Topic 6: Rate
of Reaction
Chemistry 1 (CEM 3114)
6.1
Experimental determination of a rate law
• Define rate of reaction, rate equation, order of reaction and rate
constant
• Calculate the rate constant from initial rates
• Deduce the order of a reaction (zero-, first- and second-) and the rate
constant by the initial rates method.
• Predict an initial rate from rate equations and experimental data
6.2
Half-life of a first-order reaction
• Define half-life of a first-order reaction
• Use the half-life (t½) of a first-order reaction in calculations
6.3
6.4
Theoretical Models for Chemical Kinetics
• Explain collision theory,
• Explain Transition state Theory (activation energy and catalyst)
Reaction Mechanisms
• Define mechanism of reaction
• Verify that a suggested reaction mechanism is consistent with the
observed kinetics
• Define rate of reaction, rate equation, order of reaction and
rate constant
• Calculate the rate constant from initial rates
• Deduce the order of a reaction (zero-, first- and second-) and
the rate constant by the initial rates method.
• Predict an initial rate from rate equations and experimental
data
A
reactant
01
Definition
Defined as the change of concentration of a reactant or a product
per unit time.
B
product
02
Formula
03
Formation of Product
The rate of reaction depends on how fast reactant A is used up or
how fast the product B is formed.
04
How to measure the rate of reaction
• Based on the reactant
• Based on the product
Based on product
𝑅𝑎𝑡𝑒 =
•
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐵
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒
A
B
𝑅𝑎𝑡𝑒 =
(-) indicates that
concentration of A
decreases with time
dt = change in time
•
d[A] = change in concentration of
product A
•
reactant
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝐴
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒
d[B] = change in concentration of
product B
•
Based on reactant
dt = change in time
product
Cont..
Cont..
N2 (g) + 3H2 (g) → 2NH3 (g)
Answer
Ms-1. Based on the equation above:
a) Express the rate in terms of changes
in [N2], [H2] and [NH3] with time.
b) Identify the rate of change of NH3
and H2.
Question
The rate of formation of N2 is 0.0156
We Create
Quality Professional
k = rate
PPT Presentation
rate = kcx
constant at certain temperature
c = concentration of the reactant at certain temperature (mol L-1)
x = order of reaction, x=0,1 and 2
Unit of rate = mol dm-3 s-1 or mol dm-3 min-1
Rate Equation = Rate Law
Equation used to calculate the rate of reactions by using the constant and concentration of reactants.
1
2
3
Is the exponent of the reactant
concentration in the rate equation
It can only be found experimentally.
Overall order of reaction is the sum of the
order of reaction.
aA + bB → cC + dD
• Overall order = (n + m)
• n and m are obtained through experiments only and not from the number
of moles given from the stoichiometric equations.
The rate equation for the
oxidation of iodide ions by
hydrogen peroxide is as follows:
a) Identify the order of reaction
with respect to
i. H2O2
ii. Iiii. H+
b) Identify the overall order of
the reaction?
Question
Rate = k [H2O2] [I-] [H+]0
Answer
1
Rate constant, k, is a constant of
proportionality in the rate equation.
2
The units of k depend on the overall order of
reaction.
Rate = k [A][B]
k=
3
4
𝒓𝒂𝒕𝒆
𝑨 [𝑩]
rate constant does not depend on concentrations
Rate ≠ rate constant, k
2A + B + 3C → products
Answer
rate = k [A] [B]2
a) Identify the overall order
of reaction?
b) Identify the order of
reaction with respect to
substance C?
c) Identify the unit for the
rate constant, k?
Question
The rate equation is given
by:
3P + Y → P3Y
Experiment
Initial concentration (M)
Initial rate
P
Y
1
0.15
0.75
(M min-1)
4.7 x 10-3
2
0.15
2.25
4.2 x 10-2
3
0.60
0.75
1.9 x 10-2
• The method of initial rates is a commonly used technique for deriving rate laws.
• The measurement is repeated for several sets of initial concentration conditions
to see how the reaction rate varies.
Method to Determine Order of Reaction
Step 1
Identify [A] is changed but [B] and [C]
are kept constant
Step 2
Write down the rate of equation
Step 3
Assigning equation 1 and equation 2
Step 4
Dividing equation 1 and equation 2
The following rate data were
following reaction.
oC
for the
Identify the
rate-law expression and the rateconstant for this reaction?
Question 1
obtained at 25
2 A(g) + B(g) → 3 C(g)
Cont..
Cont..
Answer
Below is the results of an
reactants used in the experiment
are all unknown labelled as A, B
and
C. State the order of
reaction for A, B and C and
Question 2
experiment from a student, the
predict the rate equation of the
reaction.
Cont..
Cont..
Answer
Based on the Table given:
a)
Calculate the order of reaction of
b)
Write the rate equation.
c)
Determine the rate constant of
the reaction, with its unit. Leave
your answer in three significant
figures.
d)
Question 3
substance A, B, and C.
Determine the value of X with its
correct unit. Leave your answer in
three significant figures.
Cont..
Cont..
Answer
We Create
Qualitysulphide
Professional
Hydrogen
is removed from industrial pollution by reacting with chlorine
PPT Presentation
as follows:
H2S
(aq)
+ Cl2 (aq) → S(s) + 2HCl(aq)
The reaction above is first order with respect to each reactant
a) Write the rate equation for the reaction. What is the overall order of reaction?
b) Calculate the rate of loss of hydrogen sulphide and the rate of formation of hydrochloric acid at
28 oC if the rate constant is 5.6 x 10-4 dm3 mol-1 min-1 when the concentration of H2S and Cl2
respectively are 2.5 x 10-4 M and 4.8 x 10-2 M.
