Transcript Chemistry Homework Help
Chapter 14 Chemical Kinetics
Factors that Affect Reaction Rates
• Kinetics is the study of how fast chemical reactions occur.
• There are 4 important factors which affect rates of reactions: – reactant concentration, – temperature, – action of catalysts, and – surface area.
• Goal: to understand chemical reactions at the molecular level.
Reaction Rates
• Speed of a reaction is measured by the change in concentration with time.
• For a reaction A B Average rate change in number of moles of B moles change in time of B
t
• Suppose A reacts to form B. Let us begin with 1.00 mol A.
Reaction Rates
Reaction Rates
– At
t
= 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present.
– At
t
= 20 min, there is 0.54 mol A and 0.46 mol B.
– At
t
= 40 min, there is 0.30 mol A and 0.70 mol B.
– Calculating, Average rate moles of moles
t
of B B at
t
10 moles of 0 .
26 mol 10 min 0 mol 0 10 min min 0 0 .
026 min mol/min B at
t
0
Reaction Rates
• For the reaction A B there are two ways of measuring rate: – the speed at which the products appear (i.e. change in moles of B per unit time), or – the speed at which the reactants disappear (i.e. the change in moles of A per unit time).
Average rate with respect to A
moles of
t
A
Reaction Rates
Change of Rate with Time
• For the reaction A B there are two ways of • Most useful units for rates are to look at molarity. Since volume is constant, molarity and moles are directly proportional.
• Consider: C 4 H 9 Cl(
aq
) + H 2 O(
l
) C 4 H 9 OH(
aq
) + HCl(
aq
)
Reaction Rates
Change of Rate with Time
C 4 H 9 Cl(
aq
) + H 2 O(
l
) C 4 H 9 OH(
aq
) + HCl(
aq
) – We can calculate the average rate in terms of the disappearance of C 4 H 9 Cl.
– The units for average rate are mol/L·s or
M/s
.
– The average rate decreases with time.
– We plot [C 4 H 9 Cl] versus time.
– The rate at any instant in time (instantaneous rate) is the slope of the tangent to the curve.
– Instantaneous rate is different from average rate.
– We usually call the instantaneous rate the rate.
Reaction Rates
Reaction Rate and Stoichiometry
• For the reaction C 4 H 9 Cl(
aq
) + H 2 O(
l
) we know
Rate
• In general for
C
4
H
9
t
C 4 H 9 OH(
aq
) + HCl(
aq
)
Cl
C
4
H
9
OH
t
Rate
1
a a
A
t + b
B
1
b
c
C
t
+ d
D
1
c
t
1
d
t
Concentration and Rate
• In general rates increase as concentrations increase.
NH 4 + (
aq
) + NO 2 (
aq
) N 2 (
g
) + 2H 2 O(
l
)
Concentration and Rate
• For the reaction NH 4 + (
aq
) + NO 2 (
aq
) N 2 (
g
) + 2H 2 O(
l
) we note – as [NH 4 + ] doubles with [NO 2 ] constant the rate doubles, – as [NO 2 ] doubles with [NH 4 + ] constant, the rate doubles, – We conclude rate [NH 4 + ][NO 2 ].
• Rate law: • The constant
k
Rate
k
[ NH
4
][ NO
2
]
is the rate constant.
Concentration and Rate
Exponents in the Rate Law
• For a general reaction with rate law
Rate
k
[ reactant 1 ]
m
[ reactant 2 ]
n
we say the reaction is order in reactant 2.
m
th order in reactant 1 and • The overall order of reaction is
m + n +
….
• A reaction can be zeroth order if
m
,
n
, … are zero.
n
• Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry.
th
Concentration and Rate
Using Initial Rates to Determines Rate Laws
• A reaction is zero order in a reactant if the change in concentration of that reactant produces no effect.
• A reaction is first order if doubling the concentration causes the rate to double.
• A reacting is
n
th order if doubling the concentration causes an 2
n
increase in rate.
• Note that the rate constant does not depend on concentration.
The Change of Concentration with Time
First Order Reactions
• Goal: convert rate law into a convenient equation to give concentrations as a function of time.
• For a first order reaction, the rate doubles as the concentration of a reactant doubles.
