15. Chemical Kinetics

Integrated Rate Law

First Order Integrated Rate Laws

The rate of a first-order reaction is followed by spectroscopy,
monitoring the absorbance of a colored reactant at 520 nm.
The reaction occurs in a 1.00-cm sample cell, and the only
colored species in the reaction has an extinction coefficient
of 5.60 * 103 M-1 cm-1 at 520 nm. (d) How long does it take for the absorbance to fall to 0.100?

Some reactions are so rapid that they are said to be
diffusion-controlled; that is, the reactants react as quickly
as they can collide. An example is the neutralization of
H3O+ by OH-, which has a second-order rate constant of
1.3 * 1011 M-1 s-1 at 25 °C.
(a) If equal volumes of 2.0 M HCl and 2.0 M NaOH are
mixed instantaneously, how much time is required for
99.999% of the acid to be neutralized?

The first-order rate constant for the decomposition of
N2O5, 2 N2O51g2¡4 NO21g2 + O21g2, a t 70 C i s
6.82 * 10-3 s-1. Suppose we start with 0.0250 mol of
N2O51g2 in a volume of 2.0 L. (a) How many moles of
N2O5 will remain after 5.0 min?

Integrated Rate Law Concept 3

The gas-phase decomposition of NO2, 2 NO21g2¡
2 NO1g2 + O21g2, is studied at 383 C, giving the following
data:
Time (s) 3no2 4 (M)
0.0 0.100
5.0 0.017
10.0 0.0090
15.0 0.0062
20.0 0.0047
(c) Predict the reaction rates at the beginning of the
reaction for initial concentrations of 0.200 M, 0.100 M,
and 0.050 M NO2.

1.36×10–3 M–1•hr–1

2.26×10–3 M–1•hr–1

Iodine-123 is used to study thyroid gland function. As this radioactive isotope breaks down, after 5.7 hrs the concentration of iodine-123 is 56.3% complete. Find the rate constant of this reaction.

The tabulated data were collected for this reaction at 500 °C:
CH3CN(g)¡CH3NC( g)
Time (h) [Ch3Cn] (M)
0.0 1.000
5.0 0.794
10.0 0.631
15.0 0.501
20.0 0.398
25.0 0.316
a. Determine the order of the reaction and the value of the rate
constant at this temperature.

Integrated Rate Law Example 2

Integrated Rate Law Concept 2

As described in Exercise 14.41, the decomposition of sulfuryl
chloride 1SO2Cl22 is a first-order process. The rate
constant for the decomposition at 660 K is 4.5 * 10-2 s-1.
(b) At what time will the partial pressure of SO2Cl2 decline
to one-tenth its initial value?

The tabulated data show the concentration of AB versus time
for this reaction:
AB( g)¡A( g) + B( g)
Time (s) [AB] (M)
0 0.950
50 0.459
100 0.302
150 0.225
200 0.180
250 0.149
300 0.128
350 0.112
400 0.0994
450 0.0894
500 0.0812
Determine the order of the reaction and the value of the rate
constant. Predict the concentration of AB at 25 s.

Kinetics: Initial Rates and Integrated Rate Laws

Nitrosyl bromide decomposes at 10 °C. 
NOBr1g2S NO1g2 + 1>2 Br21g2 
Use the following kinetic data to determine the order of the 
reaction and the value of the rate constant for consumption 
of NOBr.
<TABLE><img src="https://lightcat-files.s3.amazonaws.com/problem_images/846509d862fee737-1671979208306.jpg" alt="" />

Consider the following concentration–time data for the 
decomposition reaction AB S A + B. 
<TABLE> 
(b) What is the molarity of AB after a reaction time of 
192 min?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/ae901de880772170-1671984464716.jpg" alt="" />

Integrated Rate Law Example 1

Second Order and Zeroth Order Integrated Rate Laws

The reaction 2 NO1g2 + O21g2S 2 NO21g2 has the thirdorder
rate law rate = k3NO423O24, where k = 25 M-2 s-1.
Under the condition that 3NO4 = 2 3O24, the integrated
rate law is
13O242 = 8 kt +113O24022
What are the concentrations of NO, O2, and NO2 after
100.0 s if the initial concentrations are 3NO4 = 0.0200 M
and 3O24 = 0.0100 M?

Indicate the order of reaction consistent with each observation.
a. The half-life of the reaction gets shorter as the initial concentration is increased.

You wish to determine the reaction order and rate constant 
for the following thermal decomposition reaction: 
AB2 S 1>2 A2 + B2 
(c) Describe how you would determine the value of the rate 
constant.

