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Chemistry

Catherine E. Housecroft, Edwin C. Constable

Chapter 15

Reaction kinetics - all with Video Answers

Educators

WH

Chapter Questions

07:01

Problem 1

(a) The data plotted in Figure $15.4 \mathrm{a}$ refer to a reaction: $A \rightarrow$ products. Determine the rate of this reaction. (b) Figure $15.4 \mathrm{b}$ describes a different reaction: $A \rightarrow$ products, in which the rate changes as a function of time. Determine the rates of reaction at times $t_{1}$ and $t_{2}$ marked on the graph.

WH
Wilhamena Hobbs
Numerade Educator
01:11

Problem 2

For a reaction $A \rightarrow$ products which is zero order with respect to A, sketch a graph of (a) rate of reaction against time, and (b) $[\mathrm{A}]$ against time. Repeat the exercise for reactions that are first and second order with respect to A.

David Collins
David Collins
Numerade Educator
01:20

Problem 3

For a reaction $A \rightarrow$ products which is first order with respect to A, show that the units of the rate constant are $s^{-1}$. Similarly, confirm that the units of the second order rate constant are $\mathrm{dm}^{3} \mathrm{mol}^{-1} \mathrm{s}^{-1}$.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
04:27

Problem 4

What is meant by each of the following terms: (a) rate of reaction; (b) differential and integrated forms of a rate equation; (c) order of a reaction (both the overall order and the order with respect to a given reactant); (d) rate constant, pseudo-nth order rate constant and overall rate constant; (e) activation energy; (f) catalysis and autocatalysis; (g) unimolecular step; (h) bimolecular step?

Anatole Borisov
Anatole Borisov
Numerade Educator
View

Problem 5

Iron(III) oxidizes iodide according to the following equation: $$2 \mathrm{Fe}^{3+}+2 \mathrm{I}^{-}-2 \mathrm{Fe}^{2+}+\mathrm{I}_{2}$$ Write down a rate equation for this reaction if doubling the iodide concentration increases the rate by a factor of four, and doubling the $\mathrm{Fe}^{3+}$ ion concentration doubles the rate.

Angela Williamson
Angela Williamson
Numerade Educator
05:34

Problem 6

2-Chloro-2-methylpropane (Me_CCl) reacts with water according to the equation: $$\mathrm{Me}_{3} \mathrm{CCl}+\mathrm{H}_{2} \mathrm{O}-\mathrm{Me}_{3} \mathrm{COH}+\mathrm{HCl}$$ Changes in concentration of $\mathrm{Me}_{3} \mathrm{CCl}$ with time in an experiment carried out at $285 \mathrm{K}$ are as follows:
$$\begin{array}{ll}\text { Time/s } & 10^{4}\left|\mathrm{Me}_{3} \mathrm{CCl}\right| / \mathrm{moldm}^{-3} \\20.0 & 2.29 \\
25.0 & 1.38 \\30.0 & 0.90 \\34.5 & 0.61 \\39.5 & 0.42 \\44.5 & 0.26\end{array}$$
(a) Determine the order of this reaction with respect to $\mathrm{Me}_{3} \mathrm{CCl}$.
(b) Calculate a rate constant assuming the rate equation to be of the form: Rate $=k\left[\mathbf{M e}_{3} \mathrm{CCl}\right]^{n}$.
(c) Does the rate equation in (b) necessarily mean that only $\mathrm{Me}_{3} \mathrm{CCl}$ is involved in the rate-determining step?
[Data from: A. Allen et al. (1991) J. Chem. Educ., vol. $68, p .609 .$]

David Collins
David Collins
Numerade Educator
05:33

Problem 7

The kinetics of reactions between alkenes and $\mathbf{I}_{2}$ depend upon the alkene and the solvent. The data below give the results of the reaction of pent-1-ene with $\mathrm{I}_{2}$ in two different solvents; the alkene is always in vast excess. Determine the order with respect to iodine and the pseudo-nth order rate constant in each reaction.
Reaction I: Solvent $=1,2$ -dichloroethane (TABLE CAN'T COPY)
Reaction II: Solvent = acetic acid (TABLE CAN'T COPY)
[Data from: K. W. Field et al. (1987) J. Chem. Educ., vol. $64, \text { p. } 269 .$]

