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Unformatted text preview: CHAPTER 6 KINETICS
(IB TOPICS 6 AND 16) SUMMARY
Reaction rate
Rate of a reaction is the decrease in the concentration of a reactant or the increase of the
concentration of a product with unit time. For a A → b B, rate = − 1 Δ[ A] 1 Δ[ B]
; rate is a
=
a Δt b Δt positive quantity.
Rates can be determined by measuring the change in the concentration of a reactant or product
with time. Possible methods are pressure measurements for gases using a manometer or
pressure gauge, volume measurement for gases using a gas syringe, color changes using a
colorimeter or spectrophotometer, heat changes using a thermometer, mass changes using a
balance, pH changes using a pH meter, titrations, etc.
Collision Theory
• The reactant particles must collide together. • Particles must have the correct geometrical alignment. • Particles must have a minimum energy of E ≥ E a , the activation energy. • Activation energy is the minimum energy required for reactants to react in order to
convert into products (via a transition state or activated complex). • Transition state is an unstable arrangement in which the bonds are in the process of
being broken and formed and presents the maximum point on a potential energy
diagram; it can not be isolated. Factors that Influence Rates of Reactions
• Increase in concentration: Greater number of particles per unit volume per time means
greater frequency of collisions and faster rate. • Increase in temperature: This causes an increase in average kinetic energy; particles
collide more frequently and more forcefully. Thus number of particles with
E ≥ E a increases greatly and rate increases (more forceful collisions is a more important
factor than more frequent collisions). • Increasing the surface area of solids reactants: This increases the number of particles
that can collide, i.e., increases the frequency of successful collisions. • Catalysts: Lower the activation energy of reaction by providing an alternate pathway
and thus increase the rate of reaction. Catalysts are specific to reactions and are used in
industry.
o Homogeneous catalysis: Where the catalyst is in the same phase as the
reactants, e.g., esterification reaction to produce sweet smelling compounds
for perfumes, and in the food industry. o Heterogeneous catalysis: Where the catalyst and reactants are in different
phases e.g., in the manufacture of ammonia, sulfuric acid, hydrogenation of
alkenes etc. o A catalyst does not change the position of equilibrium; rather it increases the
rate of both the forward and reverse reactions to the same extent; does not
change ΔH of a reaction. • Rate expression (law) is the dependence of rate on concentration expressed
mathematically. • For the reaction: A + B + C → products, rate =k[A]m[B]n[C]p, where m, n, and p are the
orders of the reaction with respect to each reactant A, B, C. The overall order = (m + n + p). © IBID Press 2007 1 CHAPTER 6 KINETICS
(IB TOPICS 6 AND 16) SUMMARY
Orders of reaction are obtained experimentally, not from Stoichiometry; however any
mechanism must be consistent with overall Stoichiometry of the reaction.
• Rate constant, k, is the constant in the rate expression. It is temperature dependent. Units
of rate constant depend on the rate expression; units of zero order rate constant, ko = units
of rate = mol dm−3 s−1. Units of 1st order rate constant, k1 = s−1. Units of 2nd order rate
constant, k2 = dm3 mol−1 s−1; units of 3rd order rate constant, k3 = dm6 mol−2 s−1 (units must
not be memorized, but easily derived from the appropriate rate expression). • The rate expression, determined only experimentally, need not be a simple one, i.e., it
need not contain whole numbers, or positive numbers for that matter although this is often
the case. • In general, given the rate as a function of concentration, reaction order can be determined
as follows: • If only one reactant is involved, since rate = k [conc.]n, find the ratio of the rates at two
different concentrations and apply the relation: n
rate2 ⎛ [conc 2 ] ⎞
⎟ ; n is the reaction order.