For the thermal decomposition of nitrous oxide, 2 N2O1g2S 
2 N21g2 + O21g2, values of the parameters in the Arrhenius 
equation are A = 4.2 * 109 s-1 and Ea = 222 kJ>mol. If a 
stream of N2O is passed through a tube 25 mm in diameter 
and 20 cm long at a flow rate of 0.75 L/min at what temperature 
should the tube be maintained to have a partial 
pressure of 1.0 mm of O2 in the exit gas? Assume that the 
total pressure of the gas in the tube is 1.50 atm.

The rate constant for the decomposition of gaseous NO2 to 
NO and O2 is 4.7>1M ~ s2 at 383 °C. Consider the decomposition 
of a sample of pure NO2 having an initial pressure 
of 746 mm Hg in a 5.00 L reaction vessel at 383 °C. 
(c) What is the mass of O2 in the vessel after a reaction time 
of 1.00 min?

You wish to determine the activation energy for the following 
first-order reaction: 
AS B + C 
(b) How would you use these data to determine the activation 
energy?

A 0.500 L reaction vessel equipped with a movable piston 
is filled completely with a 3.00% aqueous solution of 
hydrogen peroxide. The H2O2 decomposes to water and O2 
gas in a first-order reaction that has a half-life of 10.7 h. 
As the reaction proceeds, the gas formed pushes the piston 
against a constant external atmospheric pressure of 
738 mm Hg. Calculate the PV work done (in joules) after a 
reaction time of 4.02 h. (You may assume that the density 
of the solution is 1.00 g/mL and that the temperature of the 
system is maintained at 20 °C.)

The following reaction has a rate constant of 3.7 × 10–3 M•s–1 at 25°C:A → B + CCalculate the concentration of C after 2.7 × 10–3 sec where [A]0 was 0.750 M at 25°C; assume [C]0 = 0 M.

This reaction was monitored as a function of time:
A → B + C
A plot of ln[A] versus time yields a straight line with
slope -0.0045/s.
a. What is the value of the rate constant (k) for this reaction at
this temperature?

Indicate the order of reaction consistent with each observation
c. The half-life of the reaction gets longer as the initial concentration is increased.

Iodine atoms combine to form I2 in liquid hexane solvent with a
rate constant of 1.5 * 1010 L>mol # s. The reaction is second
order in I. Since the reaction occurs so quickly, the only way to
study the reaction is to create iodine atoms almost instantaneously,
usually by photochemical decomposition of I2. Suppose
a flash of light creates an initial [I] concentration of 0.0100 M.
How long will it take for 95% of the newly created iodine atoms
to recombine to form I2?

14.5 Integrated Rate Laws | General Chemistry

The Integrated Rate Laws

The gas phase decomposition of HI has the following rate law: 
2 HI1g2¡H21g2 + I21g2 Rate = k3HI42 
At 443 °C, k = 30.1 M-1 min-1. If the initial concentration 
of HI is 0.010 M, what is the concentration after 1.5 hours? 
(LO 14.8) 
(a) 6.9 * 10-3 M (b) 1.8 * 10-3 M 
(c) 3.6 * 10-4 M (d) 8.9 * 10-4 M

For the decomposition of urea, NH2CONH2 (aq) + H+(aq) + 2 H2O (l) → 2 NH4+ (aq) + HCO3– (aq), the rate constant is 3.24 × 10–4 s–1 at 35°C. The initial concentration of urea is 2.89 mol/L. What fraction of urea has decomposed after 3.5 minutes?

A certain substance X decomposes. Fifty percent of X remains 
after 100 minutes. How much X remains after 200 minutes if 
the reaction order with respect to X is (c) second order?

Molecular Orbital Theory, Integrated Rate Laws, The Arrhenius Equation, Stoichiometry Word Problem

The decomposition of N2O5 is a first-order reaction. At 25 °C, 
it takes 5.2 h for the concentration to drop from 0.120 M 
to 0.060 M. How many hours does it take for the concentration 
to drop from 0.030 M to 0.015 M? From 0.480 M to 
0.015 M?

The reaction 2 NO2¡2 NO + O2 has the rate constant
k = 0.63 M- 1s - 1. (b) If the initial concentration
of NO2 is 0.100 M, how would you determine
how long it would take for the concentration to decrease
to 0.025 M?

