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Rates of Chemical Reactions
© Jim Birk
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Questions for Consideration
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1. What conditions affect reaction rates?2. How do molecular collisions explain
chemical reactions?3. How do concentration, temperature, and
catalysts affect molecular collisions and reaction rates?
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Outline
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1. Reaction Rates definition
2. Collision Theory
3. Conditions That Affect Reaction Rates
– concentration, temperature,
catalysis, surface area
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Reaction Rates
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Reaction Rates
Reaction rate is a measure of how fast a reaction
occurs. Some reactions are inherently fast
and some are slow:
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Reaction Rates
How do we measure rates in our
everyday lives?
How do we measure rates of
chemical reactions?
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Expressing the Reaction Rate
reaction rate - changes in the concentrations of reactants or products per
unit time
reactant concentrations decrease while product concentrations
increase
rate of reaction = -
for
A B
change in concentration of A
change in time
= -conc A2-conc A1
t2-t1
(conc A)-
t
Reaction Rates
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Concentration of O3 at Various Time in its Reaction with C2H4 at 303K
C2H4(g) + O3(g) C2H4O(g) + O2(g)
Time (s) Concentration of O3 (mol/L)
0.0
20.0
30.0
40.0
50.0
60.0
10.0
3.20x10-5
2.42x10-5
1.95x10-5
1.63x10-5
1.40x10-5
1.23x10-5
1.10x10-5
(conc A)-
t
Reaction Rates
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The concentrations of O3 vs. time during its reaction with C2H4
C2H4(g) + O3(g) C2H4O(g) + O2(g)
- [C2H4]
t
rate =
- [O3]
t=
Reaction Rates
(conc A)-
t
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Plots of [C2H4] and [O2] vs. time.
Tools of the
Laboratory
Reaction Rates
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C2H4(g) + O3(g) C2H4O(g) + O2(g)
Reaction Rates
- [C2H4]
t-
[O3]
t
(conc A)-
t
[O2]
t
[C2H4O]
t
(conc B)
t
A B
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H 2 + I 2 2HI
Reaction Rates
- [H2]
t-
[I2]
t
1 [HI]
2 t
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In general, for the reaction
aA + bB cC + dD
rate = 1
a- = -
[A]
t
1
b
[B]
t
1
c
[C]
t= +
1
d
[D]
t= +
The numerical value of the rate depends upon the substance that
serves as the reference. The rest is relative to the balanced
chemical equation.
Reaction Rates
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PLAN:
SOLUTION:
Because it has a nonpolluting product (water vapor), hydrogen gas is used for fuel aboard the space shuttle and may be used by Earth-bound engines in the near future.
2H2(g) + O2(g) 2H2O(g)
(a) Express the rate in terms of changes in [H2], [O2], and [H2O] with time.
(b) When [O2] is decreasing at 0.23 mol/L*s, at what rate is [H2O] increasing?
Choose [O2] as a point of reference since its coefficient is 1. For every molecule of O2 which disappears, 2 molecules of H2 disappear and 2 molecules of H2O appear, so [O2] is disappearing at half the rate of change of H2 and H2O.
-1
2
[H2]
t= -
[O2]
t= +
[H2O]
t
1
2
0.23mol/L*s = +[H2O]
t
1
2; = 0.46mol/L*s
[H2O]
t
rate =(a)
[O2]
t- = -(b)
Sample Problem
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Sample Problem
How is the rate of disappearance of ozone related to the rate of
appearance of oxygen in the following equation: 2O3 (g) → 3 O2 (g)? If
the rate of appearance of oxygen is 6.0 x 10 -5 M/s at a particular instant,
what is the value of the rate of disappearance of ozone at this same time?
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Worksheet # 10-1
1. Consider the reaction: 4PH3 (g)→ P4(g) + 6 H2 (g)
If, in a certain experiment, over a specific time period, 0.0048 mol PH3 is
consumed in a 2.0 L container each second of reaction, what are the rates
of production of P4 and H2 in this experiment?
2. The decomposition of N2O5 proceeds according to the equation:
2N2O5 → 4NO2 + O2
If the rate of decomposition of N2O5 at a particular instant in a reaction
vessel is 4.2 x 10 -7 M/s, what is the rate of appearance of
a) NO2
b) O2
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Worksheet # 10-1: Answers
1. Consider the reaction: 4PH3 (g)→ P4(g) + 6 H2 (g)
If, in a certain experiment, over a specific time period, 0.0048 mol PH3 is
consumed in a 2.0 L container each second of reaction, what are the rates
of production of P4 and H2 in this experiment? ∆P4/ ∆t = 0.0006 M/sec
∆H2/ ∆t = 0.0036 M/sec
2. The decomposition of N2O5 proceeds according to the equation:
2N2O5 → 4NO2 + O2
If the rate of decomposition of N2O5 at a particular instant in a reaction
vessel is 4.2 x 10 -7 M/s, what is the rate of appearance of
a) NO2 8.4 x 10 -7 M/s
b) O2 2.1 x 10 -7 M/s
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Collision Theory
How do you think reactants lead to products?
