hence, since the nucleophile is only present in the second step (NaOH is neutraulized by the HCl formed in the fast second step)2, it is not linked to the rate of the reaction (NaOH concentration does not relate to the rate of reaction).

During part B of this experiment, t-butyl chloride concentration was varied. It was seen that the reaction time kept drastically lowering when as the concentration of the t-butyl chloride in the reaction solution increased. Refering to Table 1, the fastest reaction (in lowest amount of time of 27 seconds) occurred when the concentration of t-butyl chloride was relatively highest (0.06 M), followed by a slower reaction (49 seconds) when concentration of butyl in reaction solution was lower (0.03 M), and lastly followed by the slowest reaction (64 seconds) when the concentration was the lowest (0.015 M). Hence, this clearly proves that the substrate had a major effect on the rate of the SN1 reaction. Referring to Table I (b), it was calculated that the rate order of t-butyl chloride was the one. This in turn also proves that the overall reaction is first order as the rate of the reaction is only affected by concentration of one molecule, that being the substrate, which in this case was t-butyl chloride.

Experiment two showed the effect of temperature variation on the reaction. The room temperature of the lab was at 19.5°C. At the lowest experimented temperature, 9.5°C, the k value of the reaction was 8.64 x 10-4 s-1 (referring to Table V). When the experiment was performed at the room temperature of 19.5°C, the k value increased to 2.15 x 10-3 s-1. While at the highest experimenting temperature, 29.5°C, the k value of the reaction was seen to be the highest at 5.27 x 10-3 s-1. From this it can be concluded that as the temperature increased, the k value of the reaction increased as well. Referring to Table 2, it can also be noted that, as the temperature increased, the time of reaction decreased significantly. These effects are due to the fact that increase in temperature causes greater amount of reactant molecules to gain enough kinetic energy to overcome the activation energy required of the reaction (enough energy to go through the first rate-determining step).4 As a result, an increase in temperature corresponds to an increase in the number of successful collisions among the reactant molecules. Thus, the reaction would occur faster and so the time for the reaction to occur would decrease. Referring to Figure 1 (Arrhenius plot), the activation energy of the reaction was calculated to be 45.76cal/mole with an error of ± 4.19cal/mole.

The third experiment showed the effect of solvent polarity on the reaction. It was observed that, as the ratio of water to acetone decreased, the time of the reaction increased, and so, the rate of the reaction decreased. This is probably due to the fact that water have higher polarity than acetone as water acetone has a longer hydrocarbon chain than water. Since the reactant in this experiment, t-butyl chloride, is a slightly polar molecule, its polar nature during the transition state of the reaction increases tremendously. As a result, water (with comparatively much higher polarity), will allow increased salvation of the carbocation and chlorine anion that formed during the first rate-determining ionization step, by lowering the energy of the transition state. This is because water, a protic solvent, forms hydrogen bonds with both of the aforementioned ions in order to increase the solvolysis. While acetone is an aprotic solvent and not able to form the hydrogen bonds. Hence, higher ratio of water to acetone of a solvent is expected to result to a higher rate of hydrolysis reaction due to a better ability to solvate charged intermediate, which is exactly what was observed in experiment.5

The last experiment showed the effects of structural variation in the substrate on the reaction. In this experiment, t-butyl chloride was replaced with isopropyl chloride. As a result, no reaction took place after 5 minutes of waiting and even after heating it for 7 minutes. This is due to the fact that isopropyl chloride is a secondary halide while t-butyl is a tertiary halide. The t-butyl chloride was able to react because it was able to create a stable carbocation as it had a tertiary carbon which allows hyper conjugation and induction to occur. While on the other hand, isopropyl results into a far less stable carbocation as it does not allow for enough hyper conjugation and induction as it does not have any C-C sigma bonds that t-butyl chloride has. The t-butyl chloride would form more substituted carbocations than isopropyl. As a result, it is favourable to form a carbocation with t-butyl chloride than with isopropyl chloride as tertiary halides undergo SN1 reactions more efficiently.

