Chapter 13: Problem 79
The rate of a reaction depends both on inherent factors and on concentration. The rate constant \(k\) is associated with the inherent factors. What are they?
Chapter 13: Problem 79
The rate of a reaction depends both on inherent factors and on concentration. The rate constant \(k\) is associated with the inherent factors. What are they?
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Get started for freeA reaction is exothermic, with \(\Delta E_{\mathrm{rxn}}=-40 \mathrm{~kJ}\), and the transition state is \(20 \mathrm{~kJ}\) higher in energy than the reactants. Sketch a reaction-energy profile consistent with this information, complete with labels for the distances representing \(\Delta E_{\mathrm{rxn}}\) and \(E_{\mathrm{a}} .\)
The mechanism for the endothermic reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}+\mathrm{X}\) is Step \(1: \mathrm{A}+\mathrm{A} \rightarrow \mathrm{C}+\mathrm{D}(\mathrm{slow})\) Step \(2: \mathrm{B}+\mathrm{D} \rightarrow \mathrm{X}+\mathrm{A}\) (fast) (a) Draw the reaction-energy profile for this reaction and label reactants, products, reaction intermediates, transition states, activation energies, and \(\Delta E_{\mathrm{rxn}} .\) (Hint: First draw a profile for step \(1 .\) Make it a very endothermic reaction, and remember that a slow reaction has a large value for \(E_{\mathrm{a}}\) Then draw a profile for step 2, using the line representing the step 1 products as the reactants line for step \(2 .\) Remember that a fast reaction has a small value for \(E_{\mathrm{a}}\). (b) What is the rate law for this reaction? (c) If you wanted to quadruple the rate of this reaction, by what factor would you have to increase the concentration of \(\mathrm{A}\) ?
Reactions go faster when heated. Astudent claims this is because as temperature increases, the activation energy \(E_{\mathrm{a}}\) for a reaction decreases. Is this student correct or incorrect? If incorrect, then explain what happens to \(E_{\mathrm{a}}\) upon heating a reaction.
Determine the value of \(k\) for a reaction for which: (a) The fraction of collisions having energy \(>E_{\mathrm{a}}\) is \(0.42\) and the fraction of collisions having the proper orientation is \(0.15\). (b) The fraction of collisions having energy \(>E_{\mathrm{a}}\) is \(0.42\) and the fraction of collisions having the proper orientation is \(0.30\). (c) The fraction of collisions having energy \(>E_{\mathrm{a}}\) is \(0.84\) and the fraction of collisions having the proper orientation is \(0.15\). (d) The fraction of collisions having energy \(>E_{\mathrm{a}}\) is \(0.84\) and the fraction of collisions having the proper orientation is \(0.30\).
Suppose a postulated mechanism does generate the experimental rate law, and when the elementary steps are added together, the balanced equation for the overall reaction is generated. What can you say about the postulated mechanism?
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