Chemistry

Problem

A synthetic chemist investigates a reaction network in which three independent elementary processes occur simultaneously in a well-mixed, isothermal solution: (1)

A + B \rightarrow C

(rate constant

k_1

) (2)

A + C \rightarrow D

(rate constant

k_2

) (3)

2C \rightarrow E

(rate constant

k_3

) At

t = 0

the concentrations are

[A]_0 = 0.200\,\text{M}

[B]_0 = 0.150\,\text{M}

, and

[C]_0 = 0.0500\,\text{M}

. (a) Write the differential rate expressions for

\frac{d[A]}{dt}

\frac{d[C]}{dt}

, and

\frac{d[E]}{dt}

in terms of the rate constants and instantaneous concentrations. (b) Using

k_3 = 0.80\,\text{M}^{-1}\,\text{s}^{-1}

, calculate the initial rate of formation of

E

, including units. (c) For each elementary reaction, state its molecularity and briefly discuss how molecularity influences the expected frequency of successful collisions.

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