Rate [ A]
t
k
[ ln
t
ln 0 A
kt
] ln
t
0
kt
The Change of Concentration with Time
First Order Reactions
• A plot of ln[A]
t
versus t is a straight line with slope and intercept ln[A] 0 .
k
• In the above we use the natural logarithm, ln, which is log to the base
e
.
The Change of Concentration with Time
ln
t
kt
First Order Reactions
ln 0
The Change of Concentration with Time
Second Order Reactions
• For a second order reaction with just one reactant 1
t
kt
1 0 • A plot of 1/[A]
t
intercept 1/[A] 0 versus t is a straight line with slope
k
• For a second order reaction, a plot of ln[A]
t
linear.
vs.
t
and is not
The Change of Concentration with Time
Second Order Reactions
1
t
kt
1 0
The Change of Concentration with Time
Half-Life
• Half-life is the time taken for the concentration of a reactant to drop to half its original value.
• For a first order process, half life,
t
½ [A] 0 to reach ½[A] 0 .
• Mathematically,
t
1 2 ln 2
k
k
is the time taken for 0 .
693
The Change of Concentration with Time
Half-Life
• For a second order reaction, half-life depends in the initial concentration:
t
1 2
k
1 0
Temperature and Rate
The Collision Model
• Most reactions speed up as temperature increases. (E.g. food spoils when not refrigerated.) • When two light sticks are placed in water: one at room temperature and one in ice, the one at room temperature is brighter than the one in ice.
• The chemical reaction responsible for chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light.
Temperature and Rate
The Collision Model
• As temperature increases, the rate increases.
Temperature and Rate
The Collision Model
• Since the rate law has no temperature term in it, the rate constant must depend on temperature.
• Consider the first order reaction CH 3 NC CH 3 CN. – As temperature increases from 190 C to 250 C the rate constant increases from 2.52 10 -5 s -1 to 3.16 10 -3 s -1 .
• The temperature effect is quite dramatic. Why?
• Observations: rates of reactions are affected by concentration and temperature.
Temperature and Rate
The Collision Model
• Goal: develop a model that explains why rates of reactions increase as concentration and temperature increases.
• The collision model: in order for molecules to react they must collide.
• The greater the number of collisions the faster the rate.
• The more molecules present, the greater the probability of collision and the faster the rate.
Temperature and Rate
The Collision Model
• The higher the temperature, the more energy available to the molecules and the faster the rate.
• Complication: not all collisions lead to products. In fact, only a small fraction of collisions lead to product.
The Orientation Factor
• In order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products.
Temperature and Rate
The Orientation Factor
• Consider: Cl + NOCl NO + Cl 2 • There are two possible ways that Cl atoms and NOCl molecules can collide; one is effective and one is not.
Temperature and Rate
The Orientation Factor
Temperature and Rate
Activation Energy
• Arrhenius: molecules must posses a minimum amount of energy to react. Why?
– In order to form products, bonds must be broken in the reactants.
– Bond breakage requires energy.
• Activation energy,
E a
, is the minimum energy required to initiate a chemical reaction.
Temperature and Rate
Activation Energy
• Consider the rearrangement of methyl isonitrile:
N H 3 C N C H 3 C H 3 C C N C
– In H 3 C-N C, the C-N C bond bends until the C-N bond breaks and the N C portion is perpendicular to the H 3 C portion. This structure is called the activated complex or transition state.
– The energy required for the above twist and break is the activation energy,
E a
.
– Once the C-N bond is broken, the N C portion can continue to rotate forming a C-C N bond.
Temperature and Rate
Activation Energy
• The change in energy for the reaction is the difference in energy between CH 3 NC and CH 3 CN.
• The activation energy is the difference in energy between reactants, CH 3 NC and transition state.
• The rate depends on
E a
.
• Notice that if a forward reaction is exothermic (CH 3 NC CH 3 CN), then the reverse reaction is endothermic (CH 3 CN CH 3 NC).
Temperature and Rate
Activation Energy
• How does a methyl isonitrile molecule gain enough energy to overcome the activation energy barrier?
• From kinetic molecular theory, we know that as temperature increases, the total kinetic energy increases.