David Collins
David Collins
Numerade Educator
07:34

Problem 8

Phenyldiazonium chloride is hydrolysed according to the equation: (EQUATION CAN'T COPY)
The reaction can be followed by the production of dinitrogen. The volume of $\mathrm{N}_{2}$ produced is a direct measure of the amount of starting material consumed in the reaction. Use the following data to deduce the order of the reaction with respect to phenyldiazonium chloride; the reaction has been carried out in aqueous solution. The final volume of $\mathrm{N}_{2}$ collected when the reaction has run to completion is $40.0 \mathrm{cm}^{3} .$
$$\begin{array}{cc}\text { Time/min } & \text { Volume } \mathbf{N}_{2} / \mathrm{cm}^{3} \\0 & 0 \\5 & 8.8 \\10 & 15.7 \\20 & 25.3 \\30 & 31.1 \\40 & 34.5 \\50 & 36.7 \\60 & 38.0\end{array}$$

Preeti Kumari
Preeti Kumari
Numerade Educator
11:30

Problem 9

The dimerization of cyclic dienone (I) is as follows: (EQUATION CAN'T COPY)
I absorbs light at $460 \mathrm{nm}\left(\varepsilon_{\max }=225 \mathrm{dm}^{3} \mathrm{mol}^{-1} \mathrm{cm}^{-1}\right)$ and the rate of the reaction is followed by UV-VIS spectroscopy (path length $=1 \mathrm{cm}$ ). Use the tabulated data to determine (a) the order of reaction with respect to I and (b) the rate constant.
$$\begin{array}{|c|l|}\hline \text { Time/min } & \text { Absorbance } \\\hline 0 & 1.20 \\5 & 1.10 \\10 & 1.00 \\20 & 0.81 \\30 & 0.72 \\35 & 0.67 \\45 & 0.59 \\55 & 0.54 \\75 & 0.45 \\120 & 0.33\end{array}$$
[Data from: H. M. Weiss $e t$ al. (1990) J. Chem. Educ., vol. $67, \text { p. } 707 .$]

Susan Hallstrom
Susan Hallstrom
Numerade Educator
00:31

Problem 10

Phenolphthalein is an acid-base indicator. Below $\mathrm{pH} 8$ it is colourless and can be represented as $\mathrm{H}_{2} \mathrm{P},$ while at higher $\mathrm{pH}$ values it is pink and has the form $[\mathrm{P}]^{2-} .$ In strongly alkaline solution, the colour fades as the following reaction occurs: $$[\mathrm{P}]^{2-}+[\mathrm{OH}]^{-} \longrightarrow[\mathrm{POH}]^{3-}$$ An investigation of the kinetics of this reaction using a colorimeter (with a constant path length $=1 \mathrm{cm}$ ) yielded the following data: Experiment $1:\left[\mathrm{OH}^{-}\right]=0.20 \mathrm{mol} \mathrm{dm}^{-3}$ $$\begin{array}{ll}\text { Time/min } & \text { Absorbance } \\0 & 0.560 \\1 & 0.454 \\2 & 0.361 \\3 & 0.292 \\4 & 0.228 \\\hline\end{array}$$ Experiment $2:\left[\mathrm{OH}^{-}\right]=0.10 \mathrm{mol} \mathrm{dm}^{-3}$ $$\begin{array}{ll}\text { Time/min } & \text { Absorbance } \\0 & 0.560 \\2 & 0.449 \\4 & 0.361 \\6 & 0.301 \\8 & 0.247\end{array}$$ Experiment $3:\left[\mathrm{OH}^{-}\right]=0.05 \mathrm{mol} \mathrm{dm}^{-3}$ $$\begin{array}{cl}
\text { Time/min } & \text { Absorbance } \\0 & 0.560 \\3 & 0.468 \\6 & 0.415 \\9 & 0.368 \\12 & 0.313 \\\hline\end{array}$$
(a) Why was more than one experiment carried out? Why do you think three rather than two experiments were studied?
(b) What is the order of the reaction with respect to $[\mathrm{P}]^{2-} ?$
(c) What is the order of the reaction with respect to hydroxide ion?
(d) What other data are needed before the overall rate constant can be determined?
[Data from: L. Nicholson (1989) J. Chem. Educ., vol. $66, p .725 .$]

