Problem 17
Americium-241 is an \(\alpha\) -particle emitter, and the rate constant for decay is \(1.605 \times 10^{-3} \mathrm{y}^{-1}\) (a) Write an equation for the decay of \(^{241} \mathrm{Am}\) (b) Determine the half-life of \(^{241} \mathrm{Am}\)
Problem 19
For the reaction: \\[ A \rightarrow B+C \\] which of the following would you expect to vary over the temperature range 290 to \(320 \mathrm{K}\) (a) reaction rate; (b) rate constant; (c) \(E_{\mathrm{a}}\) (d) \([\mathrm{A}]_{0}-[\mathrm{A}] ?\)
Problem 24
The mechanism of the decomposition: \(A \rightarrow B+C\) can be written as a sequence of the elementary steps: Step I: \(A \stackrel{k_{1}}{\longrightarrow} D\) Step II: \(D \stackrel{k_{2}}{\longrightarrow} B+C\) (a) What type of a species is D? (b) For step I alone, give an expression that shows the rate of appearance of \(D\) (c) How is your answer to altered if you take into account the sequence of steps I and II? (d) Use the steady state approximation to show that the rate of formation of \(\mathrm{B}\) is directly proportional to the concentration of A.
Problem 28
The overall rate law for the following reaction: \\[ \begin{array}{l} 2 \mathrm{NO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\\ \text { is: } \quad-\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t}=k_{\text {obs }}[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right] \end{array} \\] Confirm that the following mechanism is consistent with the observed rate law: \\[ \begin{array}{l} 2 \mathrm{NO} \frac{k_{1}}{=k_{-1}} \mathrm{N}_{2} \mathrm{O}_{2} \\ \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \stackrel{k_{2}}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O} \end{array} \\]
