Download 45. kinetics ch 12

Chemical Kinetics


The rate of a reaction is the positive
quantity that expresses how the
concentration of a reactant or
product changes with time.
The rates of reactions span an
enormous range. From those that
are complete within seconds to those
that take thousands or even millions
of years.
Factors that effect reaction rates...




The physical state of the reactants: The ability of the
reactants to collide lead to a reaction. The more readily
molecules collide with each other, the more rapidly they
react. A solid that is broken in up in to pieces will react
faster than one that is not because of a greater surface
area for reactions.
The concentrations of reactants: Most chemical reactions
occur faster if the concentration of the reactants is
increased. A higher concentration calls for more collisions,
and more collisions lead to a faster reaction.
The temperature at which the reaction occurs: The rates
of chemical reactions increase as temperature is
increased. An increase in temperature leads to higher
kinetic energy of the substance and more collisions for the
reactions to take place faster.
The presence of a catalyst: Catalysts are agents that
increase reaction rates without being used up. They affect
the kinds of collisions (mechanisms) that lead up to a
reaction.
Collisions, Collisions, Collisions

On a molecular level: Rates
depend on the frequency of the
collisions between molecules,
the greater the frequency of
collisions, the greater the rate of
reaction.
Reaction Rates



A reaction rate is the change in the
concentration of reactants or
products per unit time.
The unit for a reaction rate is then
molarity per seconds (M/s).
The rate of a reaction can be based
on the rate of disappearance of a
reactant of the rate of appearance
for a product.
Example: A  B
Time (s)
[A]
[B]
0.00
1.00
0.00
20
0.54
0.46
40
0.30
0.70
• Rate of appearance of B = (D[B])
(Dt)
• Average rate = 0.46M – 0.00M = 2.3 x 10-2 M/s
20 s – 0.0 s
Rates of Reaction & Stoich.



When stoichiometric relationships in a
chemical reaction are not one to one, the
molar ratio must be applied to determining
reaction rates.
For a general reaction,
aA + bB → cC + dD,
the reaction velocity (reaction rate) can be
written in a number of different but
equivalent ways:
Example:

Example: 2HI (g)  H2 (g) + I2 (g)

Rate
= - 1 D[HI] = D[H2] = D[I2]
2
Dt
Dt
Dt
The Rate Law

In general the rate law expression for
the general reaction:
aA + bB → cC + dD
is
Rate = k[A]m[B]n




Rate = M/s
k = units will vary depending on the rate
order of the reactants
[A] & [B] = M
m & n = will be whole numbers that
determine the rate order of the reactants,
they can vary and are no way related to
the coefficients.
Reaction Rates &
Concentration

One way of studying the effect of
concentration on reaction rate is to
determine the way in which the rate
at the beginning of a reaction
depends on the starting
concentrations. Let us consider the
following reaction to illustrate:
NH4+ (aq) + NO2- (aq)  N2 (g) + 2H2O (l)
Experimental Data
Experiment #
Initial [NH4+]
Initial [NO2-]
Observed
Initial Rate
(M/s)
1
0.0100
0.200
5.4 x 10-7
2
0.0200
0.200
10.8 x 10-7
3
0.0400
0.200
21.5 x 10-7
4
0.200
0.0202
10.8 x 10-7
5
0.200
0.0404
21.6 x 10-7
6
0.200
0.0808
43.3 x 10-7
Rate Order



0 order: The concentration of the
reactants has no impact on the rate of the
reaction.
1st order: The rate doubles when
concentration is doubles ([2]1 = 2), , triples
when concentration is tripled ([3]1 = 3),
quadruples when the concentration is
quadrupled ([4]1 = 4), and so forth (raised
to the 1st power in the rate law).
2nd order: The rate quadruples when the
concentration is doubled ([2]2 = 4), the rate
increases ninefold when the concentration
is triples ([3]2 = 9), and so forth (raised to
the 2nd power in the rate law).
Rate Law Expression
• The rate law expression for this reaction is:
Rate = k[NH4+]1[NO2-]1
– take note only reactants appear in the rate law
expression
– k represents a proportionality constant called the rate
law constant (sometimes simply the rate constant).
– overall rate order for the reaction is the sum of the
rate orders for the reactants. So for the above
reaction the rate order is 2.
• Example: Determine the rate law constant for
this reaction.