Aadit Sharma
Aadit Sharma
Numerade Educator
13:37

Problem 11

The $\left[\mathrm{MnO}_{4}\right]^{-}$ ion is an oxidizing agent and the kinetics of the alcohol oxidation: (EQUATION CAN'T COPY) have been studied. $\left[\mathrm{MnO}_{4}\right]^{-}$ absorbs at $546 \mathrm{nm}$ and the change in absorbance at this wavelength during the reaction was used to monitor the reaction. If [alcohol] $\gg\left[\mathrm{MnO}_{4}^{-}\right],$ use the following data to find the order of the reaction with respect to $\left[\mathrm{MnO}_{4}\right]^{-}$.
$$\begin{array}{ll}\text { Time / min } & \text { Absorbance }^{\mathrm{a}} \\1.5 & 0.081 \\2.0 & 0.072 \\2.5 & 0.062 \\3.0 & 0.054 \\3.5 & 0.047 \\4.0 & 0.040 \\4.5 & 0.035 \\5.0 & 0.031 \\5.5 & 0.027\end{array}$$
$^{a}$ Absorbance values have been corrected to allow for the fact that it does not reach zero when $\left[\mathrm{MnO}_{4}^{-}\right]=0$ [Data from: R. D. Crouch (1994) J. Chem. Educ., vol. $71, \text { p. } 597 .$]

Tianyu Li
Tianyu Li
Numerade Educator
01:57

Problem 12

The rate equation for a reaction of the type: $A+B \rightarrow$ products is of the form:
$$-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=k[\mathrm{A}]^{x}[\mathrm{B}]$$
If kinetic runs are carried out with A in vast excess with respect to $\mathrm{B},$ the equation can be rewritten in the form:
$$-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=k_{\mathrm{obs}}[\mathrm{B}]$$
(a) Use the following kinetic data to determine values of $x$ and $k$.
(b) What is the overall order of the reaction?
$$\begin{array}{ll}\text { IAl } / \text { mol } \mathrm{dm}^{-3} & k_{\text {obs }} / \mathrm{min}^{-1} \\0.001 & 0.16 \\0.002 & 0.31 \\0.003 & 0.49 \\0.004 & 0.68\end{array}$$

Kartik Indoliya
Kartik Indoliya
Numerade Educator
03:33

Problem 13

Kinetic data for the reaction: $$2\left[\mathrm{MnO}_{4}\right]^{-}+5\left[\mathrm{C}_{2} \mathrm{O}_{4}\right]^{2-}+16 \mathrm{H}^{+} \rightarrow 2 \mathrm{Mn}^{2+}+10 \mathrm{CO}_{2}+8 \mathrm{H}_{2} \mathrm{O}$$
are tabulated below and show the results of an experiment in which the initial concentrations of $\left[\mathrm{C}_{2} \mathrm{O}_{4}\right]^{2-}$ and $\mathrm{H}^{+}$ greatly exceed that of $\left[\mathrm{MnO}_{4}\right]^{-}$.
$$\begin{array}{ll}\text { Time / s } & 10^{3} | \mathrm{MnO}_{4}-1 / \mathrm{moldm}^{-3} \\330 & 1.00 \\345 & 0.487 \\360 & 0.223 \\375 & 0.067 \\390 & 0.030 \\405 & 0.011 \\420 & 0.005\end{array}$$
(a) Which species is the reducing agent in the reaction?
(b) Why were large initial concentrations of two reagents used?
(c) Determine the order of the reaction with respect to $\left[\mathrm{MnO}_{4}\right]^{-}$
[Data from: B. Miles et al. (1990) J. Chem. Educ., vol. $67, p .269 .$]

David Collins
David Collins
Numerade Educator
00:59

Problem 14

The concentration of A during a reaction of the type: $A+2 B-$ products changes according to the data in the table.
$$\begin{array}{cl}\text { Time / min } & \text { IAl / mol dm }^{-3} \\1 & 0.317 \\5 & 0.229 \\10 & 0.169 \\15 & 0.130 \\25 & 0.091 \\40 & 0.062\end{array}$$ The reaction is $n$ th order with respect to A and zero order with respect to B. (a) Show that $n=2$ (b) Write a rate equation for the reaction. (c) Determine the rate constant.

