Chemistry

Problem

A reaction between A and 2 B produces products by the stoichiometric equation

A + 2B \rightarrow \text{products}

Kinetic experiments at 310 K yield the rate law

\text{rate} = k[A][B]

(overall order = 2) Assume the reaction takes place in a closed, constant-volume vessel that initially contains

[A]_0 = [B]_0 = 0.50\,\text{M}

and no products. a. Part 1: Derive an expression for the concentration of A as a function of time, starting from the differential rate law. Clearly state any mathematical steps used in your derivation. b. Part 2: From your integrated expression, obtain a formula for the half-life

t_{1/2}

in terms of the initial concentration

[A]_0

and the rate constant

k

. c. Part 3: Compare the dependence of half-life on initial concentration for this second-order reaction with that of a first-order reaction. Explain how experimental measurement of half-life versus initial concentration could be used to confirm the overall reaction order. d. Part 4: If

k = 2.0 \times 10^{2}\,\text{M}^{-1}\,\text{s}^{-1}

, calculate the time required for

[A]

to decrease to

0.10\,\text{M}

under the stated initial conditions.

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