• Define half-life of a first-order reaction
• Use the half-life (t½) of a first-order reaction in calculations
Definition
Example
The half-life of a reaction, symbolized by t1/2 is the
time required for the reactant concentration to drop to
one-half of its initial value.
16 g ; 1
8g;
A → Products
𝟏
𝟐
4g;
𝟏
𝟒
𝟏
2g;𝟖
Rate = kA
Formula
Rate constant, k = Gradient of the graph
Why the half-life of a first-order reaction is a constant?
•
•
Each half-life represents an equal amount of
time.
The half-life is constant (t1 = t2 = t3)
• Because it depends only on the rate constant and not
on the reactant concentration.
• Each successive half-life is an equal period of time in
which the reactant concentration decreases by a factor
of 2.
Formula
The half-life of a first-order reaction was
found
to
be
10
min
at
a
certain
temperature. Identify its rate constant?
Question 1
Answer
If 3.0 g of substance A decomposes for 36
minutes the mass of unreacted A remaining
is found to be 0.375 g. Identify the half life
of this reaction if it follows first-order
kinetics?
Question 2
Answer
Question 3
H2O2(aq), initially at a
concentration of 2.32 M, is
allowed to decompose. What
will [H2O2] be at t = 1200s?
Use k = 7.30 x 10-4 s-1 for the
first-order decomposition.
Question 4
Use k = 7.30 x 10-4 s-1 for
the first-order decomposition
of H2O2(aq) to determine the
percent [H2O2] that has
decomposed in the first
500.0s after the reaction
begins?
Consider the first-order reaction A → products, with k = 2.95 x
10-3 s-1. Identify the percent of A remains after 150 s?
• Explain collision theory
• Explain Transition state Theory (activation energy and catalyst)
Successful /
Effective
Collision
Unsuccessful
/ ineffective
Collision
We Create
Quality Professional
PPT Presentation
Effective collision is collision between reactant particles with sufficient
energy which reactant particles are then change into product in a correct
orientation.
It is a type of collision that the reactant particles are not changing into products which may be caused
by the reactant particles have not enough energy or collide in a wrong orientation.
• Catalysts are substances which
change the rate of a reaction
but is left chemically
unchanged at the end of the
reaction.
• Catalysts work by lowering the
activation energy of a reaction.
Without catalyst
Energy
With catalyst
Reactants
Products
Reaction coordinate
Activation energy, Ea is the
minimum energy that colliding
particles must take for a successful
collision to take place
Transition state
Energy
Reactants
Products
Reaction coordinate
Energy
Activation Energy Minimum energy to
make the reaction
happen – how hard
Reactants
Products
Reaction coordinate
Energy
Activated
Complex or
Transition State
Reactants
Products
Reaction coordinate
The potential energy profile for the onestep reaction follows. The energies are in
kJ/mol relative to an arbitrary zero of energy
a) What is the value of the activation
energy for this reaction?
b) Is
the
reaction
exothermic
or
endothermic?
c) Suggest a plausible structure for the
transition state.
Question
Answer
The reaction between peroxodisulphate (VI) 𝑆2 𝑂82− and iodide
ions, I- can be catalyzed by iron (III), Fe3+?
a) Suggest a mechanism for the catalytic reaction.
b) Sketch an energy profile for the catalysed and uncatalyzed reactions.
• Define mechanism of reaction
• Verify that a suggested reaction mechanism is consistent
with the observed kinetics
A mechanism for a reaction is a collection of
1
elementary processes (also called elementary steps or
elementary reactions) that explains how the overall
reaction proceeds.
When an overall reaction occurs in two or more
2
elementary steps, one of the steps is often much
slower than the others.
This slowest step in a reaction mechanism is called
3
the rate-determining step because it acts as a
bottleneck, limiting the rate at which reactants can be
converted to products
4
A catalyst is consumed in one step of a reaction and
is regenerated in a subsequent step
5
An intermediate is formed in one step and is
consumed in a subsequent step
• Each of these two reactions is called an elementary reaction.
Consider the reaction of
nitric oxide with hydrogen
• NO3 is intermediate species because is formed in Step 1 and
is consumed in Step 2 and do not appear in the overall
balanced equation.
Consider the iodide ion
catalyzed decomposition of
hydrogen peroxide to water
and oxygen.
•
Each of these two reactions is called an elementary reaction.
•
The I- known as catalyst because it consumed in Step 1 and is
regenerated in Step 2 and do not appear in the overall balanced
equation.
•
IO- is intermediate species because is formed in Step 1 and is consumed
in Step 2 and do not appear in the overall balanced equation.
The experimental rate law for the reaction
between NO2 and CO to produce NO and
Answer
CO2 is rate = k[NO2]2. The reaction is
Step 1: NO2 + NO2 → NO3 + NO (slow)
Step 2: NO3 + CO → NO2 + CO2 (fast)
a)
What is the equation for the overall
reaction?
b)
Identify the intermediate species from
the mechanism given above.
Question 1
believed to occur via two steps:
Answer
The mechanism for the reaction between HX and
H2O2 + X- → H2O + XO-
(Step 1; Slow)
H+ + XO- → HXO
(Step 2; Fast)
HXO + H+ + XO- → H2O2 + X2 (Step 3; Fast)
a)
Write the rate equation for the reaction.
b)
Write the overall equation for the reaction.
c)
Identify the catalyst of the reaction above.
d)
Identify the intermediate species of the
reaction above.
Question 2
H2O2 is shown below:
The two-step mechanism has been proposed for the gas-phase decomposition of nitrous oxide (N2O):
a) Write the chemical equation for the overall reaction.
b) Identify any intermediate species. Explain your answer.
Thank You
Thank You