Chapter 13: Problem 60
What are the characteristics of a catalyst?
Short Answer
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 13: Problem 60
What are the characteristics of a catalyst?
These are the key concepts you need to understand to accurately answer the question.
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Get started for freeConsider the reaction $$ \mathrm{A} \longrightarrow \mathrm{B} $$ The rate of the reaction is \(1.6 \times 10^{-2} M / \mathrm{s}\) when the concentration of \(\mathrm{A}\) is \(0.35 \mathrm{M}\). Calculate the rate constant if the reaction is (a) first order in A, and (b) second order in A.
Variation of the rate constant with temperature for the first-order reaction $$ 2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \longrightarrow 2 \mathrm{~N}_{2} \mathrm{O}_{4}(g)+\mathrm{O}_{2}(g) $$ is given in the following table. Determine graphically the activation energy for the reaction. $$ \begin{array}{cc} \hline T(K) & k\left(\mathrm{~s}^{-1}\right) \\ \hline 298 & 1.74 \times 10^{-5} \\ 308 & 6.61 \times 10^{-5} \\ 318 & 2.51 \times 10^{-4} \\ 328 & 7.59 \times 10^{-4} \\ 338 & 2.40 \times 10^{-3} \\ \hline \end{array} $$
At \(25^{\circ} \mathrm{C},\) the rate constant for the ozone-depleting reaction \(\mathrm{O}(g)+\mathrm{O}_{3}(g) \longrightarrow 2 \mathrm{O}_{2}(g)\) is \(7.9 \times 10^{-15} \mathrm{~cm}^{3} /\) molecule \(\cdot\) s. Express the rate constant in units of \(1 / M \cdot \mathrm{s}\)
How does a catalyst increase the rate of a reaction?
Polyethylene is used in many items, including water pipes, bottles, electrical insulation, toys, and mailer envelopes. It is a polymer, a molecule with a very high molar mass made by joining many ethylene molecules together. (Ethylene is the basic unit, or monomer for polyethylene.) The initiation step is $$ \mathrm{R}_{2} \stackrel{k_{1}}{\longrightarrow} 2 \mathrm{R} \cdot \quad \text { initiation } $$ The \(\mathrm{R} \cdot\) species (called a radical) reacts with an ethylene molecule (M) to generate another radical $$ \mathrm{R} \cdot+\mathrm{M} \longrightarrow \mathrm{M}_{1} $$ Reaction of \(\mathrm{M}_{1} \cdot\) with another monomer leads to the growth or propagation of the polymer chain $$ \mathrm{M}_{1} \cdot+\mathrm{M} \stackrel{k_{\mathrm{p}}}{\longrightarrow} M_{2} \cdot \quad \text { propagation } $$ This step can be repeated with hundreds of monomer units. The propagation terminates when two radicals combine \(\mathrm{M}^{\prime}+\mathrm{M}^{\prime \prime} \cdot \stackrel{k_{1}}{\longrightarrow} \mathrm{M}^{\prime}-\mathrm{M}^{\prime \prime} \quad\) termination The initiator frequently used in the polymerization of ethylene is benzoyl peroxide \(\left[\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}\right)_{2}\right]:\) $$ \left[\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}\right)_{2}\right] \longrightarrow 2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO} $$ This is a first-order reaction. The half-life of benzoyl peroxide at \(100^{\circ} \mathrm{C}\) is 19.8 min. (a) Calculate the rate constant (in \(\min ^{-1}\) ) of the reaction. (b) If the half-life of benzoyl peroxide is \(7.30 \mathrm{~h},\) or \(438 \mathrm{~min},\) at \(70^{\circ} \mathrm{C},\) what is the activation energy (in \(\mathrm{kJ} / \mathrm{mol}\) ) for the decomposition of benzoyl peroxide? (c) Write the rate laws for the elementary steps in the above polymerization process, and identify the reactant, product, and intermediates. (d) What condition would favor the growth of long, highmolar-mass polyethylenes?
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