• We can show the fraction of molecules,
f
, with energy equal to or greater than
E a
is
f
e
E a RT
where
R
is the gas constant (8.314 J/mol·K).
Temperature and Rate
Activation Energy
Temperature and Rate
The Arrhenius Equation
• Arrhenius discovered most reaction-rate data obeyed the Arrhenius equation:
k
Ae
E a RT
–
k
is the rate constant,
E a
is the activation energy, constant (8.314 J/K-mol) and
T R
is the gas is the temperature in K.
– –
A A
is called the frequency factor.
is a measure of the probability of a favorable collision.
– Both
A
and
E a
are specific to a given reaction.
Temperature and Rate
Determining the Activation Energy
• If we have a lot of data, we can determine
E a
and graphically by rearranging the Arrhenius equation:
A
ln
k
E a RT
ln
A
• From the above equation, a plot of ln
k
versus 1/
T
will have slope of –
E a /R
and intercept of ln
A
.
Temperature and Rate
Temperature and Rate
Determining the Activation Energy
• If we do not have a lot of data, then we recognize ln
k
1
E a RT
1 ln
A
and ln
k
2
E a RT
2 ln
A
ln
k
1 ln
k
2
E a RT
1 ln
A
E a RT
2 ln
A
ln
k
1
k
2
E a R
1
T
2 1
T
1
Reaction Mechanisms
• The balanced chemical equation provides information about the beginning and end of reaction.
• The reaction mechanism gives the path of the reaction.
• Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction.
Elementary Steps
• Elementary step: any process that occurs in a single step.
Reaction Mechanisms
Elementary Steps
• Molecularity: the number of molecules present in an elementary step.
– Unimolecular: one molecule in the elementary step, – Bimolecular: two molecules in the elementary step, and – Termolecular: three molecules in the elementary step.
• It is not common to see termolecular processes (statistically improbable).
Reaction Mechanisms
Multistep Mechanisms
• Some reaction proceed through more than one step: NO 2 (
g
) + NO 2 (
g
) NO 3 (
g
) + CO(
g
) NO 3 (
g
) + NO(
g
NO 2 (
g
) + CO 2 (
g
) ) • Notice that if we add the above steps, we get the overall reaction: NO 2 (
g
) + CO(
g
) NO(
g
) + CO 2 (
g
)
Reaction Mechanisms
Multistep Mechanisms
• If a reaction proceeds via several elementary steps, then the elementary steps must add to give the balanced chemical equation.
• Intermediate: a species which appears in an elementary step which is not a reactant or product.
Reaction Mechanisms
Rate Laws for Elementary Steps
• The rate law of an elementary step is determined by its molecularity: – Unimolecular processes are first order, – Bimolecular processes are second order, and – Termolecular processes are third order.
Rate Laws for Multistep Mechanisms
• Rate-determining step: is the slowest of the elementary steps.
Reaction Mechanisms
Rate Laws for Elementary Steps
Reaction Mechanisms
Rate Laws for Multistep Mechanisms
• Therefore, the rate-determining step governs the overall rate law for the reaction.
Mechanisms with an Initial Fast Step
• It is possible for an intermediate to be a reactant.
• Consider 2NO(
g
) + Br 2 (
g
) 2NOBr(
g
)
Reaction Mechanisms
Mechanisms with an Initial Fast Step
2NO(
g
) + Br 2 (
g
) 2NOBr(
g
• The experimentally determined rate law is ) Rate =
k
[NO] 2 [Br 2 ] • Consider the following mechanism
Step 1: NO(g) + Br 2
k
(g) NOBr
k
-1 2 (g) (fast) Step 2: NOBr 2
k
(g) + NO(g) 2NOBr(g) (slow)
Reaction Mechanisms
Mechanisms with an Initial Fast Step
• The rate law is (based on Step 2 ): Rate =
k
2 [NOBr 2 ][NO] • The rate law should not depend on the concentration of an intermediate (intermediates are usually unstable).