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Collision Theory
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• In order for a reaction to occur, reactant molecules must collide
– with proper orientation
– with enough energy
• Only a small fraction of the collisions that do occur meet these requirements.
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Collision Theory
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Ea
21Chemical Equations: Kinetics
Collision Theory
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• In order for reactants to convert to products, an energy barrier called the activation energy, Ea, must be overcome.
• Collisions that have the proper orientation and have at least the minimum Ea can convert to products.
Activation Energy
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Activation Energy
Reactants must overcome an energy barrier before they can change to products!
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• Energy is required to break bonds in reactants before the reactants can be converted into products
– The minimum amount of energy needed to overcome
the energy barrier is called the activation energy, Ea
– Reactions with large activation energies tend to be slow because a relatively small fraction of reactants have sufficient energy for an effective collision
– Reactions with small activation energies tend to be fast because a large fraction of reactants have sufficient energy for an effective collision 12-24
Activation Energy
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Activation Energy, n. The useful quantity of energy available in one cup of coffee.
Activation Energy: Analogy
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Activation Energy
Each reaction has its own reaction diagram, which shows the amount of energy required to form the activated complex as the reaction progresses.
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• Activated complex
– Short-lived, unstable, high-energy chemical species that must be achieved before products can form
– Formed from reactant molecules that collide with the proper orientation and sufficient energy
– Actual structure is unknown
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Activation Energy
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• The following reaction is an endothermic reaction:
2NO2(g) → 2NO(g) + O2(g)
Draw an energy diagram that shows the relative energies of the reactants, products, and the activated complex. Label the diagram with molecular representations of reactants, products, and a possible structure for the activated complex.
Sample Problem
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2NO2(g) → 2NO(g) + O2(g)
Sample Problem
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• Consider the following reaction that occurs in smog:
NO(g) + O3(g) O2(g) + NO2(g)
• Which of the following collisions has a proper orientation?
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Proper Orientation
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The importance of molecular orientation to an effective collision.
NO + NO3 2 NO2
Proper Orientation
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Nature of the transition state in the reaction between CH3Br and OH-.
CH3Br + OH- CH3OH + Br -
transition state or activated complex
Proper Orientation
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Reaction energy diagram for the reaction of CH3Br and OH-.
Proper Orientation
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Reaction energy diagrams and possible transition states.
Proper Orientation
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Reaction progress
Po
ten
tia
l E
ne
rgySOLUTION:
PROBLEM: A key reaction in the upper atmosphere is
O3(g) + O(g) 2O2(g)
The Ea(fwd) is 19 kJ, and the Hrxn for the reaction is -392 kJ. Draw a reaction energy diagram for this reaction, postulate a transition state, and calculate Ea(rev).
PLAN: Consider the relationships among the reactants, products and transition state. The reactants are at a higher energy level than the products and the transition state is slightly higher than the reactants.
O3+O
2O2
Ea= 19kJ
Hrxn = -392kJ
Ea(rev)= (392 + 19)kJ =
411kJ
OO
OO
breakingbond
formingbond
transition state
Sample Problem
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Worksheet # 10-2
1. Draw a rough sketch of the energy profile for each of the following cases:
a) ∆H = 10 kJ/mol, Ea = 25 kJ/mol
b) ∆H = - 10 kJ/mol, Ea = 50 kJ/mol
c) ∆H = - 50 kJ/mol, Ea = 25 kJ/mol
2. The activation energy for the reaction:H2 + I2 → 2HI
is 167 kJ/mol and the ∆H for the reaction is +28 kJ/mol. What is the activation energy for the decomposition of HI?
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Worksheet # 10-2: Answers
1. Draw a rough sketch of the energy profile for each of the following cases:
a) ∆H = 10 kJ/mol, Ea = 25 kJ/mol
b) ∆H = - 10 kJ/mol, Ea = 50 kJ/mol
c) ∆H = - 50 kJ/mol, Ea = 25 kJ/mol
2. The activation energy for the reaction:H2 + I2 → 2HI
Is 167 kJ/mol and the ∆H for the reaction is +28 kJ/mol. What is the activation energy for the decomposition of HI? Ea = 139 kJ/mol
a) b, c)
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Energy of activation
Video of energy of activation: (bauer book: chapter 12)
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Reaction Rate
Conditions that affect reaction rate:
– Temperature• Higher temperatures generally cause reactions to occur
faster.
– Reactant concentration• Increasing the concentration of a reactant generally
increases the reaction rate.
