15. Chemical Kinetics

Arrhenius Equation

Energy Diagrams, Catalysts, and Reaction Mechanisms

When dealing with TWO rate constants or&nbsp;TWO temperatures then we use the Two-Point Form of the Arrhenius Equation.&nbsp;

The accompanying graph shows plots of ln k versus 1>T
for two different reactions. The plots have been extrapolated
to the y-intercepts. Which reaction (red or blue) has
(b) the larger value for the
frequency factor, A? [Section 14.5]
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/96e6ffcf6df10607-1666025322434.jpg" alt="" />

If the rate of a reaction increases by a factor of 2.5 when the 
temperature is raised from 20 °C to 30 °C, what is the value 
of the activation energy in kJ/mol? By what factor does the 
rate of this reaction increase when the temperature is raised 
from 120 °C to 130 °C?

A reaction has a rate constant of 0.0117>s at 400.0 K and
0.689>s at 450.0 K.
a. Determine the activation barrier for the reaction.

The activation energy of an uncatalyzed reaction is
95 kJ>mol. The addition of a catalyst lowers the activation
energy to 55 kJ>mol. Assuming that the collision
factor remains the same, by what factor will the catalyst
increase the rate of the reaction at (a) 25 C

(a) The activation energy for the isomerization of methyl
isonitrile (Figure 14.6) is 160 kJ>mol. Calculate the fraction
of methyl isonitrile molecules that has an energy
equal to or greater than the activation energy at 500 K.
(b) Calculate this fraction for a temperature of 520 K.
What is the ratio of the fraction at 520 K to that at 500 K?

Which of these two reactions would you expect to have the
smaller orientation factor? Explain.
a. O( g) + N2( g)¡NO( g) + N(g)
b. NO( g) + Cl2( g)¡NOCl( g) + Cl( g)

Arrhenius Equation Concept 1

The enzyme urease catalyzes the reaction of urea,
1NH2CONH22, with water to produce carbon dioxide and
ammonia. In water, without the enzyme, the reaction proceeds
with a first-order rate constant of 4.15 * 10-5 s-1 at
100 C. In the presence of the enzyme in water, the reaction
proceeds with a rate constant of 3.4 * 104 s-1 at 21 C.
(c) In actuality, what would you expect
for the rate of the catalyzed reaction at 100 C as compared
to that at 21 C?

The reaction between ethyl iodide and hydroxide ion in
ethanol 1C2H5OH2 solution, C2H5I1alc2 + OH- 1alc2 ¡
C2H5OH1l2 + I - 1alc2, has an activation energy of
86.8 kJ>mol and a frequency factor of 2.10 * 1011 M-1 s-1.
(d) Assuming the frequency factor and activation
energy do not change as a function of temperature,
calculate the rate constant for the reaction at 50 C.

The kinetics of this reaction were studied as a function of temperature. 
(The reaction is first order in each reactant and second 
order overall.) 
C2H5Br(aq) + OH- (aq)¡C2H5OH(l ) + Br - (aq) 
Temperature (°C) k (L,mol # s) 
25 8.81 * 10- 5 
35 0.000285 
45 0.000854 
55 0.00239 
65 0.00633 
b. Determine the rate constant at 15 °C.

Consider these two gas-phase reactions: 
a. AA( g) + BB( g)¡2 AB( g) 
b. AB( g) + CD( g)¡AC( g) + BD( g) 
If the reactions have identical activation barriers and are carried 
out under the same conditions, which one would you expect to 
have the faster rate?

A reaction with an activation energy Ea = 55.00 kJ/mol is run at temperature of 30ºC. Determine the temperature required to increase the rate constant 3 times.