• Assume NOBr 2 is unstable, so we express the concentration of NOBr 2 in terms of NOBr and Br 2 assuming there is an equilibrium in step 1 [ NOBr 2 ]
k
1 [ NO][Br 2 ]
k
1 we have
Reaction Mechanisms
Mechanisms with an Initial Fast Step
• By definition of equilibrium:
k
1
[ NO][Br
2
]
k
1
[ NOBr
2
]
• Therefore, the overall rate law becomes Rate
k
2
k k
1 1 [ NO][Br 2 ] [ NO]
k
2
k k
1 1 [ NO] 2 • Note the final rate law is consistent with the [Br 2 ] experimentally observed rate law.
Catalysis
• A catalyst changes the rate of a chemical reaction.
• There are two types of catalyst: – homogeneous, and – heterogeneous.
• Chlorine atoms are catalysts for the destruction of ozone.
Homogeneous Catalysis
• The catalyst and reaction is in one phase.
Catalysis
Catalysis
Homogeneous Catalysis
• Hydrogen peroxide decomposes very slowly: 2H 2 O 2 (
aq
) 2H 2 O(
l
) + O 2 (
g
) • In the presence of the bromide ion, the decomposition occurs rapidly: – 2Br (
aq
) + H 2 O 2 (
aq
) + 2H + (
aq
) – Br 2 (
aq
) is brown.
– Br 2 (
aq
) + H 2 O 2 (
aq
) 2Br (
aq
Br ) + 2H 2 + ( (
aq aq
) + 2H ) + O 2 ( 2
g
O( ).
l
).
– Br is a catalyst because it can be recovered at the end of the reaction.
Catalysis
Homogeneous Catalysis
• Generally, catalysts operate by lowering the activation energy for a reaction.
Catalysis
Catalysis
Homogeneous Catalysis
• Catalysts can operate by increasing the number of effective collisions.
• That is, from the Arrhenius equation: catalysts increase
k
be increasing
A
or decreasing
E a
.
• A catalyst may add intermediates to the reaction.
• Example: In the presence of Br , Br 2 (
aq
) is generated as an intermediate in the decomposition of H 2 O 2 .
Catalysis
Homogeneous Catalysis
• When a catalyst adds an intermediate, the activation energies for both steps must be lower than the activation energy for the uncatalyzed reaction. The catalyst is in a different phase than the reactants and products.
Heterogeneous Catalysis
• Typical example: solid catalyst, gaseous reactants and products (catalytic converters in cars).
• Most industrial catalysts are heterogeneous.
Catalysis
Heterogeneous Catalysis
• First step is adsorption (the binding of reactant molecules to the catalyst surface).
• Adsorbed species (atoms or ions) are very reactive.
• Molecules are adsorbed onto active sites on the catalyst surface.
Catalysis
Catalysis
Heterogeneous Catalysis
• Consider the hydrogenation of ethylene: C 2 H 4 (
g
) + H 2 (
g
) C 2 H 6 (
g
),
H
= -136 kJ/mol.
– The reaction is slow in the absence of a catalyst.
– In the presence of a metal catalyst (Ni, Pt or Pd) the reaction occurs quickly at room temperature.
– First the ethylene and hydrogen molecules are adsorbed onto active sites on the metal surface.
– The H-H bond breaks and the H atoms migrate about the metal surface.
Catalysis
Heterogeneous Catalysis
– When an H atom collides with an ethylene molecule on the surface, the C-C bond breaks and a C-H bond forms.
– When C 2 H 6 forms it desorbs from the surface.
– When ethylene and hydrogen are adsorbed onto a surface, less energy is required to break the bonds and the activation energy for the reaction is lowered.
Enzymes
• Enzymes are biological catalysts.
• Most enzymes are protein molecules with large molecular masses (10,000 to 10 6 amu).
Catalysis
Enzymes
• Enzymes have very specific shapes.
• Most enzymes catalyze very specific reactions.
• Substrates undergo reaction at the active site of an enzyme.
• A substrate locks into an enzyme and a fast reaction occurs.
• The products then move away from the enzyme.
Catalysis
Enzymes
• Only substrates that fit into the enzyme lock can be involved in the reaction.
• If a molecule binds tightly to an enzyme so that another substrate cannot displace it, then the active site is blocked and the catalyst is inhibited (enzyme inhibitors).
• The number of events (turnover number) catalyzed is large for enzymes (10 3 - 10 7 per second).
Catalysis
Enzymes