Assume that you are studying the first-order conversion of
a reactant X to products in a reaction vessel with a constant
volume of 1.000 L. At 1 p.m., you start the reaction
at 25 °C with 1.000 mol of X. At 2 p.m., you find that
0.600 mol of X remains, and you immediately increase the
temperature of the reaction mixture to 35 °C. At 3 p.m.,
you discover that 0.200 mol of X is still present. You want
to finish the reaction by 4 p.m. but need to continue it until
only 0.010 mol of X remains, so you decide to increase the
temperature once again. What is the minimum temperature
required to convert all but 0.010 mol of X to products
by 4 p.m.?

Chlorine monoxide (ClO) decomposes at room temperature 
according to the reaction 
2 ClO1g2¡Cl21g2 + O21g2 
The concentration of ClO was monitored over time, and 
three graphs were made:
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/96d7e963ce96e3b2-1671986868973.jpg" alt="" /><img src="https://lightcat-files.s3.amazonaws.com/problem_images/5eea5d715a948e51-1671986872370.jpg" alt="" />
What is the rate law for the reaction? (LO 14.9) 
(a) Rate = k (b) Rate = k3ClO4 
(c) Rate = k3ClO42 (d) Rate = k3ClO43 
M14_MCMU6230_

(a) For the generic reaction A S B what quantity, when
graphed versus time, will yield a straight line for a
first-order reaction?

This reaction was monitored as a function of time:
AB → A + B
A plot of 1/[AB] versus time yields a straight line with a slope of
+0.55/Ms.
b. Write the rate law for the reaction.

Some reactions are so rapid that they are said to be 
diffusion-controlled; that is, the reactants react as quickly 
as they can collide. An example is the neutralization of 
H3O+ by OH-, which has a second-order rate constant of 
1.3 * 1011 M-1 s-1 at 25 °C. 
(b) Under normal laboratory conditions, would you expect 
the rate of the acid–base neutralization to be limited by 
the rate of the reaction or by the speed of mixing?

Consider the following concentration–time data for the
decomposition reaction AB S A + B.
<TABLE>
(a) Determine the order of the reaction and the value of the
rate constant.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/8b3ea4174d53cd18-1671984478820.jpg" alt="" />

For the reaction A → &nbsp;B, the rate constant is 0.0837 M–1•sec–1. How long would it take for [A] to decrease by 85%?

Dinitrogen pentoxide decomposes in the gas phase to form nitrogen
dioxide and oxygen gas. The reaction is first order in
dinitrogen
pentoxide and has a half-life of 2.81 h at 25 °C. If a 1.5-L
reaction vessel initially contains 745 torr of N2O5 at 25 °C, what
partial pressure of O2 is present in the vessel after 215 minutes?

The tabulated data were collected for this reaction at a certain
temperature:
X2Y¡2 X + Y
Time (h) [X2y] (M)
0.0 0.100
1.0 0.0856
2.0 0.0748
3.0 0.0664
4.0 0.0598
5.0 0.0543
c. What is the concentration of X after 10.0 hours?

Sucrose 1C12H22O112, commonly known as table sugar,
reacts in dilute acid solutions to form two simpler sugars,
glucose and fructose, both of which have the formula
C6H12O6. At 23 C and in 0.5 M HCl, the following data
were obtained for the disappearance of sucrose:
Time (min) 3C12H22o11 4 1M2
0 0.316
39 0.274
80 0.238
140 0.190
210 0.146
(a) Is the reaction first order or second order with respect to
3C12H22O114?

The rate constant for the first-order decomposition of gaseous
N2O5 to NO2 and O2 is 1.7 * 10-3 s-1 at 55 °C.
(a) If 2.70 g of gaseous N2O5 is introduced into an evacuated
2.00 L container maintained at a constant temperature
of 55 °C, what is the total pressure in the
container after a reaction time of 13.0 minutes?

Integrated Rate Law Example 3

Integrated Rate Law Concept 1

The tabulated data were collected for this reaction at a certain
temperature:
X2Y¡2 X + Y
Time (h) [X2y] (M)
0.0 0.100
1.0 0.0856
2.0 0.0748
3.0 0.0664
4.0 0.0598
5.0 0.0543
a. Determine the order of the reaction and the value of the rate
constant at this temperature.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/f1c80bfdf11035e5-1674509007175.jpg" alt="" />

Which of the following linear plots do you expect for a
reaction A¡products if the kinetics are (a) zero order, [Section 14.4]
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/fe3831e00d552752-1666282854514.jpg" alt="" />

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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.

Arrhenius Equation

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.

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.