15. Chemical Kinetics

Rate Law

Rate law and reaction order | Kinetics | AP Chemistry | Khan Academy

This graph shows a plot of the rate of a reaction versus the
concentration of the reactant.

a. What is the order of the reaction with respect to A?

Consider the reaction of peroxydisulfate ion 1S2O82-2
with iodide ion 1I - 2 in aqueous solution:
S2O8 2 - 1aq2 + 3 I - 1aq2¡2 SO42 - 1aq2 + I3- 1aq2
At a particular temperature, the initial rate of disappearance
of S2O82 - varies with reactant concentrations in the
following manner:
Experiment 3S2o8
24 1M 2 3I4 1M 2 Initial Rate 1M,s2
1 0.018 0.036 2.6 * 10-6
2 0.027 0.036 3.9 * 10-6
3 0.036 0.054 7.8 * 10-6
4 0.050 0.072 1.4 * 10-5
(a) Determine the rate law for the reaction and state the
units of the rate constant.

14.2 Rate Laws | General Chemistry

A reaction A + B¡C obeys the following rate law:
Rate = k3B42. (a) If [A] is doubled, how will the rate
change? Will the rate constant change?

How to Find the Rate Law and Rate Constant (k)

This graph shows a plot of the rate of a reaction versus the concentration of the reactant A for the reaction A ¡ products.

c. Write a rate law for the reaction including an estimate for the
value of k.

The relative rates of the reaction A + B S AB in vessels
(1)–(3) are 4:4:1. Red spheres represent A molecules, and
blue spheres represent B molecules.
(1)-(3) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/c5168167c1a7e2f9-14.46.jpg" alt="" />
(a) What is the order of the reaction in A and B?

Kinetics: Initial Rates and Integrated Rate Laws

Initial rate data at 25 °C are listed in the table for the reaction 
NH4 
+1aq2 + NO2 
-1aq2S N21g2 + 2 H2O1l2 
<TABLE> 
(b) What is the value of the rate constant?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/2272fb3ce49ca83a-1672422736940.jpg" alt="" />

Consider the following reaction:
2 NO1g2 + 2 H21g2¡N21g2 + 2 H2O1g2
(d) What is the
reaction rate at 1000 K if [NO] is decreased to 0.010 M and
3H24 is increased to 0.030 M?

Rate Law Example 2

The iodide ion reacts with hypochlorite ion (the active
ingredient in chlorine bleaches) in the following way:
OCl - + I - ¡OI - + Cl - . This rapid reaction gives
the following rate data:
3oCl4 1M 2 3I4 1M 2 Initial Rate 1M,s2
1.5 * 10-3 1.5 * 10-3 1.36 * 10-4
3.0 * 10-3 1.5 * 10-3 2.72 * 10-4
1.5 * 10-3 3.0 * 10-3 2.72 * 10-4
(b) Calculate the
rate constant with proper units.

The following diagrams represent mixtures of NO(g) and
O21g2. These two substances react as follows:
2 NO1g2 + O21g2¡2 NO21g2
It has been determined experimentally that the rate is
second order in NO and first order in O2. Based on this
fact, which of the following mixtures will have the fastest
initial rate? [Section 14.3]
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/b99b44c22585abd1-1666284814503.jpg" alt="" />

This graph shows a plot of the rate of a reaction versus the concentration of the reactant A for the reaction A ¡ products.

a. What is the order of the reaction with respect to A?

Rate Law Concept 2

Rate Law Example 3

The iodide ion reacts with hypochlorite ion (the active
ingredient in chlorine bleaches) in the following way:
OCl - + I - ¡OI - + Cl - . This rapid reaction gives
the following rate data:
3oCl4 1M 2 3I4 1M 2 Initial Rate 1M,s2
1.5 * 10-3 1.5 * 10-3 1.36 * 10-4
3.0 * 10-3 1.5 * 10-3 2.72 * 10-4
1.5 * 10-3 3.0 * 10-3 2.72 * 10-4
(a) Write the rate law for this reaction.

