chem342 environmental chemistry -...
TRANSCRIPT
CHEM 11132 Basic Physical Chemistry I
Course content:
Thermodynamics (10 L)
Electrochemistry (10 L)
Chemical Kinetics (10 L) :
Basic concepts; rates of reactions, elementary reactions, rate expressions, order and
the rate constant of a reaction, molecularity. Experimental determination of rate
laws; fitting data to rate laws, obtaining data for different timescales. Introduction to
theories about reaction rates; collision theory and activated complex theory.
Complex reactions and reaction mechanisms; rate determining steps, pre-
equilibrium hypothesis, steady-state approximation and their applications.
Temperature dependence of reaction rates: Arrhenius rate law and deviation. Chain
reactions, fast reactions and catalysis.
CHEM 11111 Calculations in Chemistry
Chemistry…….....…?
CHEMISTRY…
IS THIS WHAT YOU THINK?
Linus Pauling
‘Chemistry is wonderful.
I feel sorry for people who don’t know
anything about chemistry. They are missing
an important source of happiness.
Most people don’t feel that.’
Chemical Reactions
• Definition: A Process which produces chemical change.
• Review- Chemical vs. Physical Change
• Bonds are broken
• Reactants and Products
Reactants Products
3 Major Groupings of Chemical
Reactions
1. Precipitation
Reactions
2. Oxidation-Reduction
Reactions
3. Acid-Base
Neutralization
Reactions
SOLID - SOLID ?
Elephant’s Toothpaste
Mix: Saturated Solution of KI with 30%
solution of Hydrogen Peroxide and
detergent.
)g(OOH2)aq(OH222
KI
22
Chemistry
Biology
Plant Sciences
Geology
Environmental Science
Health and MedicineNuclear Chemistry
Physics
Astronomy
Biochemistry
Biology
“The Central Science”
Chemistry in the Home
Everything in your home is Chemistry
Cooking is Chemistry
Chemical changes are responsible for changes in flavour and texture
Chemistry keeps food fresh
Water-Wine-
Milk-Beer
CHEM 11132 Basic Physical Chemistry I
Course content:
Thermodynamics (10 L)
Electrochemistry (10 L)
Chemical Kinetics (10 L) :
Basic concepts; rates of reactions, elementary reactions, rate expressions, order and
the rate constant of a reaction, molecularity. Experimental determination of rate
laws; fitting data to rate laws, obtaining data for different timescales. Introduction to
theories about reaction rates; collision theory and activated complex theory.
Complex reactions and reaction mechanisms; rate determining steps, pre-
equilibrium hypothesis, steady-state approximation and their applications.
Temperature dependence of reaction rates: Arrhenius rate law and deviation. Chain
reactions, fast reactions and catalysis.
CHEM 11111 Calculations in Chemistry
Textbooks
P. W. AtkinsThe Elements of Physical Chemistry (Third Ed., Ch. 10)
P. W. AtkinsPhysical Chemistry
Michael J. Pilling & Paul W. Seakins
Reaction Kinetics
Any Physical Chemistry Text Book; Levine, Daniel &
Alberty, Barrow.
Chemistry…….....…?
Chemical reaction……?
Combustion Reactions with Hydrogen
2H2 + O2 → 2H2O
Chemical reaction……• bonds break - this requires energy
• bonds form - this releases energy
• overall for the reaction– exothermic reaction - releases energy
– endothermic reaction - absorbs energy
"Everyone has Problems -
but Chemists have Solutions"
Will the reaction occur?
How far will the reaction proceed?
How fast will the reaction proceed?
How?
Chemical kinetics
Kinetics …
• studies the rates at which chemical
reactions occur.
• gives information about how the
reaction occur, that is, the reaction
mechanism
CHEMICAL KINETICS
• Area of chemistry concerned with rates of reactions
– How rapidly food spoils
– Rate of fuel burning in automobiles
– How quickly medicines work
– Development of catalysts
© Boardworks Ltd 200740 of 39
What does rate of reaction mean?
The speed of different chemical reactions varies hugely.
Some reactions are very fast and others are very slow.
What is the rate of these reactions?
The speed of a reaction is called the rate of the reaction.
rusting baking explosion
slow fast very fast
Airbag Reaction
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
65g of sodium azide ≈ N2 (35 litres)
fully inflated within about 30 milliseconds
Airbag reaction
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
Requirements for reaction
• Molecules must meet (collisions)
• Molecules must transfer enough energy to
overcome the activation barrier
• They must meet in the right orientation
Activation Energy, Ea
Energy barrier (hump) that must be
overcome for a
chemical reaction to proceed
A2(g) + B2(g) 2AB(g)
How is the reaction going to occur?