Once the rate law constant is
determined the rate could be
calculated at any reactant
concentration.
Example: Determine the rate of
the reaction when [NH4+] = 2.13M
and [NO2-] = 0.986M.
1st Order Rate Law
• Where X is the concentration of a
reactant at any moment in time,
(X)o is the initial concentration of
this reactant, k is the constant for
the reaction, and t is the time since
the reaction started.
• This equation is useful in
calculating how much of a
substance remains after a certain
amount of time has passed, or to
calculate how long it takes until the
concentration is at a certain point.
First Order Reactions


If the rate law of a
reaction is first order
with respect to [A], then
the graph of ln[A]
versus time (t) creates
a straight line with a
negative slope.
The value of the slope
of the line is equal to
the negative value of
the rate constant (k).
Half-lives are 1st Order

The equation for the half-life of a
substance is derived from this
equation.

Half-life - The length of time it
takes for exactly half of the nuclei
of a radioactive sample to decay.
2nd Order Rate Law
• Where X is the concentration of a
reactant at any moment in time,
(X)o is the initial concentration of
this reactant, k is the constant for
the reaction, and t is the time
since the reaction started.
• This equation is useful in
calculating how much of a
substance remains after a certain
amount of time has passed, or to
calculate how long it takes until
the concentration is at a certain
point.
Second Order Reactions


If the rate law for a
reaction is second
order with respect to
[A], a graph of 1/[A]
versus time (t)
creates a straight
line with a positive
slope.
The value of the
slope of the line is
equal to the value of
the rate constant (k).
MC #1
Relatively slow rates of chemical reaction
are associated with which of the following?
(A) The presence of a catalyst
(B) High temperature
(C) High concentration of reactants
(D) Strong bonds in reactant molecules
(E) Low activation energy
MC #2
The proposed steps for a catalyzed reaction between
Ce4+ and Tl+ are represented above. The products of
the overall catalyzed reaction are
Step 1: Ce4+ + Mn2+ ---> Ce3+ + Mn3+
Step 2: Ce4+ + Mn3+ ---> Ce3+ + Mn4+
Step 3: Mn4+ + Tl+ ---> Tl3+ + Mn2+
(A) Ce4+ and Tl+
(B) Ce3+ and Tl3+
(C) Ce3+ and Mn3+
(D) Ce3+ and Mn4+
(E) Tl3+ and Mn2+
MC #3
(CH3)3CCl(aq) + OH¯ ---> (CH3)3COH(aq) + Cl¯
For the reaction represented above, the experimental
rate law is given as follows. Rate = k [(CH3)3CCl]
If some solid sodium solid hydroxide is added to a
solution that is 0.010-molar in (CH3)3CCl and 0.10-molar
in NaOH, which of the following is true? (Assume the
temperature and volume remain constant.)
(A) Both the reaction rate and k increase.
(B) Both the reaction rate and k decrease.
(C) Both the reaction rate and k remain the same.
(D) The reaction rate increases but k remains the same.
(E) The reaction rate decreases but k remains the same.
MC #4 & 5
Questions 4 & 5:
H3AsO4 + 3I¯ + 2 H3O+ ---> H3AsO3 + I3¯ + H2O
The oxidation of iodide ions by arsenic acid in acidic aqueous solution
occurs according to the stoichiometry shown above. The experimental rate
law of the reaction is: Rate = k [H3AsO4] [I¯] [H3O+]
4. What is the order of the reaction with respect to I¯?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
5. According to the rate law for the reaction, an increase in the concentration of
hydronium ion has what effect on this reaction?
(A) The rate of reaction increases.
(B) The rate of reaction decreases.
(C) The value of the equilibrium constant increases.
(D) The value of the equilibrium constant decreases.
(E) Neither the rate nor the value of the equilibrium constant is changed.
FRQ #1: slide 1
A(g) + B(g)  C(g) + D(g)
• For the gas-phase reaction represented
above, the following experimental data
were obtained:
Experiment
Initial [A] (mol L-1)
Initial [B] (mol L-1)
Initial Reaction
Rate (mol L-1 s-l)
1
2
3
4
0.033
0.034
0.136
0.202
0.034
0.137
0.136
0.233
6.6710-4
1.0810-2
1.0710-2
?
FRQ #1: slide 2
(a) Determine the order of the reaction with respect to reactant A. Justify
your answer.
(b) Determine the order of the reaction with respect to reactant B. Justify
your answer.
(c)
Write the rate law for the overall reaction.
(d) Determine the value of the rate constant, k, for the reaction. Include
units with your answer.
(e)
Calculate the initial reaction rate for experiment 4.
(f)
The following mechanism has been proposed for the reaction.
Step 1: B + B  E + D slow
Step 2: E + A  B + C
fast equilibrium
• Provide two reasons why the mechanism is acceptable.
(g) In the mechanism in part (f), is species E a catalyst, or is it an
intermediate? Justify your answer.