The following data were measured for the reaction
BF31g2 + NH31g2 ¡ F3BNH31g2:
Experiment 3bF3 4 1M 2 3nH3 4 1M 2 Initial Rate 1M,s2
1 0.250 0.250 0.2130
2 0.250 0.125 0.1065
3 0.200 0.100 0.0682
4 0.350 0.100 0.1193
5 0.175 0.100 0.0596
(c) Calculate the rate
constant with proper units?

Consider the reaction A + B¡C + D. Is each of the following
statements true or false? (b) If the reaction is an elementary
reaction, the rate law is second order.

Consider the following concentration–time data for the 
reaction of iodide ion and hypochlorite ion 1OCl-2. The 
products are chloride ion and hypoiodite ion 1OI-2. 
<TABLE> 
(b) Determine the rate law, and calculate the value of the 
rate constant.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/ae8980315adbbfa4-1672424866786.jpg" alt="" />

Kinetics Rate Laws

The reaction 2 NO1g2 + O21g2¡2 NO21g2 is second
order in NO and first order in O2. When 3NO4 = 0.040 M,
and 3O24 = 0.035 M, the observed rate of disappearance
of NO is 9.3 * 10-5 M>s. (b) What is the value of the
rate constant?

A reaction in which A, B, and C react to form products is zero
order in A, one-half order in B, and second order in C.
e. By what factor does the reaction rate change if [C] is doubled 
(and the other reactant concentrations are held constant)?

A reaction in which A, B, and C react to form products is first
order in A, second order in B, and zero order in C
c. By what factor does the reaction rate change if [A] is doubled
(and the other reactant concentrations are held constant)?

This graph shows a plot of the rate of a reaction versus the
concentration of the reactant.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/425c0d53539f906b-1655213347336.jpg" alt="" />
b. Make a rough sketch of a plot of [A] versus time

Rate Law Concept 1

Consider a hypothetical reaction between A, B, and C
that is first order in A, zero order in B, and second order
in C. (a) Write the rate law for the reaction.

What are the units of k for each type of reaction?
b. second-order reaction

Consider the reversible, first-order interconversion of two 
molecules A and B: 
A kfkrB 
where kf = 3.0 * 10-3 s-1 is the rate constant for the forward 
reaction and kr = 1.0 * 10-3 s-1 is the rate constant 
for the reverse reaction. We’ll see in Chapter 15 that a reaction 
does not go to completion but instead reaches a state of 
equilibrium with comparable concentrations of reactants and 
products if the rate constants kf and kr have comparable values. 
(c) What are the relative concentrations of B and A when 
the rates of the forward and reverse reactions become 
equal?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/6a6c9e39b8133951-1672073576594.jpg" alt="" />

The reaction 2 NO1g2 + O21g2¡2 NO21g2 is second
order in NO and first order in O2. When 3NO4 = 0.040 M,
and 3O24 = 0.035 M, the observed rate of disappearance
of NO is 9.3 * 10-5 M>s. (c) What are the units of the rate constant?

The tabulated data were collected for this reaction:
CH3Cl( g) + 3 Cl2( g) ¡ CCl4( g) + 3 HCl( g
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/7decf3c6e8e9b2b4-1674517354523.jpg" alt="" />
Write an expression for the reaction rate law and calculate the 
value of the rate constant, k. What is the overall order of the 
reaction?

You may have been told not to mix bleach and ammonia.
The reason is that bleach (sodium hypochlorite) reacts with
ammonia to produce toxic chloramines, such as NH2Cl.
For example, in basic solution:
OCl-1aq2 + NH31aq2S OH-1aq2 + NH2Cl1aq2
(a) The following initial rate data for this reaction were
obtained in basic solution at 25 °C
<TABLE>
What is the rate law for the reaction? What is the 
numerical value of the rate constant k, including the correct 
units?

