Sequential Reactions and Intermediates (25.7)
• Sequential reactions (elementary) involve multiple reactions in which one
or more intermediates are formed
– The differential form of the rate is written with respect to product formation
– Rate law only involves intermediate since it is the only species that generates products
kA
kI
A 

I 

P
Rate 

d P 
 k I I 
dt
• Intermediate concentration is extremely hard to measure, so we need to
 we can measure
relate it to quantities
– We should be able to measure reactant concentration, so we rely on the fact that A only
decays in one way

dA
 k A A
dt
A  A0 ek t
A
• Since the intermediate only formsfrom the reactant, we can express its

concentration in terms of A
– The first reaction creates I, the second reaction depletes it (hence the negative sign)
dI
 k A A  k I I 
dt
I 
kA
ekA t  ek I t A0

kI  k A
Sequential Reactions and Rate Determining Steps (25.7)
• Concentration of product can be determined using a simple mass balance
principle
– The sum of concentrations of all substances at any time must be equal to the initial
concentration of reactant
A0  A  I  P
kA ek I t  kI ekA t 
1A0
P  
 kI  kA

• The size of the rate constants is an indication of how quickly each part of


the reaction proceeds
– If kI is much larger than kA, the intermediate does not last very long and thus does not
build up in the reaction
– If kA is much larger than kI, then the reactant decomposes quickly and a significant
amount of intermediate will form
• The rate-determining (or rate-limiting) step is the slowest step in the
mechanism and it dictates how quickly products will form
– If first step is rate-limiting, the reaction looks like it is one step (i.e., decay of reactant
and formation of product follow first order kinetics)
– If second step is rate-limiting, reaction follows first-order for intermediate
Parallel Reactions (25.8)
• Parallel reactions involve the reactant decaying into more than one
product
– The rate of decay of the reactant is related to the rate constants of both processes
kB
kC
B 

 A 
C

d A
 k B B  kC C 
dt

A  A0 ek
B
kC t
• The rates of formation of each product has a simple form due to the

simplicity
of the differential rate equation

– The product concentration (P = B or C) differs based on the rate constant
dP 
 k P A  k P A0 ekB kC t
dt
P  

kP
A0 1 ekB kC t
kB  kC

• The
to the ratio of the rate constants for
 ratio of concentrations is related

a parallel set of reactions
– The overall yield (ϕ) of a product in the reaction is the ratio of the concentration of the
product of interest over the sum of all product concentrations
B  kB
C kC

k1
k1  k 2  k 3  ...
Reversible Reactions and Equilibrium (25.10)
• Reversible reactions are ones in which the reactants can be generated
from products
– Each direction of the reaction has a rate constant associated with it
kA



A
B



kB
Rate 

dA
d B
 kA A  k B B  
dt
dt
• If the reaction starts with only A, after a certain length of time the

concentrations of A and B stabilize (i.e., equilibrium is obtained)
Aeq  A0

kB 
B

A
1
 eq  0

 kA  kB 
kB
kA  kB
• At equilibrium, rate of change of A and B are zero


– Equilibrium constant (K) can be expressed
as a ratio of rate constants
dAeq
dt


dBeq
dt
 kA Aeq  kB Beq  0
kA Beq

K
kB Aeq
Concentration Profile for Sequential Reactions
Rate-Limiting Behavior in Sequential Reactions
Concentration Profile for Parallel Reactions
Concentration Profile for Reversible Reaction