Arrhenius Equation Example 3

The data shown here were collected for the first-order reaction: 
N2O( g)¡N2( g) + O( g) 
Use an Arrhenius plot to determine the activation barrier and 
frequency factor for the reaction. 
Temperature (K) Rate Constant (1 , s) 
800 3.24 * 10- 5 
900 0.00214 
1000 0.0614 
1100 0.955

In a hydrocarbon solution, the gold compound
1CH323AuPH3 decomposes into ethane 1C2H62 and a
different gold compound, 1CH32AuPH3. The following
mechanism has been proposed for the decomposition of
1CH323AuPH3:
Step 1: 1CH323 AuPH3 Δ k1 k -1 1CH323Au + PH3 1fast2
Step 2: 1CH323 Au ¡k2 C2H6 + 1CH32Au 1slow2
Step 3: 1CH32Au + PH3 ¡k3 1CH32AuPH3 1fast2
(f) What would be the effect on the reaction
rate of adding PH3 to the solution of 1CH323AuPH3?

Calculate the fraction of atoms in a sample of argon gas at 
400 K that has an energy of 10.0 kJ or greater.

The following data shows the rate constant of a reaction measured at numerous temperatures. Use the Arrhenius plot to determine the frequency factor for the reaction.<img src="https://static.studychannel.pearsonprd.tech/courses/general-chemistry/thumbnails/images/8d86ddfb"class="fr-fic fr-dii">

A reaction has a rate constant of 0.000122>s at 27 °C and 
0.228>s at 77 °C. 
b. What is the value of the rate constant at 17 °C?

The rate constant of a reaction at 32°C is 0.060/s. If the frequency factor is 3.1 × 1015 s–1, what is the activation barrier?

Ethyl chloride vapor decomposes by the first-order reaction:
C2H5Cl¡C2H4 + HCl
The activation energy is 249 kJ>mol, and the frequency factor is
1.6 * 1014 s - 1. What fraction of the ethyl chloride decomposes in 15 minutes at
this temperature?

The activation energy of an uncatalyzed reaction is
95 kJ>mol. The addition of a catalyst lowers the activation
energy to 55 kJ>mol. Assuming that the collision
factor remains the same, by what factor will the catalyst
increase the rate of the reaction at (b) 125 C?

In order to relate the plot of a graph to the Arrhenius equation then we manipulate it into the Linear Form of the equation.&nbsp;

The tabulated data show the rate constant of a reaction measured 
at several different temperatures. Use an Arrhenius plot to 
determine the activation barrier and frequency factor for the 
reaction. 
Temperature (K) Rate Constant (1 , s) 
300 0.0134 
310 0.0407 
320 0.114 
330 0.303 
340 0.757

Arrhenius Equation Example 1

Arrhenius Equation Example 2

The activation energy of a reaction is 56.8 kJ>mol and the frequency
factor is 1.5 * 1011> s. Calculate the rate constant of
the reaction at 25 °C.

The other forms of the Arrhenius Equation

The rate constant (k) for a reaction was measured as a function
of temperature. A plot of ln k versus 1>T (in K) is linear and has
a slope of -7445 K. Calculate the activation energy for the reaction.

The activation barrier for the hydrolysis of sucrose into glucose
and fructose is 108 kJ>mol. If an enzyme increases the rate of the
hydrolysis reaction by a factor of 1 million, how much lower must
the activation barrier be when sucrose is in the active site of the
enzyme? (Assume that the frequency factors for the catalyzed and
uncatalyzed reactions are identical and a temperature of 25 °C.)

A certain first-order reaction has a rate constant of 
1.0 * 10-3 s-1 at 25 °C. 
(b) What is the Ea (in kJ/mol) if the same temperature 
change causes the rate to triple?

Arrhenius Equation Concept 2

The accompanying graph shows plots of ln k versus 1>T
for two different reactions. The plots have been extrapolated
to the y-intercepts. Which reaction (red or blue) has
(a) the larger value for Ea,
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/ff0d59beef4c5845-1666025115768.jpg" alt="" />

The temperature dependence of the rate constant for a reaction 
is tabulated as follows:
Temperature (K) k 1M 1 s1 2 
600 0.028 
650 0.22 
700 1.3 
750 6.0 
800 23
Calculate Ea and A.