Activated complex-hypothetical
an effectivecollision
comesapart
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
Factors That Affect Reaction Rates
1. Physical state of the reactants
Important when reactants are of different phases (higher SA faster reaction)
2. Concentration of Reactants
For most reactions higher [reactant] faster reaction
3. Temperature
Increasing T will also increase the reaction rate
4. Presence of Catalyst
© Boardworks Ltd 200756 of 39
Effect of concentration on rate of reaction
The higher the concentration of a dissolved reactant, the
faster the rate of a reaction.
Why does increased concentration increase the rate of
reaction?
At a higher concentration, there are more particles in the
same amount of space. This means that the particles are
more likely to collide and therefore more likely to react.
higher concentrationlower concentration
The ratio of successful collisions to unsuccessful collisions
will stay the same, but there will be more successful
collisions.
© Boardworks Ltd 200757 of 39
Concentration and particle collisions
© Boardworks Ltd 200758 of 39
Animations
© Boardworks Ltd 200759 of 39
Rate of reaction
reaction rate: change in concentration of a
product or a reactant per unit time.
Rate – change in some variable per unit time
timerate
1
Δt
t in c, ion,concentrat in change
Rate = ______________ = ______________change in timechange in time
in [products] in [reactants]
reactant
Rates of Chemical Reactions
Rate of a chemical reaction refers to the change in
concentration of a substance per unit of time
Let’s consider the rate at which you give me 3 rupees….
your 3 rupees my 3 rupees
Let’s say that it took you 5 seconds to give it to me.
your 3 rupees my 3 rupees
reactants products
What is the rate of the reaction with respect to me [products]?
Rate = change in concentration of money
change in time
Remember, change () is always [ final – initial]
Rate = + [3-0 rupees]
[5-0 secs]
Positive because I am the product
which gains the money
Rate = 0.6 rupees/sec
What is the rate with respect to you?
Rate of reaction = [0-3 rupees]
[5-0 secs]
Negative because you are the
reactant and you are losing money
Rate of reaction = 0.6 rupees/sec
***Therefore, you can determine the rate of reaction either
by using the reactants or the products. It will give you the
same rate of reaction****
Rate = ______________ = ______________change in timechange in time
in [products] in [reactants]
rate = + [product] = - [reactant]
t t
reactant
Let’s consider the rates for chemical reaction
NO(g) + ½ O2 (g) NO2(g)
Rate of the disappearance of NO:
Rate = -[NO]
t Rate of the disappearance of O2:
Rate = -[O2]
t
Rate of the appearance of NO2:
Rate = +[NO2]
t
67
© 2009 Brooks/Cole - Cengage
Reaction rate = change in concentration of a reactant or product with time.
–initial rate
–average rate
–instantaneous rate
Reaction Rates
© Boardworks Ltd 200768 of 39
What equipment is needed to investigate the rate of
hydrogen production?
gas syringe
rubber bung
rubber connecterglass tube
conical
flask
magnesium
hydrochloric
acid
© Boardworks Ltd 200769 of 39
© Boardworks Ltd 200770 of 39
hydro
gen
pro
duce
d (
cm3)
time (seconds)10 20 30 40 50
10
20
30
40
50
60
70
0
0
x
y
Calculating rate of reaction from graphs
rate of reaction =
x
y
rate of reaction =
20s
45cm3 rate of reaction = 2.25cm3/s
The gradient of the graph is equal to the initial rate of reaction
at that time
How can the rate of reaction be calculated from a graph?
c
Δt
Chemical
Kinetics
Reaction Rates
The average rate of
the reaction over
each interval is the
change in
concentration divided
by the change in time:
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
Average Rate, M/s
Chemical
Kinetics
Reaction Rates
• A plot of concentration
vs. time for this reaction
yields a curve like this.
• The slope of a line
tangent to the curve at
any point is the
instantaneous rate at
that time.
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
Chemical
Kinetics
Reaction Rates
• The reaction slows
down with time because
the concentration of the
reactants decreases.
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g)
average rate = -[Br2]
t= -
[Br2]final – [Br2]initial
tfinal - tinitial
slope of
tangentslope of
tangentslope of
tangent
instantaneous rate = rate for specific instance in time
From last two lectures……..
