Chapter 12: Problem 8
Provide a conceptual rationale for the differences in the half-lives of zero-, first-, and second-order reactions.
Chapter 12: Problem 8
Provide a conceptual rationale for the differences in the half-lives of zero-, first-, and second-order reactions.
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Get started for freeThe reaction $$ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g) $$ was studied at \(-10^{\circ} \mathrm{C}\). The following results were obtained where $$ \text { Rate }=-\frac{\Delta\left[\mathrm{Cl}_{2}\right]}{\Delta t} $$
A popular chemical demonstration is the "magic genie" procedure, in which hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst. The activation energy of this (uncatalyzed) reaction is \(70.0 \mathrm{~kJ} / \mathrm{mol}\). When the catalyst is added, the activation energy (at \(20 .{ }^{\circ} \mathrm{C}\) ) is \(42.0 \mathrm{~kJ} / \mathrm{mol}\). Theoretically, to what temperature \(\left({ }^{\circ} \mathrm{C}\right)\) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at \(20 .{ }^{\circ} \mathrm{C} ?\) Assume the frequency factor \(A\) is constant and assume the initial concentrations are the same.
Theophylline is a pharmaceutical drug that is sometimes used to help with lung function. You observe a case where the initial lab results indicate that the concentration of theophylline in a patient's body decreased from \(2.0 \times 10^{-3} M\) to \(1.0 \times 10^{-3} M\) in 24 hours. In another 12 hours the drug concentration was found to be \(5.0 \times 10^{-4} M\). What is the value of the rate constant for the metabolism of this drug in the body?
Consider the hypothetical reaction $$ \mathrm{A}+\mathrm{B}+2 \mathrm{C} \longrightarrow 2 \mathrm{D}+3 \mathrm{E} $$ where the rate law is $$ \text { Rate }=-\frac{\Delta[\mathrm{A}]}{\Delta t}=k[\mathrm{~A}][\mathrm{B}]^{2} $$ An experiment is carried out where \([\mathrm{A}]_{0}=1.0 \times 10^{-2} M\), \([\mathrm{B}]_{0}=3.0 \mathrm{M}\), and \([\mathrm{C}]_{0}=2.0 \mathrm{M} .\) The reaction is started, and after \(8.0\) seconds, the concentration of \(\mathrm{A}\) is \(3.8 \times 10^{-3} \mathrm{M}\). a. Calculate the value of \(k\) for this reaction. b. Calculate the half-life for this experiment. c. Calculate the concentration of A after \(13.0\) seconds. d. Calculate the concentration of \(\mathrm{C}\) after \(13.0\) seconds.
Experiments have shown the average frequency of chirping of individual snowy tree crickets (Oecanthus fultoni) to be \(178 \mathrm{~min}^{-1}\) at \(25.0^{\circ} \mathrm{C}, 126 \mathrm{~min}^{-1}\) at \(20.3^{\circ} \mathrm{C}\), and \(100 . \mathrm{min}^{-1}\) at \(17.3^{\circ} \mathrm{C}\). a. What is the apparent activation energy of the reaction that controls the chirping? b. What chirping rate would be expected at \(15.0^{\circ} \mathrm{C}\) ? c. Compare the observed rates and your calculated rate from part b to the rule of thumb that the Fahrenheit temperature is 42 plus \(0.80\) times the number of chirps in \(15 \mathrm{~s}\).
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