– Surface area• Increasing the surface area increases the reaction rate if
the reactant is a solid.
– Presence of a catalyst• Adding a catalyst increases the rate of the reaction.
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• Increasing the concentration of reactants or the reaction temperature increases reaction rate by increasing the number of effective collisions.
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Effect of Concentration
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• Increasing the concentration of one or more reactants increases the number of effective collisions by increasing the total number of collisions (fraction of collisions that are effective remains the same).
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Effect of Concentration
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Effect of Concentration
• Changing the concentration of a reactant can change the reaction rate:
12-42Figure 12.3
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Effect of Concentration
How do you express the effect of concentration of a reactant on reaction rate?
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Effect of Concentration
zero order, first order, second order
In math a α x0
a α x1
a α x2
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Effect of Concentration
In chemistryrate α x0
rate α x1
rate α x2
Thus, for A → Brate α [A]0
rate α [A]1
rate α [A]2
zero order, first order, second order
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Effect of Concentration
rate = -[A]
t= k [A]0
zero order rate equation
[A]t - [A]0 = - kt
Integrated Rate Laws
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rate = -[A]
t= k [A]
first order rate equation
ln[A]t
[A]o
= - kt ln [A]t = -kt + ln [A]o
Effect of Concentration
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1
[A]t
1
[A]0
- = kt1
[A]t
1
[A]0
+= kt
rate = -[A]
t= k [A]2
second order rate equation
Effect of Concentration
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Units of the Rate Constant k for Several Overall Reaction Orders
Overall Reaction Order Units of k (t in seconds)
0 mol/L*s (or mol L-1 s-1)
1 1/s (or s-1)
2 L/mol*s (or L mol -1 s-1)
3 L2 / mol2 *s (or L2 mol-2 s-1)
Effect of Concentration
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Effect of Concentration
However, the order of a reaction with respect to a particular reactant cannot be determined from the balanced chemical reaction.
They can only be obtained from experiments.
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Effect of Concentration
The reaction A + 2B products has the rate law,rate = k[A][B]3. If the concentration of B is doubled while that of A is unchanged, by what factor will the rate of reaction increase?
Answer: 8
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The reaction A + 2B products was found to have the rate law, rate = k[A] [B]2. Predict by what factor the rate of reaction will increase when the concentration of A is doubled and the concentration of B is also doubled.
Answer: 8
Effect of Concentration
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At 25C the rate constant for the first-order decomposition of a pesticide solution is6.40 103 min1. If the starting concentration of pesticide is 0.0314 M, what concentration will remain after 62.0 min at 25C?
Answer: 2.11 102 M
Effect of Concentration
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It takes 42.0 min for the concentration of a reactant in a first-order reaction to drop from 0.45 M to 0.32 M at 25C. How long will it take for the reaction to be 90% complete?
Answer: 284 min
Effect of Concentration
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Sucrose, C12H22O11, reacts slowly with water in the presence of an acid to form two other sugars, glucose and fructose, both of which have the same molecular formulas, but different structures.
C12H22O11 + H2O C6H12O6 (glucose) + C6H12O6 (fructose)The reaction is first order and has a rate constant of 6.2 105/s at 35C when the H+ concentration is 0.10 M. Suppose that the initial concentration of sucrose in the solution is 0.40 M.
a. What will the sucrose concentration be after 2.0 hours?b. How many minutes will it take for the sucrose concentration to drop to 0.30 M?
Answer: a. 0.26 M b. 77 min
Effect of Concentration
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PLAN:
SOLUTION:
At 10000C, cyclobutane (C4H8) decomposes in a first-order reaction, with the very high rate constant of 87s-1, to two molecules of ethylene (C2H4).
(a) If the initial C4H8 concentration is 2.00M, what is the concentration after 0.010 s?
(b) What fraction of C4H8 has decomposed in this time?
Find the [C4H8] at time, t, using the integrated rate law for a 1st order reaction. Once that value is found, divide the amount decomposed by the initial concentration.
; ln2.00
[C4H8]= (87s-1)(0.010s)
[C4H8] = 0.83mol/L
ln[C4H8]0
[C4H8]t
= kt(a)
(b) [C4H8]0 - [C4H8]t
[C4H8]0
=2.00M - 0.87M
2.00M= 0.58
Sample Problem
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Worksheet # 10 - 3
1. At 700 K, the rate constant for the following reaction is 6.2 104 min1. How many minutes are required for 20% of a sample of cyclopropane to isomerize to propene?
C3H6 (cyclopropane) C3H6 (propene)
2. A certain first-order reaction A B is 25% complete in 42 min at 25C. What is its rate constant?
3. A second - order reaction has a rate constant of 3.00 103 s1.The time required for the reaction to be 75.0% complete is _____?
