Chapter 14: Problem 75
(a) What is a catalyst? (b) What is the difference between a homogeneous and a heterogeneous catalyst? (c) Do catalysts affect the overall enthalpy change for a reaction, the activation energy, or both?
Chapter 14: Problem 75
(a) What is a catalyst? (b) What is the difference between a homogeneous and a heterogeneous catalyst? (c) Do catalysts affect the overall enthalpy change for a reaction, the activation energy, or both?
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Get started for freeCobalt-60 is used in radiation therapy to treat cancer. It has a first-order rate constant for radioactive decay of $k=1.31 \times 10^{-1} \mathrm{yr}^{-1}$. Another radioactive isotope, iron59, which is used as a tracer in the study of iron metabolism, has a rate constant of $k=1.55 \times 10^{-2}\( day \)^{-1}$. (a) What are the half-lives of these two isotopes? (b) Which one decays at a faster rate? (c) How much of a 1.00-mg sample of each isotope remains after three half-lives? How much of a \(1.00-\mathrm{mg}\) sample of each isotope remains after five days?
(a) The activation energy for the reaction $\mathrm{A}(g) \longrightarrow \mathrm{B}(g)\( is \)100 \mathrm{~kJ} / \mathrm{mol}$. Calculate the fraction of the molecule A that has an energy equal to or greater than the activation energy at \(400 \mathrm{~K} .(\mathbf{b})\) Calculate this fraction for a temperature of \(500 \mathrm{~K}\). What is the ratio of the fraction at $500 \mathrm{~K}\( to that at \)400 \mathrm{~K}$ ?
The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism: $$ \begin{aligned} \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{I}^{-}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{IO}^{-}(a q)(\text { slow }) \\ \mathrm{IO}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)+\mathrm{I}^{-}(a q) \quad(\text { fast }) \end{aligned} $$ (a) Write the chemical equation for the overall process. (b) Identify the intermediate, if any, in the mechanism. (c) Assuming that the first step of the mechanism is rate determining, predict the rate law for the overall process.
(a) Can an intermediate appear as a reactant in the first step of a reaction mechanism? (b) On a reaction energy profile diagram, is an intermediate represented as a peak or a valley? (c) If a molecule like \(\mathrm{Cl}_{2}\) falls apart in an elementary reaction, what is the molecularity of the reaction?
(a) The gas-phase decomposition of sulfuryl chloride $\left(\mathrm{SO}_{2} \mathrm{Cl}_{2}\right), \mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\( is first order in \)\mathrm{SO}_{2} \mathrm{Cl}_{2}\(. At \)300^{\circ} \mathrm{C}$ the half-life for this process is two and a half days. What is the rate constant at this temperature? (b) At \(400^{\circ} \mathrm{C}\) the rate constant is \(0.19 \mathrm{~min}^{-1}\). What is the half-life at this temperature?
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