Chapter 14: Problem 76
(a) Most commercial heterogeneous catalysts are extremely finely divided solid materials. Why is particle size important? (b) What role does adsorption play in the action of a heterogeneous catalyst?
Chapter 14: Problem 76
(a) Most commercial heterogeneous catalysts are extremely finely divided solid materials. Why is particle size important? (b) What role does adsorption play in the action of a heterogeneous catalyst?
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Get started for freeThe isomerization of methyl isonitrile $\left(\mathrm{CH}_{3} \mathrm{NC}\right)\( to acetonitrile \)\left(\mathrm{CH}_{3} \mathrm{CN}\right)$ was studied in the gas phase at \(215^{\circ} \mathrm{C}\), and the following data were obtained: $$ \begin{array}{rc} \hline \text { Time (s) } & {\left[\mathrm{CH}_{3} \mathrm{NC}\right](M)} \\ \hline 0 & 0.0165 \\ 2000 & 0.0110 \\ 5000 & 0.00591 \\ 8000 & 0.00314 \\ 12,000 & 0.00137 \\ 15,000 & 0.00074 \\ \hline \end{array} $$ (a) Calculate the average rate of reaction, in \(M / s\), for the time interval between each measurement. (b) Calculate the average rate of reaction over the entire time of the data from \(t=0\) to \(t=15,000 \mathrm{~s} .(\mathbf{c})\) Which is greater, the average rate between \(t=2000\) and $t=12,000 \mathrm{~s}\(, or between \)t=8000\( and \)t=15,000 \mathrm{~s} ?(\mathbf{d})$ Graph \(\left[\mathrm{CH}_{3} \mathrm{NC}\right]\) versus time and determine the instantaneous rates in \(M / \mathrm{s}\) at \(t=5000 \mathrm{~s}\) and $t=8000 \mathrm{~s}$.
You perform a series of experiments for the reaction $\mathrm{A} \rightarrow 2 \mathrm{~B}$ and find that the rate law has the form, rate \(=k[\mathrm{~A}]^{x} .\) Determine the value of \(x\) in each of the following cases: (a) The rate increases by a factor of \(6.25,\) when \([\mathrm{A}]_{0}\) is increased by a factor of \(2.5 .(\mathbf{b})\) There is no rate change when \([\mathrm{A}]_{0}\) is increased by a factor of \(4 .(\mathbf{c})\) The rate decreases by a factor of \(1 / 2,\) when \([\mathrm{A}]_{0}\) is cut in half.
Cobalt-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?
For the elementary process $\mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{NO}_{3}(g)$ the activation energy \(\left(E_{a}\right)\) and overall \(\Delta E\) are $154 \mathrm{~kJ} / \mathrm{mol}\( and \)136 \mathrm{~kJ} / \mathrm{mol}$, respectively. (a) Sketch the energy profile for this reaction, and label \(E_{a}\) and \(\Delta E\). (b) What is the activation energy for the reverse reaction?
The human body is characterized by an extremely complex system of interrelated chemical reactions. A large number of enzymes are necessary for many of these reactions to occur at suitable rates. Enzymes are very selective in the reactions they catalyze, and some are absolutely specific. Use the lock-and- key model to account for the specificity of an enzyme.
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