The decomposition reaction of N2O5 in carbon tetrachloride
is 2 N2O5¡4 NO2 + O2. The rate law is first order
in N2O5. At 64 C the rate constant is 4.82 * 10-3 s-1.
(a) Write the rate law for the reaction.

The iodide ion reacts with hypochlorite ion (the active
ingredient in chlorine bleaches) in the following way:
OCl - + I - ¡OI - + Cl - . This rapid reaction gives
the following rate data:
3oCl4 1M 2 3I4 1M 2 Initial Rate 1M,s2
1.5 * 10-3 1.5 * 10-3 1.36 * 10-4
3.0 * 10-3 1.5 * 10-3 2.72 * 10-4
1.5 * 10-3 3.0 * 10-3 2.72 * 10-4
(c) Calculate the rate
when 3OCl-4 = 2.0 * 10-3 M and 3I - 4 = 5.0 * 10 - 4 M.

Consider the reaction A + B¡C + D. Is each of the following
statements true or false? (c) If the reaction is
an elementary reaction, the rate law of the reverse reaction is
first order.

A reaction in which A, B, and C react to form products is zero
order in A, one-half order in B, and second order in C.
a. Write a rate law for the reaction.

Rate Law Example 1

The following data were collected for the desturction of O3 by H (O3 + H → O2 + OH) at very low concentrations  (b) Calculate the rate constant

A reaction in which A, B, and C react to form products is first
order in A, second order in B, and zero order in C.
b. What is the overall order of the reaction?

Rate Law Concept 3

The following reaction is first order in A (red spheres) and
first order in B (blue spheres):
A + B¡Products Rate = k[A][B]
(1) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/5cbaae5654e51dd7-14-40-1-4.jpg" alt="" />
(2) <img src="" alt="" />
(3) <img src="" alt="" />
(4) <img src="" alt="" />
(b) What are the relative values of the rate constant k for
vessels (1)–(4)?

Consider the tabulated data showing the initial rate of a
reaction (A ¡ products) at several different concentrations
of A. What is the order of the reaction? Write a rate law for the
reaction including the value of the rate constant, k.

Given the following chemical reaction, A → B. If the concentration of A is doubled the rate increases by a factor of 2.83, what is the order of the reaction with respect to A.

Trimethylamine and chlorine dioxide react in water in an 
electron transfer reaction to form the trimethylamine cation 
and chlorite ion: 
1CH323 N1aq2 + ClO21aq2 + H2O1l2S 
1CH323 NH+1aq2 + ClO2 
-1aq2 + OH-1aq2 
Initial rate data obtained at 23 °C are listed in the following 
table. 
<TABLE> 
(b) What would be the initial rate in an experiment with 
initial concentrations 31CH323 N4 = 4.2 * 10-2 M and 
3ClO24 = 3.4 * 10-2 M?

The following data were measured for the reaction
BF31g2 + NH31g2 ¡ F3BNH31g2:
Experiment 3bF3 4 1M 2 3nH3 4 1M 2 Initial Rate 1M,s2
1 0.250 0.250 0.2130
2 0.250 0.125 0.1065
3 0.200 0.100 0.0682
4 0.350 0.100 0.1193
5 0.175 0.100 0.0596
(b) What is
the overall order of the reaction?

Consider the reversible, first-order interconversion of two
molecules A and B:
A kfkrBwhere kf = 3.0 * 10-3 s-1 is the rate constant for the forward
reaction and kr = 1.0 * 10-3 s-1 is the rate constant
for the reverse reaction. We’ll see in Chapter 15 that a reaction
does not go to completion but instead reaches a state of
equilibrium with comparable concentrations of reactants and
products if the rate constants kf and kr have comparable values.
(a) What are the rate laws for the forward and reverse
reactions?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/6a6c9e39b8133951-1672073576594.jpg" alt="" />

The reaction 2NO1g2 + 2 H21g2S N21g2 + 2 H2O1g2 is 
first order in H2 and second order in NO. Write the rate law, 
and specify the units of the rate constant.