Anna Miller
Anna Miller
Numerade Educator
02:40

Problem 15

Indium- 115 is a $\beta$ -particle emitter with a half-life of $6 \times 10^{14} \mathrm{y} .$ (a) Write an equation for the decay of $^{115}$ In. (b) What is the rate constant for the decay?

Cheryl Glor
Cheryl Glor
Numerade Educator
02:40

Problem 16

Polonium-211 decays by $\alpha$ -particle emission.
(a) Write an equation for the decay process.
(b) If the half-life of $^{211}$ Po is $0.52 \mathrm{s},$ what is the rate constant for the decay?

Cheryl Glor
Cheryl Glor
Numerade Educator
02:40

Problem 17

Americium- 241 is an $\alpha$ -particle emitter, and the rate constant for decay is $1.605 \times 10^{-3} \mathrm{y}^{-1}$.
(a) Write an equation for the decay of $^{241} \mathrm{Am}$.
(b) Determine the half-life of $^{241} \mathrm{Am}$.

Cheryl Glor
Cheryl Glor
Numerade Educator
01:08

Problem 18

The solvolysis (reaction of a substrate with the solvent) of 2-chloro-2-methylpropane is first order with respect to the substrate. The rate constant, $k$ varies with temperature as shown below. Find $E_{a}$ for the reaction.
$$\begin{array}{ll}\text { Temperature } / \mathbf{K} & \mathbf{1 0}^{\mathbf{5}} \mathbf{k} / \mathbf{s}^{-\mathbf{1}} \\
288 & 2.78 \\298 & 8.59 \\308 & 26.1\end{array}$$
[Data from: J. A. Duncan and D. J. Pasto (1975) J. Chem. Educ., vol. $52, \text { p. } 666 .$]

Farhana Sharmin
Farhana Sharmin
Numerade Educator
03:17

Problem 19

For the reaction: $$A \rightarrow B+C$$ which of the following would you expect to vary over the temperature range 290 to $320 \mathrm{K}$ : (a) reaction rate; (b) rate constant; (c) $E_{\mathrm{a}}$ (d) $[\mathrm{A}]_{0}-[\mathrm{A}] ?$

Preeti Kumari
Preeti Kumari
Numerade Educator
03:59

Problem 20

Hydrogen peroxide decomposes as follows: $$2 \mathrm{H}_{2} \mathrm{O}_{2}--2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}$$ The rate constant for the reaction varies with temperature as follows:
$$\begin{array}{ll}\text { Temperature/K } & k / \mathrm{s}^{-1} \\295 & 4.93 \times 10^{-4} \\298 & 6.56 \times 10^{-4} \\
305 & 1.40 \times 10^{-3} \\310 & 2.36 \times 10^{-3} \\320 & 6.12 \times 10^{-3}\end{array}$$
Determine the activation energy for this reaction.

David Collins
David Collins
Numerade Educator
03:21

Problem 21

Figure 15.18 showed how the ratio of the rate constants, $\frac{k_{2}}{k_{1}},$ for a reaction changes as a function of the energy of activation and the result was valid for a rise in temperature from 300 to $310 \mathrm{K}$. For values of $E_{\mathrm{a}}$ of 10,30,50,70,90,110,130 and $150 \mathrm{kJ} \mathrm{mol}^{-1},$ determine $\frac{k_{2}}{k_{1}}$ for a change in temperature from (a) 320 to $330 \mathrm{K}$ and (b) 420 to $430 \mathrm{K} .$ Plot $\frac{k_{2}}{k_{1}}$ as a function of $E_{\mathrm{a}} .$ What significant differences are there between your graphs and Figure $15.18 ?$ Comment critically on the statement that a rise in temperature of $10 \mathrm{K}$ leads to an approximate doubling of the rate of reaction.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:56

Problem 22

(a) Explain briefly what you understand by the steady state approximation, and indicate under what circumstances it is valid.
(b) Are the following steps unimolecular or bimolecular?
$$\begin{aligned}&\mathrm{H}_{2} \rightarrow 2 \mathrm{H}^{*}\\&\mathrm{H}^{*}+\mathrm{Br}_{2} \rightarrow \mathrm{HBr}+\mathrm{Br}^{*}\\&2 \mathrm{Cl}^{*} \rightarrow \mathrm{Cl}_{2}\\&\mathrm{Cl}^{*}+\mathrm{O}_{3} \rightarrow \mathrm{ClO}^{*}+\mathrm{O}_{2}\\&\mathrm{O}_{3} \rightarrow \mathrm{O}_{2}+\mathrm{O}^{*}
\end{aligned}$$

Adriano Chikande
Adriano Chikande
Numerade Educator
00:15

Problem 23

Write a rate equation for each of the elementary steps in problem $15.22 \mathrm{b}$.