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Worksheet # 10 – 3: Answers
1. At 700 K, the rate constant for the following reaction is 6.2 104 min1. How many minutes are required for 20% of a sample of cyclopropane to isomerize to propene?
Answer: 360 minC
3H6 (cyclopropane) C3H6 (propene)
2. A certain first-order reaction A B is 25% complete in 42 min at 25C. What is its rate constant? Answer: 6.8 103 min1
3. A second-order reaction has a rate constant of 3.00 103 s1.The time required for the reaction to be 75.0% complete is _____?Answer: 1000 s
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A plot of [N2O5] vs. time for three half-lives.
t1/2 =
for a first-order process
ln 2
k
0.693
k=
Effect of Concentration
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Effect of Concentration
Half- life – time required for the concentration of a substance to be reduced to one-half of its original value
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Effect of Concentration
An Overview of Zero-Order, First-Order, and Simple Second-Order Reactions
Zero Order First Order Second Order
Half-life
Rate law rate = k rate = k [A] rate = k [A]2
[A]0/2k ln 2/k 1/k [A]0
Effect of Concentration
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Effect of Concentration
A certain first-order reaction A B is 25% complete in 42 min at 25C. What is the half-life of the reaction?
Answer: 101 min
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PLAN:
SOLUTION:
Cyclopropane is the smallest cyclic hydrocarbon. Because its 600 bond angles allow poor orbital overlap, its bonds are weak. As a result, it is thermally unstable and rearranges to propene at 10000C via the following first-order reaction:
CH2
H2C CH2(g)
H3C CH CH2 (g)
The rate constant is 9.2s-1, (a) What is the half-life of the reaction? (b) How long does it take for the concentration of cyclopropane to reach one-quarter of the initial value?
Use the half-life equation, t1/2 = 0.693
k, to find the half-life.
One-quarter of the initial value means two half-lives have passed.
t1/2 = 0.693/9.2s-1 = 0.075s(a) 2 t1/2 = 2(0.075s) = 0.150s(b)
Sample Problem
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Sample Problem
A certain first order reaction has a half life of 20.0 minutes.a. Calculate the rate constant for this reaction.b. How much time is required for this reaction to be 75%
complete?
Answers:a) k = 0.693/t ½ = 0.693/20 = 0.00347 /minb)
time = 40.0 minutes
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Sample Problem
The isomerization of cyclopropane to form propeneH2C — CH2
\ / CH3 CH = CH2
CH2
is a first-order reaction. At 760 K, 15% of a sample of cyclopropane changes to propene in 6.8 min. What is the half-life of cyclopropane at 760 K?
Answer: 29 min
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An Overview of Zero-Order, First-Order, and Simple Second-Order Reactions
Zero Order First Order Second Order
Plot for straight line
Slope, y-intercept
Half-life
Rate law rate = k rate = k [A] rate = k [A]2
Units for k mol/L*s 1/s L/mol*s
Integrated rate law in straight-line form
[A]t =
k t + [A]0
ln[A]t =
-k t + ln[A]0
1/[A]t =
k t + 1/[A]0
[A]t vs. t ln[A]t vs. t 1/[A]t = t
k, [A]0 -k, ln[A]0k, 1/[A]0
[A]0/2k ln 2/k 1/k [A]0
Effect of Concentration
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Worksheet # 10 - 4
1. The rate constant for the first order reaction A B + C is k =
3.3 x 10–2 min–1 at 57 K. What is the half-life for this reaction at
57 K?
2. The half-life of the zero order reactionA B is 0.56 minutes.
If the initial concentration of A is 3.4 M, what is the rate constant?
3. The rate constant for the second order reaction 2NO2
N2O4 is 2.79 L/mol min at 48 oC. If the initial concentration of
NO2 is 1.05 M , what is the half-life?
4. The decomposition of dimethylether at 504°C is first order with
a half-life of 1570. seconds. What fraction of an initial amount of
dimethylether remains after 4710. seconds?
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Worksheet # 10 - 4: Answers
1. The rate constant for the first order reaction A B + C is k = 3.3 x
10–2 min–1 at 57 K. What is the half-life for this reaction at 57 K?
Answer: 21 min
2. The half-life of the zero order reactionA B is 0.56 minutes. If the
initial concentration of A is 3.4 M, what is the rate constant?
Answer: 3.04 mol/L min
3. The rate constant for the second order reaction 2NO2 N2O4 is
2.79 L/mol min at 48 oC. If the initial concentration of NO2 is 1.05 M ,
what is the half-life?
Answer: 0.34 min
4. The decomposition of dimethylether at 504°C is first order with a half-
life of 1570. seconds. What fraction of an initial amount of dimethylether
remains after 4710. seconds?
Answer: 1/8