Values of Ea = 6.3 kJ>mol and A = 6.0 * 108>1M # s2 
have been measured for the bimolecular reaction: 
NO1g2 + F21g2S NOF1g2 + F1g2 
(a) Calculate the rate constant at 25 °C.

14.4 Collision Theory and the Arrhenius Equation

At 28 C, raw milk sours in 4.0 h but takes 48 h to sour 
in a refrigerator at 5 C. Estimate the activation energy in 
kJ>mol for the reaction that leads to the souring of milk.

(a) Based on the following energy profile, predict
whether kf > kr or kf < kr. [Section 15.1]
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/373965792b115acd-1666025679671.jpg" alt="" />

Ethyl chloride vapor decomposes by the first-order reaction:
C2H5Cl¡C2H4 + HCl
The activation energy is 249 kJ>mol, and the frequency factor is
1.6 * 1014 s - 1. Find the value of the rate constant at 710 K.

Arrhenius Equation Concept 3

The reaction 2 N2O5¡2 N2O4 + O2 takes place at around
room temperature in solvents such as CCl4. The rate constant at
293 K is found to be 2.35 * 10 - 4 s - 1, and at 303 K the rate constant
is found to be 9.15 * 10 - 4 s - 1. Calculate the frequency
factor for the reaction.

The Arrhenius Equation

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Clutch Prep

1. Intro to General Chemistry

2. Atoms & Elements

3. Chemical Reactions

4. BONUS: Lab Techniques and Procedures

5. BONUS: Mathematical Operations and Functions

6. Chemical Quantities & Aqueous Reactions

7. Gases

8. Thermochemistry

9. Quantum Mechanics

10. Periodic Properties of the Elements

11. Bonding & Molecular Structure

12. Molecular Shapes & Valence Bond Theory

13. Liquids, Solids & Intermolecular Forces

14. Solutions

16. Chemical Equilibrium

17. Acid and Base Equilibrium

18. Aqueous Equilibrium

19. Chemical Thermodynamics

20. Electrochemistry

21. Nuclear Chemistry

22. Organic Chemistry

23. Chemistry of the Nonmetals

24. Transition Metals and Coordination Compounds

[BOOK CHEM] Clutch Version

Intro to Chemical Kinetics

Chemical Kinetics is the study of factors affecting reaction rates, which examines the speed by which reactants are consumed to make products.

Average Rate of Reaction

Average (General) Rate is the change in the concentration of a compound over a period of time.

The Arrhenius Equation&nbsp;illustrates the temperature dependence of the rate constant k.&nbsp;

Rate Law

Rate Law represents an equation for a chemical reaction that connects the reaction rate with the concentrations or pressures of the reactants and the rate constant.&nbsp;

Factors Influencing Rates

There are 4 major factors that directly influence how fast or slow a reaction proceeds.

Stoichiometric Rate Calculations

When the rate of one compound is know, the rate of another compound is calculated through rate-to-rate comparison.

Collision Theory

According to Collision Theory:chemical reaction is successful when 2 energetic reactants successfully collide.

Integrated Rate Law

When we include the variable of time to our Rate Law then we obtain the Integrated Rate Laws.&nbsp;

Catalyst

Catalyst is a substance that increases the rate of reaction by lowering the Activation Energy (Ea) of a reaction.

Instantaneous Rate

<div title="Page 1">&nbsp;Instantaneous Rate is the rate a reaction at any particular point in time.</div>

Reaction Mechanism

<div title="Page 1">A Reaction Mechanism is a step-by-step sequence of elementary steps by which an overall chemical change occurs.</div>

Half-Life

Half-Life is the time it takes for half&nbsp;of a reactant to decay in a certain time period.

Energy Diagrams

Energy Diagram represents a curved plot illustrating the energies of reactants, products and transition states of a reaction.