Suzana Milea
Suzana Milea
Numerade Educator
02:41

Problem 24

The mechanism of the decomposition: $A \rightarrow B+C$ can be written as a sequence of the elementary steps:
$$\begin{aligned}&\text { Step I: } A \stackrel{k_{1}}{\longrightarrow} D\\&\text { Step II: } \mathrm{D} \stackrel{k_{2}}{-\mathrm{B}+\mathrm{C}}\end{aligned}$$
(a) What type of a species is $\mathrm{D} ?$ (b) For step I alone, give an expression that shows the rate of appearance of D. (c) How is your answer to (b) altered if you take into account the sequence of steps I and II? (d) Use the steady state approximation to show that the rate of formation of B is directly proportional to the concentration of A.

Iryna Ivaniuk
Iryna Ivaniuk
Numerade Educator
06:24

Problem 25

The following data were obtained for the urease-catalysed hydrolysis of urea where $V$ is the initial velocity of reaction and $[\mathrm{S}]$ is the substrate concentration.
$$\begin{array}{cl}|\mathrm{S}| / \mathrm{mmol} \mathrm{dm}^{-3} & V / \mathrm{mmol} \min ^{-1} \\2.5 & 3.5 \times 10^{-5} \\5.0 & 6.2 \times 10^{-5} \\8.5 & 8.0 \times 10^{-5} \\10.0 & 8.6 \times 10^{-5} \\15.0 & 9.4 \times 10^{-5} \\
18.0 & 9.8 \times 10^{-5} \\40.0 & 1.2 \times 10^{-4}\end{array}$$
Show that these data are consistent with Michaelis-Menten kinetics. Determine the maximum velocity and the Michaelis constant for the reaction. [Data based on: K. R. Natarajan (1995) J. Chem. Educ., vol. $72, \text { p. } 556 .$]

Justin Leonesio
Justin Leonesio
Numerade Educator
13:37

Problem 26

The cobalt(III) complex $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{NO}_{2}\right)\right]^{2+}$ possesses two linkage isomers (see Section 23.5 ) in which the $\left[\mathrm{NO}_{2}\right]^{-}$ is bonded to $\mathrm{Co}^{3+}$ through either the $\mathrm{N}$ or $\mathrm{O}$ atom. Over a period of days, the O-bonded isomer converts to the N-bonded isomer; let this be represented as: Isomer I $\rightarrow$ Isomer II The isomerization can be followed using IR spectroscopy by monitoring the disappearance of an absorption at $1060 \mathrm{cm}^{-1} .$ Data are tabulated below and the infinity reading $(t=\infty)$ corresponds to the absorbance at $1060 \mathrm{cm}^{-1}$ when isomerization is complete.
$$\begin{array}{cc}\text { Time / days } & \text { Absorbance } \\0 & 0.480 \\0.125 & 0.462 \\0.5 & 0.414 \\2.0 & 0.349 \\4.0 & 0.283 \\11.0 & 0.156 \\18.0 & 0.118 \\\infty & 0.108\end{array}$$
(a) Correct each absorbance value for the fact that the absorption at $1060 \mathrm{cm}^{-1}$ does not fully disappear at $t=\infty .$ (b) Plot the corrected absorbance values against time. What information does the graph give you? (c) Find the order of the reaction with respect to I, and determine the rate constant.
[Data from: W. H. Hohman (1974) J. Chem. Educ., vol. $51, \text { p. } 553 .$]