• Reaction Rates
initial rate - instantaneous rate at t = 0
average rate - Δ[A] over a specific time interval
instantaneous rate - rate at a specific time
The rate is the instantaneous slope, and this varies
with time
Chemical
Kinetics
Reaction Rates
• Note that the average
rate decreases as the
reaction proceeds.
• This is because as the
reaction goes forward,
there are fewer
collisions between
reactant molecules.
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
Rate = ______________ = ______________change in timechange in time
in [products] in [reactants]
rate = + d[product] = - d[reactant]
dt dt
reactant
i.e.
[(amount of material)(volume)-1] [time]-1
common units: mol dm-3 s-1
Units
ratio of concentration upon time,
Exercise 1Symbolically, [A], [Br]
rate = + [ ]
t
Reaction Rates and Stoichiometry
• The molar ratios between reactants and products
correspond to the rates of reaction.
• Relative rates – relationship between rates of
reactant disappearance and product appearance at a
given time.
O2 + 2H2 →2 H2O
Or, equivalently
dt
Ad1r
A
Where vA is the stoichiometric coefficient of
species A
example: express the rate of reaction for each
reactant and product in the reaction:
4 NH3(g) + 5 O2(g) 4 NO(g) + 6H2O (g)
d[NH3]
dt- 1
4NH3:
d[O2]
dt- 1
5O2:
d[NO]
dt+ 1
4NO:
d[H2O]
dt+
16
H2O:
Reaction Rates and Reaction
Stoichiometry
Look at the reaction
O3(g) + NO(g) NO2(g) + O2(g)
dt
]Od[+ =
dt
]NOd[+ =
dt
d[NO]- =
dtOd
- = rate 223
Another Example
2 NOCl (g) 2 NO + 1 Cl2 (g)
dt
d[Cl+ =
dt
d[NO]
2
1 =
dt
NOCld
2
1- = rate 2 ]
WHY? 2 moles of NOCl disappear for every 1 mole Cl2 formed.
The General Case
a A + b B c C + d D
rate = -1 d[A] = -1 d[B] = +1 d[C] = +1 d[D]
a dt b dt c dt d dt
Why do we define our rate in this way?
Obtain a single rate for the entire equation, not
just for the change in a single reactant or product.
Chemical
Kinetics
Concentration and Rate
Each reaction has its own equation that
gives its rate as a function of reactant
concentrations.
this is called its Rate Law
To determine the rate law we measure the rate
at different starting concentrations.
Chemical
Kinetics
Concentration and Rate
Compare Experiments 1 and 2:
when [NH4+] doubles, the initial rate doubles.
Chemical
Kinetics
Concentration and Rate
Likewise, compare Experiments 5 and 6:
when [NO2-] doubles, the initial rate doubles.
Chemical
Kinetics
Concentration and Rate
This equation is called the rate law, and
k is the rate constant.
RATE LAW
aA + bB products
•Rate of reaction changes as concentration of
reactants change at constant temperature
RATE LAW:
equation describing the relationship between
concentration of a reactant and the rate
RATE LAW
aA + bB products
•Rate of reaction changes as concentration of
reactants change at constant temperature
RATE LAW:
equation describing the relationship between
concentration of a reactant and the rate
Rate = k[A]m[B]n
where k is called the rate constant and is
independent of concentration
k increases with T
The rate law expresses the relationship of the rate of a
reaction to the rate constant and the concentrations of
the reactants raised to some powers.
The reaction orders are empirically determined.
For the general reaction:
the rate equation
aA + bB + cC … mM + nN ….
dt= k [A]x [B]y [C]z …
-d[A]
• the rate law can only be determined by experiment, not from the stoichiometric equation
• x is the order of the reaction with respect to A,y is the order of the reaction with respect to B…
• the overall order of the reaction is given by x + y + z …
• there is no relationship between a and x, b and y ….
THE RATE CONSTANT
1. The units of k depends on the overall order of
reaction
2. The value of k is independent of concentration
and time
3. The value refers to a specific temperature
and changes if we change temperature
4. Its value is for a specific reaction
example
H2 (g) + 2 ICl (g) 2 HCl (g) + I2 (s)
dt= k[H2][ICl]rate =
-d[H2]from experiment:
the reaction is:
• first order with respect to H2
• first order with respect to ICl
• second order overall
questionfor the reaction:
2 NO (g) + O2 (g) 2 NO2 (g)
rate = k[NO]2[O2]
what is the order of reaction with respect to the
reactants and the overall order of reaction?