=⎜
⎜
⎟
rate1 ⎝ [conc1 ] ⎠
• If two reactants, A and B, are involved, rate = k [A]m [B]n: • Find the ratio of the rates when [B] is constant but [A] changes. Using the equation above,
find the order with respect to A. • Repeat the process when [A] is constant but [B] changes to determine the order with respect
to B. Orders of reaction
o
Zeroorder reaction is when the rate of a reaction is independent of the
concentration of a reactant: rate=k [A]0 = k. Graph of [A] vs time is a straight line, with
a negative slope = rate. [A]t = [A]0 – kt.
o
Firstorder reaction is where the rate doubles when concentration doubles: rate =k
[A]1. Graph of [A] against time is an exponential curve; graph of ln [A] vs. t is a
straight line with a negative slope where slope = k the rate constant. Halflife of a first
order reaction is a constant; t1/2=0.693/k. Integrated form of first order equation: ln
ln [A]t = − kt + ln [A]0 OR ln [A]0 – ln[A]t = kt OR o [ A]0
= kt
[ A]t
; [A]t = [A]0ekt (the last two equations are given in the Data Book). o
irstorder reaction is where the rate doubles when concentration doubles: rate =k
[A]1. Graph of [A] against time is an exponential curve; graph of ln [A] vs. t is a
straight line with a negative slope where slope = k the rate constant. Halflife of a first
order reaction is a constant; t1/2=0.693/k. Integrated form of first order equation: ln [A]t ln
= − kt + ln [A]0 OR ln [A]0 – ln[A]t = kt OR
equations are given in the Data Book). [ A]0
= kt
[ A]t
; [A]t = [A]0ekt (the last two o
If the rate quadruples when concentration doubles: rate = k [A]2. Graph of 1/[A]
against time is a straight line for a second order reaction with a positive slope = k.
© IBID Press 2007 2 CHAPTER 6 KINETICS
(IB TOPICS 6 AND 16) SUMMARY
o
For a thirdorder reaction, if rate = k[A]3, then as [A] doubles, rate increases 8
times.
o
Rate increases with temperature when concentrations are constant, k increases
rapidly with T and is temperature dependent, producing a straight line graph of ln k vs
1/T with a negative slope. Slope of the line =  Ea/R. Thus Ea can be determined; T
must be in Kelvin, not °C.
o Arrhenius Equation gives the dependence of k on T (equation given in the Data
Ea − RT
booklet): k = A e
: ln k = ln A −
o Ea ⎛ 1 ⎞
⎜⎟
R ⎝T ⎠ OR log10 k = log10 A − Ea ⎛ 1 ⎞
⎜ ⎟ where: A, the
2.303 R ⎝ T ⎠ Arrhenius constant is the collision factor that represents the frequency of successful
collisions with the favourable geometry, R is the Ideal Gas Constant (= 8.314 J mol1 K1
), Ea is the activation energy (the minimum energy required for a reaction to occur),
and T must be in Kelvin scale.
• Molecularity is based on proposed mechanism and refers to the number of particles in
the slow, ratedetermining step (i.e., the number of species involved in making the
transition state or the activated complex of the slow step). • Mechanism is a model of how a reaction occurs.
o The slowest step of a mechanism is called the ratedetermining step. o
Intermediates are species produced in earlier steps that are consumed in later
steps.
o
Transition state is an unstable arrangement in which the bonds are in the process
of being broken and formed and presents the maximum point on a potential energy
diagram; it can not be isolated.
o Mechanism must account for overall Stoichiometry, rate expression, etc. o Rate of overall reaction is the rate of the slowest step. o
Stoichiometry of an equation gives no information about the rate expression or
about the mechanism of a reaction. However any mechanism must be consistent with
overall Stoichiometry, rate expression, etc. For a 3rd order reaction, the first step
(containing a maximum of two particles) cannot be the slow, rate determining step. A Unimolecular step A Bimolecular step •
A unimolecular step involves a •
A bimolecular steps involves
single species as a reactant.
collision of two species (that form a
transition state or an activated complex
that can not be isolated).
•
Its rate law is therefore 1st order •
Its rate law is 1st order with respect to
with respect that reactant.
each of the colliding species and is
therefore 2nd order overall.
(N.B. Shading indicates Topic 16 (AHL) material.) © IBID Press 2007 3 ...
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