A reaction A + B¡C obeys the following rate law:
Rate = k3B42. (b) What are the
reaction orders for A and B? What is the overall reaction
order?

Consider a hypothetical reaction between A, B, and C
that is first order in A, zero order in B, and second order
in C. (e) By what factor does the
rate change when the concentrations of all three reactants
are tripled?

The react ion between ethyl bromide 1C2H5Br2
and hydroxide ion in ethyl alcohol at 330 K,
C2H5Br1alc2 + OH- 1alc2¡ C2H5OH1l2 + Br - 1alc2,
is first order each in ethyl bromide and hydroxide ion.
When 3C2H5Br4 is 0.0477 M and 3OH- 4 is 0.100 M, the
rate of disappearance of ethyl bromide is 1.7 * 10-7 M>s.
(c) How would the rate of
disappearance of ethyl bromide change if the solution
were diluted by adding an equal volume of pure ethyl alcohol
to the solution?

The react ion between ethyl bromide 1C2H5Br2
and hydroxide ion in ethyl alcohol at 330 K,
C2H5Br1alc2 + OH- 1alc2¡ C2H5OH1l2 + Br - 1alc2,
is first order each in ethyl bromide and hydroxide ion.
When 3C2H5Br4 is 0.0477 M and 3OH- 4 is 0.100 M, the
rate of disappearance of ethyl bromide is 1.7 * 10-7 M>s.
(a) What is the value of the rate constant?

Consider the following concentration–time data for the 
reaction of iodide ion and hypochlorite ion 1OCl-2. The 
products are chloride ion and hypoiodite ion 1OI-2. 
<TABLE> 
(a) Write a balanced equation for the reaction.

Concentration–time data for the conversion of A and B to 
D are listed in the following table. 
<TABLE> 
(c) What is the rate law?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/70171cd4a23a0e44-1672430008965.jpg" alt="" />

The following pictures represent the progress of a reaction 
in which two A molecules combine to give a more complex 
molecule A2, 2 AS A2. 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/5127b9e912acd468-1672250427206.jpg" alt="" /> 
(b) What is the rate law?

In the experiments on the reaction 2 ICl (g) + H2 (g) → I2 (g) + 2 HCl (g), the following initial rate data were obtained. What is the overall order of the reaction?<img src="https://static.studychannel-prd.pearsonprd.tech/courses/general-chemistry/thumbnails/images/b7a1680a"class="fr-fic fr-dii">

The following reaction is first order in A (red spheres) and
first order in B (blue spheres):
A + B¡Products Rate = k[A][B]
(1) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/2549b0677efc664a-1672243876248.jpg" alt="" />
(2) <img src="" alt="" />
(3) <img src="" alt="" />
(4) <img src="" alt="" />
(a) What are the relative rates of this reaction in vessels 
(1)–(4)? Each vessel has the same volume.

Consider the following reaction between mercury(II)
chloride and oxalate ion:
2 HgCl21aq2 + C2O4 2 - 1aq2¡2 Cl - 1aq2 + 2 CO21g2 + Hg2Cl21s2
The initial rate of this reaction was determined for several
concentrations of HgCl2 and C2O4
2 -, and the following rate
data were obtained for the rate of disappearance of C2O4
2 - :
Experiment 3HgCl2 4 1M 2 3C2o4
24 1M 2 Rate 1M,s2
1 0.164 0.15 3.2 * 10-5
2 0.164 0.45 2.9 * 10-4
3 0.082 0.45 1.4 * 10-4
4 0.246 0.15 4.8 * 10-5
(c) What is
the reaction rate when the initial concentration of HgCl2
is 0.100 M and that of C2O4
2- is 0.25 M if the temperature
is the same as that used to obtain the data shown?