• second order with respect to NO
• first order with respect to O2
• third order overall
Units
Reaction order enables us to understand how the reaction depends on reactant concentrations.
aA + bB bC + dD
This reaction is zero order in A, first order in B, and first order overall. The exponent zero tells us that the rate of this reaction is independent of the concentration of A.
www.deakin.edu.au<[email protected]>
107
Example : A + B → C
Changing [B] ⇒ no effect ⇒ rate ∝ [B]0
Double [A] ⇒ rate ∝ 22 ⇒ rate ∝ [A]2
Rate = k [A]2 [B]0 = k [A]2
Quick check
Experiment [A] / M [B] / M Init. rate / M s-1
1 0.10 4.0 × 10-5
2 4.0 × 10-5
0.10
0.10 0.20
3 16 × 10-50.20 0.10
Method of Initial Rates
a. Determine the rate law of the reaction
b. Calculate the rate constant
c. Calculate the rate when [NO]= 0.050 M and [H2]
= 0.150
Temperature and Rate
• Generally, as
temperature
increases, so does
reaction rate.
• This is because k is
temperature
dependent.
Temperature and Rate
• In a chemical reaction, bonds are broken and new
bonds are formed. In order for molecules to react,
they must collide.
• Collisions are either effective or ineffective due to
orientation of molecules.
• Collisions must have enough energy to overcome the
barrier to reaction, the activation energy.
• Temperature affects the number of collisions.
• Not all collisions leads to a reaction
• For effective collisions proper orientation of
the molecules must be possible
Chemical
Kinetics
Maxwell–Boltzmann Distributions
• Temperature is
defined as a
measure of the
average kinetic
energy of the
molecules in a
sample.
• At any temperature there is a wide distribution of
kinetic energies.
Chemical
Kinetics
Maxwell–Boltzmann Distributions
• As the temperature
increases, the curve
flattens and
broadens.
• Thus at higher
temperatures, a
larger population of
molecules has
higher energy.
Chemical
Kinetics
Maxwell–Boltzmann Distributions
• If the dotted line represents the activation
energy, as the temperature increases, so does
the fraction of molecules that can overcome
the activation energy barrier.
• As a result, the
reaction rate
increases.
Chemical
Kinetics
Maxwell–Boltzmann Distributions
This fraction of molecules can be found through the expression:
where R is the gas constant and T is the temperature in Kelvin .
Arrhenius Equation
Arrhenius developed an equation for the mathematical
relationship between k and Ea.
RT
EexpAk a
Ea = activation energy (kJ mol-1), and is the
minimum kinetic energy required to allow reaction to occur
A = the frequency factor or pre-exponential factor (same units as k),
is the fraction of sufficiently energetic collisions that actually
lead to reaction.
T = Kelvin temperature
R = ideal gas constant (8.314 J mol-1 K-1)
k is the rate constant
Ea/RTdecreases
-Ea/RTincreases
e-Ea/RT
increases kincreases
REACTIONSPEEDS UP
If Tincreases
RT
EexpAk a
Arrhenius Equation
AlnT
1
R
Ekln
RT
EAlnkln
Aek
a
a
RT
Ea
y = m x + c
RT
EexpAk a
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
Last week……
Rate law
Reaction order
Rate constant
Units
Maxwell–Boltzmann Distributions
Arrhenius Equation
RT
EexpAk a
Types of Rate Laws
1. Differential rate law or rate law
Shows how the reaction rate changes with concentration
2. Integrated rate law
Shows how concentration changes with time
Graphical determination of the order
TIME OUT FOR CALCULUS
Deriving the Integrated Rate
Expressions
• First-order reactions –
A B, then the rate of disappearance of A is:k
][][
Akdt
AdR
Rearranging gives:
kdtA
Ad
][
][
At time t = 0, [A] = [A]0And when t = t, [A] = [A]
Integrating:
.constkt]Aln[ xdx
x
that
call
ln1
Re
.const]Aln[
]A[]A[,0tat
0
0
ln[A] = ln[A]0 - kt
Integrated form of the
1st order rate expression
y = c + mx
0]Aln[kt]Aln[
dtk]A[
]A[d
ln[A]
t / s
slope = -k
Intercept = ln[A]0
Recall ln[A] = ln[A]o - kt
Antilog gives:
[A] = [A]0 e-kt
Intercept = [A]0
Example 01The concentration of N2O5 in liquid bromine varied with time as follows:
t/s 0 200 400 600 1000
[N2O5] /(mol L-1) 0.110 0.073 0.048 0.032 0.014
Confirm that the reaction is first order in N2O5 and determine the rate constant.
