15. Chemical Kinetics

Half-Life

Kinetics:  The Half Life

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.
(c) What is the half-life of N2O5 at 70 C ?

The desorption (leaving of the surface) of a single molecular 
layer of n-butane from a single crystal of aluminum oxide is 
found to be first order with a rate constant of 0.128>s at 150 K. 
b. If the surface is initially completely covered with n-butane 
at 150 K, how long will it take for 25% of the molecules to 
desorb (leave the surface)? For 50% to desorb?

Anthropologists can estimate the age of a bone or other sample of
organic matter by its carbon-14 content. The carbon-14 in a living
organism is constant until the organism dies, after which carbon-
14 decays with first-order kinetics and a half-life of 5730 years.
Suppose a bone from an ancient human contains 19.5% of the
C-14 found in living organisms. How old is the bone?

The average rate of a reaction decreases during a reaction.

The rate of zero order reactions are not dependent on concentrations.

The rate of a first order reaction is dependent on concentrations.

The half-life of a first order reaction is dependent on the initial concentration of reactant.

Which of the following statements is False?

From the following data for the first-order gas-phase 
isomerization of CH3NC at 215 C, calculate the firstorder 
rate constant and half-life for the reaction:
Time (s) Pressure CH3nC (torr) 
0 502 
2000 335 
5000 180 
8000 95.5 
12,000 41.7 
15,000 22.4<img src="https://lightcat-files.s3.amazonaws.com/problem_images/2f17fd7519bba5b6-1666282322244.jpg" alt="" />

The half-life for the radioactive decay of C-14 is 5730 years and is
independent of the initial concentration. How long does it take
for 25% of the C-14 atoms in a sample of C-14 to decay?

What is the half-life (in minutes) of the reaction in Problem 
14.74 when the initial C4H6 concentration is 0.0200 M? 
How many minutes does it take for the concentration of 
C4H6 to drop from 0.0100 M to 0.0050 M?

Radioactive plutonium-239 (t1/2 = 2.41 × 105 yr) is used in nuclear reactors and atomic bombs. If there are 5.70 × 102 g of plutonium isotope in a small atomic bomb, how long will it take for the substance to decay to 3.00 × 102 g?

Decomposition of a certain substance Y at 45°C was found to be zero order. What is the half-life of substance Y if it took 15.5 minutes to decompose 67% of this substance? [Y]0 = 0.25 M.

Half-life of a first-order reaction | Kinetics | AP Chemistry | Khan Academy

(a) The gas-phase decomposition of SO2Cl2, SO2Cl21g2
¡SO21g2 + Cl21g2, is first order in SO2Cl2. At 600 K
the half-life for this process is 2.3 * 105 s. What is the
rate constant at this temperature?

The half-life for the first-order decomposition of N2O4 is 
1.3 * 10-5 s. 
N2O41g2S 2 NO21g2 
If N2O4 is introduced into an evacuated flask at a pressure 
of 17.0 mm Hg, how many seconds are required for the 
pressure of NO2 to reach 1.3 mm Hg?

Half-Life Example 2

The half-life for radioactive decay (a first-order process) of 
plutonium- 
239 is 24,000 years. How many years does it take for 
one mole of this radioactive material to decay until just one 
atom remains?

Americium-241 is used in smoke detectors. It has
a first-order rate constant for radioactive decay of
k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is
used to test for thyroid functioning, has a rate constant
for radioactive decay of k = 0.011 day-1. (b) Which one decays at
a faster rate?

Half-Life Concept 1

Consider the first-order decomposition of A molecules (red 
spheres) in three vessels of equal volume. 
(1)-(3) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/2982315c4631d263-X.jpg" alt="" /> 
(c) How will the rates and half-lives be affected if the 
volume 
of each vessel is decreased by a factor of 2?

Americium-241 is used in smoke detectors. It has
a first-order rate constant for radioactive decay of
k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is
used to test for thyroid functioning, has a rate constant
for radioactive decay of k = 0.011 day-1. (c) How much of a 1.00-mg sample of each
isotope remains after three half-lives?

Consider the data presented in Exercise 14.19. (c) What is the half-life for the reaction?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/4b77ad9198d695af-1666282429548.jpg" alt="" />

Consider the first-order decomposition of A molecules (red 
spheres) in three vessels of equal volume. 
(1)-(3) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/8253c45da0283740-1672043152095.jpg" alt="" /> 
(b) What are the relative half-lives of the reactions in vessels 
(1)–(3)?

The half-life for the radioactive decay of U-238 is 4.5 billion
years and is independent of initial concentration. How long
will it take for 10% of the U-238 atoms in a sample of U-238 to
decay?

The evaporation of a 120-nm film of n-pentane from a single
crystal of aluminum oxide is zero order with a rate constant of
1.92 * 1013 molecules>cm2 # s at 120 K.
a. If the initial surface coverage is 8.9 * 1016 molecules>cm2, 
how long will it take for one-half of the film to evaporate?

Consider two reactions. Reaction (1) has a constant halflife, 
whereas reaction (2) has a half-life that gets longer as 
the reaction proceeds. What can you conclude about the 
rate laws of these reactions from these observations?

Half-life of a second-order reaction | Kinetics | Chemistry | Khan Academy

Half-Life Example 1

Given the following diagrams at t = 0 min and
t = 30 min
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/95d2d56e775d8343-1666282180255.jpg" alt="" />
After four half-life periods for a first-order reaction, 
what fraction of reactant remains? [Section 14.4]

Half-Life Concept 3

Consider the first-order reaction AS B in which A molecules
(red spheres) are converted to B molecules (blue spheres).
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/469c44299be1e277-FOR.jpg" alt="" />
(a) Given the pictures at t = 0 min and t = 1 min, draw
pictures that show the number of A and B molecules
present at t = 2 min and t = 3 min.

Trans-cycloheptene 1C7H122, a strained cyclic hydrocarbon, 
converts to cis-cycloheptene at low temperatures. This 
molecular rearrangement is a second-order process with a 
rate constant of 0.030 M-1 s-1 at 60 °C. If the initial concentration 
of trans-cycloheptene is 0.035 M: 
(c) What is the half-life of trans-cycloheptene at an initial 
concentration of 0.075 M?

The desorption (leaving of the surface) of a single molecular
layer of n-butane from a single crystal of aluminum oxide is
found to be first order with a rate constant of 0.128>s at 150 K.
a. What is the half-life of the desorption reaction?

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. (c) Calculate the half-life of the reaction.

14.5 Integrated Rate Laws | General Chemistry

Use the data below to determine the half-life of decomposition of NOCl reaction which follows 2nd order kinetics.<img src="https://static.studychannel-prd.pearsonprd.tech/courses/general-chemistry/thumbnails/images/e692fe74"class="fr-fic fr-dii">

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
b. What is the half-life for this reaction (at the initial
concentration)?

Kinetics of Radioactive Decay

The decomposition of XY is second order in XY and has a rate
constant of 7.02 * 10 - 3 M- 1 # s - 1 at a certain temperature.
a. What is the half-life for this reaction at an initial concentration
of 0.100 M?

Half-Life Example 3

Half-Life Concept 2

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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.

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 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.