Polyethylene is used in many items, including water pipes, bottles, electrical insulation, toys, and mailer envelopes. It is a
The R •� species (called a radical) reacts with an ethylene molecule (M) to generate another radical:
The reaction of
This step can be repeated with hundreds of monomer units. The propagation terminates when two radicals combine:
The initiator frequently used in the
This is a first-order reaction. The half-life of benzoyl peroxide at
Interpretation:
The rate constant, activation energy, and the rate law of reaction are to be determined.
Concept introduction:
At a given temperature, the concentration ratio of concentration of product to concentration of reactant in a chemical reaction is called rate constant. According to the Arrhenius equation, rate constant depends on temperature.
The amount of energy required for the reaction to form products by the formation of an activated complex is called activation energy.
Half-life: The time required for the concentration of a reactant to decrease to one-half its initial value. This period of time is called the half-life of the reaction, written as
The relation between rate constant k and half-life is
Answer to Problem 135AP
Solution:
a)
b)
c)
d) A higher rate of propagation step and a lower rate of termination step.
Explanation of Solution
Given information: The initiation step is as follows:
The reaction of
The propagation terminates when two radicals combine as follows:
a) The rate constant
The relation between the rate constant and half-life is given as follows:
The value of
is given as
The rate constant for the reaction is
b) The activation energy
The half-life of benzoyl peroxide is
The rate constant for the reaction at
There are two values of rate constants
Here,
Substitute the values
The activation energy for the reaction is
c) The rate laws to be written for elementary steps in the preceding polymerization process and identify the reactant, product, and intermediates.
The rate law for the initiation step is as follows:
The rate law for the propagation step is as follows:
The rate law for the propagation step is as follows:
The ethylene monomers are the reactant molecules, and polyethylene is a product in the reaction mechanism. The intermediates are formed in the early elementary step and consumed in the next step. So, the intermediates are radicals of
d) The condition that favor the growth of long, high-molar-mass polyethylenes.
A higher rate of propagation and a lower rate of termination are favoured when the growth of long polymers take place. In the propagation step, the rate law is dependent on the concentration of monomer. If the concentration of ethylene is increased, the propagation rate also increases.
The concentration of radical fragments
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Chapter 14 Solutions
Chemistry
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