This reaction is first order in N2O5:
N2O5( g) ¡ NO3( g) + NO2( g)
The rate constant for the reaction at a certain temperature is
0.053>s.
a. Calculate the rate of the reaction when [N2O5] = 0.055 M

Consider the reaction: 
2 O3( g)¡3 O2( g) 
The rate law for this reaction is: 
Rate = k 
[O3]2 
[O2] 
Suppose that a 1.0-L reaction vessel initially contains 1.0 mol of 
O3 and 1.0 mol of O2. What fraction of the O3 will have reacted 
when the rate falls to one-half of its initial value?

The following experimental data were obtained in a study
of the reaction 2 HI1g2S H21g2 + I21g2. Predict the concentration
of HI that would give a rate of 1.0 * 10-5 M>s
at 650 K.
<TABLE><img src="https://lightcat-files.s3.amazonaws.com/problem_images/07fee03a2c202610-1672426782509.jpg" alt="" />

This graph shows a plot of the rate of a reaction versus the
concentration of the reactant.

c. Write a rate law for the reaction including the value of k.

Consider the gas-phase reaction between nitric oxide and
bromine at 273 C: 2 NO1g2 + Br21g2¡2 NOBr1g2.
The following data for the initial rate of appearance of
NOBr were obtained:
Experiment 3no4 1M 2 3br2 4 1M 2 Initial Rate 1M,s2
1 0.10 0.20 24
2 0.25 0.20 150
3 0.10 0.50 60
4 0.35 0.50 735
(b) Calculate the average value
of the rate constant for the appearance of NOBr from the
four data sets.

Consider a reaction that occurs by the following mechanism:
A + BC SAC + B
AC + D SA + CD
The potential energy profile for this reaction is as follows:
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/1a01cf5e2cac55c6-1672069675588.jpg" alt="" />
(c) Which of the two steps in the mechanism is the ratedetermining
step? Write the rate law for the overall reaction.

Kinetics: Chemistry's Demolition Derby - Crash Course Chemistry #32

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.
(b) Use the data in Appendix B to calculate the initial rate
at which the reaction mixture absorbs heat (in J/s). You
may assume that the heat of the reaction is independent
of temperature.

The following pictures represent the progress of the 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/72910fd0d23492d5-1672045008052.jpg" alt="" />
(c) Suppose that each sphere represents 6.0 * 1021 molecules 
and that the volume of the container is 1.0 L. What 
is the rate constant for the reaction in the usual units?

The following pictures represent the progress of the 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/e44b8ffa9c7c5462-1672084416077.jpg" alt="" />
(b) Draw a picture that shows the number of A and B molecules
present at t = 3 min.

Consider the reversible, first-order interconversion of two 
molecules A and B: 
A kfkrB 
where kf = 3.0 * 10-3 s-1 is the rate constant for the forward 
reaction and kr = 1.0 * 10-3 s-1 is the rate constant 
for the reverse reaction. We’ll see in Chapter 15 that a reaction 
does not go to completion but instead reaches a state of 
equilibrium with comparable concentrations of reactants and 
products if the rate constants kf and kr have comparable values. 
(b) Draw a qualitative graph that shows how the rates of 
the forward and reverse reactions vary with time.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/256b5a25fef875fd-1672079435472.jpg" alt="" />

This reaction is first order in N2O5:
N2O5( g) ¡ NO3( g) + NO2( g)
The rate constant for the reaction at a certain temperature is
0.053>s.
b. What would the rate of the reaction be at the concentration
indicated in part a if the reaction were second order? Zero
order? (Assume the same numerical value for the rate constant with the appropriate units.)

7.9 M–5/2•s–1

The data below were collected for the following reaction:CH3Cl (g) + 3 Cl2 (g) → CCl4 (g) + 3 HCl (g)<img src="https://static.studychannel-prd.pearsonprd.tech/courses/general-chemistry/thumbnails/images/fee11f08"class="fr-fic fr-dii">Calculate the value and units for the rate constant k.A.&nbsp;1.25 M–0.5•s–1B. 5.6&nbsp;M–1•s–1C. 25 M–3/2•s–1D. 7.9 M–5/2•s–1

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[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 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.