[Answer: 2.1 x 10-3 s-1]
ln[A]
t / s
slope = -k
Intercept = ln[A]0
• Second-order reactions –
Two possible cases:
Case I : A Products
Case II : A + B Products
2]A[kdt
]A[dr
Rearranging gives:kdt
]A[
]A[d2
At time t = 0, [A] = [A]0And when t = t, [A] = [A]
Integrating:
dtk]A[d]A[
12
xx
xdxxdx
x
1
12
1 112
2
2
.constkt]A[
1
0]A[
1kt
]A[
1
Integrated form of the
2nd order rate expression
.const]A[
1
]A[]A[,0tat
0
0
(1/[A]) / dm3 mol-1
t / s
slope = k
Intercept = 1/[A]0
kt]A[
1
]A[
1
0
y = c + mx
A + B Products
]B][A[kdt
]A[dr
2]A[kdt
]A[dr
If t=0, [A] = [B]
Case II :
• Zero-order reactions –
A Products
0]A[kdt
]A[dr k
dt
]A[d
constkt]A[
.const]A[
]A[]A[,0tat
0
0
0]A[kt]A[
Plotting [A] versus t will give a straight line with slope -k.
dtk]A[d1
Order
zero 1st 2nd
Rate law rate = k rate = k[A] rate = k[A]2
Integrated
rate law[A]=−kt+[A]0 ln[A]=−kt+ln[A]0 1/[A]=kt+1/[A]0
Straight-
line plot[A] vs. t ln[A] vs. t 1/[A] vs. t
Slope −k −k k
Half-life
(t1/2)
[A]o/2k 0.693/k 1/k[A]0
Experimental determination of the
rate laws and the rate constants
1. Integral Methods
• Test the data against an appropriate integral
rate law.
• e.g. ln[A] vs t or 1/[A] vs t.
Rate laws have to be determined experimentally.
Zero order:
1st order:
2nd order:
2]A[kdt
]A[d
0]A[
1kt
]A[
1
Example: 2 H2O2 2 H2O + O2
Time(min) [H2O2](mol/L)
0 0.0200
200 0.0160
400 0.0131
600 0.0106
800 0.0086
1000 0.0069
This technique simplifies the rate law by making all the
reactants except one, in large excess.
Therefore,
The dependence of the rate on each reactant can be found
by isolating each reactant in turn and keeping all other
substances (reactants) in large excess.
Using as example: r = k[A] [B]2
Make B in excess, so [B]>>[A].
Hence, by the end of the reaction [B] would not have
changed that much, although all of A has been used up
And we can say, [B] [B]0
2. Isolation Method
r = k’[A] , where k’ = k[B]02
Since A is the reactant that changes, then the rate
becomes dependent on A, and we can say
Created a ‘false’ first-order (imitating first-order)
PSEUDO-FIRST-ORDER,
where k’ is the pseudo-first-order rate constant
Keff , effective rate constant
r = k’’[B]2 , where k’’ = k[A]0
PSEUDO-SECOND-ORDER,
r = k’[A] , where k’ = k[B]02
Plot of k’ vs [B]02
Isolation method
- all reactants in large excess except one
» This means concentration of all reactants except one are
constant
The other values would be lumped into the rate constant
determined
Order thus determined is called psuedo- nth order
Example say rate is v = k [A][B]2
If B is in large excess, v = k’[A] pseudo-first order
k’ = k[B0]2
If A is in large excess, v= k’[B]2 psuedo 2nd order
3. Differential Method:
n]A[kr
]Aln[nklnrln
4. Initial Rate Method:
- often used in conjunction with the isolation method,
Recall
A + B P,
Taking ‘logs’
log Rate0 = log k + a log [A]0 + b log[B]0
y m xc
** Keep [A]0 constant for varying values of [B]0 to find b
Log Ro
log[B]0
slope = b
Intercept = log k + a log[A]0
b
0
a
00 ]B[]A[krate
** Keep [B]0 constant for varying values of [A]0 to find a from the slope
of the graph, log R0 vs log [A]0
1st order
y = mx + c
Plot: ln[A] vs. t
slope = − k
][][
Akdt
Adrate
ot AktA ]ln[]ln[
integrate
Last week……
2nd order
y = mx + c
Plot: 1/[A] vs. t
slope = k
2][][
Akdt
Adrate
ot Akt
A ][
1
][
1
integrate
zero order
y = mx + c
Plot: [A] vs. t
slope = − k
kAkdt
Adrate 0][
][
ot AktA ][][
integrate
Order
zero 1st 2nd
Rate law rate = k rate = k[A] rate = k[A]2
Integrated
rate law[A]=−kt+[A]0 ln[A]=−kt+ln[A]0 1/[A]=kt+1/[A]0
Straight-
line plot[A] vs. t ln[A] vs. t 1/[A] vs. t
Slope −k −k k
Half-life
(t1/2)
[A]o/2k 0.693/k 1/k[A]0
4. Half life method:
The half-life, t1/2, is defined as the time it takes for
the reactant concentration to drop to half its initial
valueIt is a useful indication of the rate of a chemical reaction.