The results of the experiment seem to agree with the expected results. Though, there can always be sources for errors while performing all of the experiments. First of all, to create the different type of mixtures, measurements of contents had to be made through the use of instruments such pipette and graduated cylinder. Since these instruments required the experimenter to estimate each measurement with the naked eye and so this could have lead to improper solution mixtures. Another error that possibly occurred could have been with the use of a stop watch. It was not possible to start the stop watch at the exact instant that the two solutions were mixed and stop at the exact instant the solution reached equilibrium. That could have lead to error in measuring time of reaction. Furthermore, the neutralization of NaOH was measured by timing the reaction until it turned into a yellow colour. Though, since the reaction solution progressively turned from a blue colour to a yellow colour, it was not possible to exactly judge the end of neutralization. Also, during the study of temperature variation, it was not possible to keep the temperature to be precisely at the same temperature for the entirety of one run of experiment as the temperature showed slight variations every minute. Lastly, due to limited amount of Erlenmeyer flasks available for the experiment, flasks had to be reused. Even though all the flasks were thoroughly washed with wash solvent and rinsed. Hence, this could have possibly caused contaminations which lead to errors in results. Overall, due to various reasons, there could have been errors in timing which would lead to improper calculation of rate constants and activation energy of the reaction.

Questions:

I)Let ln (x) = y

x = ey

log (x) = y*log(e)

log (x) = ln(x)*log(e)

ln (x) = log(x)/log(e)

ln (x) = 2.303 log (x) [since log(e) = 0.4343]

II) ln [RCl]0/[RCl] = kt

Let x = [RCl]0/[RCl]

ln (x) = kt

ln (x) = 2.303 log (x)

kt = 2.303 log (x)

kt = 2.303 log ( [RCl]0/[RCl] )

kt = 2.303 log ( 1/ [RCl] ) let [RCl]0 = 1 (because initial concentration is 100%)

kt = 2.303 log ( 1/ 1 – difference in [RCl] )

because [RCl]0 – [RCl] = difference in [RCl]

1 – [RCl] = difference in [RCl]

1 – difference in [RCl] = [RCl]

kt = 2.303 log ( 1/ 1 – %reaction/100 )

because %reaction/100 equals the difference in [RCl]

An apolar solvent would hinder SN2 reaction as it would not be able to solvate the reactant due to the fact that it would repel the anionic nucleophile. And since nucleophilic reactions require the solvation of reactants, SN2 reaction would not take place.

Polar protic solvents are usually acceptable for SN2 reaction as they are convenient solvents for nucleophilic substitutions because the reagents are soluble. The high polarity would dissolve the solute. Small anions are solvated more than large anions. Though, these solvents would result into slower reaction due to hydrogen bonding which causes loss of nucleophilicity.

Polar aprotic solvents prefer SN2 reactions as SN2 reactions prefer the basic nucleophilic. The aprotic solvents enhance the nucleophilicity of anions and have strong dipole moments. Also since these solvents do not have OH or NH groups, no hydrogen bonds must be broken to make room for nucleophile to attract to electrophilic carbon atom. This is the most preferred solvent for SN2 reactions.6

Alkyl iodide contains iodine atom, while alkyl chloride contains chlorine atom. Iodine has lower electro-negativity (2.5) than that of chlorine (3.0). Hence, alkyl iodide would be a less polar compound. Since water is a highly polar solvent, it will not be able to solvate alkyl iodide as much as alkyl chloride due to higher attraction to the more electro-negative atom of chlorine than that of iodine. As a result, it will not be able to increase the salvation of the transition state as much as that of alkyl chloride which has higher polarity.2 Hence, the activation energy of the alkyl iodide would not be lowered as much as that of alkyl chloride and so its Ea would be higher than 31 kJ/mol.

Structure of bromophenol blue indicator at alkaline pH.7