Tianyu Li
Tianyu Li
Numerade Educator
13:37

Problem 27

Cerium(IV) ions oxidize $\mathrm{Fe}^{2+}$ ions as follows: $$\mathrm{Ce}^{4+}(\mathrm{aq})+\mathrm{Fe}^{2+}(\mathrm{aq})-\mathrm{Ce}^{3+}(\mathrm{aq})+\mathrm{Fe}^{3+}(\mathrm{aq})$$ When the reaction is carried out as a redox titration in the presence of the indicator N-phenylanthranilic acid, the end point is when the solution becomes purple $\left(\lambda_{\max }=580 \mathrm{nm}\right) .$ If the final solution is left to stand, the purple colour fades to yellow, and the kinetics of the decay can be followed by monitoring the absorbance at $580 \mathrm{nm}$ :
$$\begin{array}{cc}\text { Time / s } & \text { Absorbance } \\30 & 0.65 \\60 & 0.60 \\90 & 0.55 \\120 & 0.52 \\180 & 0.46 \\
240 & 0.40 \\300 & 0.32 \\360 & 0.28 \\420 & 0.24 \\480 & 0.21\end{array}$$
(a) Plot the absorbance against time. How easy is it to state that the decay is not zero order? (b) Show that the decay follows first order kinetics. (c) Determine the rate constant. [Data from: S. K. Mishra et al. (1976) J. Chem. Educ., vol. $53, \text { p. } 327 .$]

Tianyu Li
Tianyu Li
Numerade Educator
01:22

Problem 28

The overall rate law for the following reaction: $$2 \mathrm{NO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})-\mathrm{N}_{2} \mathrm{O}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ $$\text { is: } \quad-\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t}=k_{\mathrm{obs}}[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right]$$ Confirm that the following mechanism is consistent with the observed rate law: (EQUATION CAN'T COPY) $$\mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \stackrel{k_{2}}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}$$

Adriano Chikande
Adriano Chikande
Numerade Educator
01:08

Problem 29

In the text, the working for the derivation of equation 15.102 was omitted. Show that the substitution for $[\mathrm{E}]$ into equation 15.101 gives equation 15.102.

Edward Zhang
Edward Zhang
Numerade Educator
13:37

Problem 30

Laccases are copper-containing enzymes that occur in fungi and bacteria. In nature, laccases catalyse various redox reactions. In the laboratory, their activity can be investigated using substrates such as compound $15.5,$ the laccase-catalysed oxidation of which is accompanied by a colour change from pale yellow to purple. The following data were recorded during experiments to investigate the affect of $\mathrm{pH}$ on the rate of oxidation of 15.5 in the presence of laccase. Each reaction initially uses $0.30 \mathrm{cm}^{3}$ of a $5.0 \times 10^{-4} \mathrm{mol} \mathrm{dm}^{-3}$ ethanol solution of 15.5 in a cuvette. (TABLE CAN'T COPY)
(a) Explain why the laccase-catalysed oxidation of 15.5 can be followed by monitoring the absorbance of the solution at $\lambda_{\max }=525 \mathrm{nm}$ What other information do you need to convert absorbance data into concentrations of product?
(b) Use the data above to illustrate how the activity of laccase is affected by $\mathrm{pH},$ and suggest a reason for the trend in activity.
[Data: Y. Lin et al.(2006) J. Chem. Educ., vol. 83 p. 638.]

Tianyu Li
Tianyu Li
Numerade Educator
26:32

Problem 31

Aspartame (see Box 35.3 ) is an artificial sweetener used in fizzy drinks. However, it decomposes in aqueous solution. The rate law for the decomposition is: $$-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=k_{\mathrm{obs}}[\mathrm{A}]$$ where $A=$ aspartame. Kinetic data (at $313 \mathrm{K}$ ) for the decomposition of aspartame in aqueous solution at $\mathrm{pH} 7.0$ are as follows: (TABLE CAN'T COPY)
(a) What is the integrated form of the rate equation?
(b) Using the data above, determine the rate constant for the decomposition of aspartame.
(c) Determine the half-life of aspartame under the conditions of the experiment.
(d) At $280 \mathrm{K},$ would the half-life be longer or shorter than the value determined in part (c)? Rationalize your answer.
[Based on data in: K. R. Williams et al. (2005) J. Chem. Educ., vol. $82, \text { p. } 924 .$]

Carlene Jimenez
Carlene Jimenez
Numerade Educator