157
© 2009 Brooks/Cole - Cengage
• Reaction is 1st order decomposition of H2O2.
Half-Life
158
© 2009 Brooks/Cole - Cengage
Half-Life
• Reaction after 1 half-life.
• 1/2 of the reactant has been consumed and 1/2 remains.
159
© 2009 Brooks/Cole - Cengage
Half-Life
• After 2 half-lives 1/4 of the reactant remains.
160
© 2009 Brooks/Cole - Cengage
Half-Life
• A 3 half-lives 1/8 of the reactant remains.
2/1
0
0 @2
1
][
][
2
][][ t
A
AAA t
t
• First-order reactions –
Remember that for a 1st order reaction: ln[A]t = ln[A]0 - kt
At time t = 0, [A] = [A]0Then at time t = t½ (half-life), [A]t½ = [A]0/2
Substituting into above equation,
ln([A]0/2) = ln[A]o – kt½ln([A]0/2) – ln[A]0 = -kt½
2/1
0
0
][
2/][ln kt
A
A
2/12
1ln kt
ln 1 – ln 2 = -kt½, where ln 1 = 0
Therefore, ln 2 = kt ½
Hence,
kt
2ln2/1 or
kt
693.02/1
What is/are the main point(s) to note from this expression??
For a 1st order reaction, the half-life is independent of reactant
concentration but dependent on k.
The half-life is constant for a 1st order reaction
time
concentration
[A]0
[A]0/2
[A]0/4
[A]0/8
Recall: [A]t = [A]0e-kt
t1/2
t1/2t1/2
Note: Radioactive decay
follows 1st order kinetics.
• Second-order reactions –
kt]A[
1
]A[
1
0t
At time t = 0, [A] = [A]0And when t = t½, [A]t½ = [A]0/2
2/1
00
kt]A[
1
2
]A[
1
2/1
00
kt]A[
1
]A[
2
2/1
0
kt]A[
1
0
2/1]A[k
1t
So t1/2 for 2nd order reactions
depends on initial concentration
Therefore, larger initial concentrations imply shorter half-lives
(so faster the reaction).
concentration
[A]0
[A]0/2
[A]0/4
[A]0/8
time
t1/2
t1/2
t1/2
0
2/1]A[k
1t
Obtaining kinetic data
Variation of reactant concentration with time
• Classical methods
Example: acid catalyzed hydrolysis of methyl acetate at 30C
COOHCHOHCHCOOCHCH 33
OH/HCl
332
n33COOCHCHkrate
If n = 1, we can use the integrated equation
0]Aln[kt]Aln[
0t33tt33 COOCHCHktCOOCHCHln
t/s
_
_
_
_
_
_
_
_
tt33COOCHCHln
tt30t33tt33 COOHCHCOOCHCHCOOCHCH
Electrochemical method
Example: oxidation of formic acid by bromine in aqueous solution
At the platinum electrode the redox process is
Conductivity measurements
Conductance, which is the reciprocal of resistance, is
directly proportional to the concentration of the ions
Eg. The hydrolysis of acetic anhydride to acetic acid can be studied by measuring the conductivity.
-Gas pressure
- Volume change
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
Using spectroscopy [Light absorbance]
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
Studying fast reactions
Method of measuring concentration has to be
fast enough to make measurements over the
time scale of the reaction
INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE
Continuous flow method
Stopped flow method
Flash photolysis