Chapter 13: Problem 31
Define activation energy. What role does activation energy play in chemical kinetics?
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Chapter 13: Problem 31
Define activation energy. What role does activation energy play in chemical kinetics?
These are the key concepts you need to understand to accurately answer the question.
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The following data were collected for the reaction between hydrogen and nitric oxide at \(700^{\circ} \mathrm{C}\) : $$ 2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g) $$ $$ \begin{array}{clll} \hline \text { Experiment } & {\left[\mathrm{H}_{2}\right]} & {[\mathrm{NO}]} & \text { Initial Rate }(M / \mathrm{s}) \\ \hline 1 & 0.010 & 0.025 & 2.4 \times 10^{-6} \\ 2 & 0.0050 & 0.025 & 1.2 \times 10^{-6} \\ 3 & 0.010 & 0.0125 & 0.60 \times 10^{-6} \\ \hline \end{array} $$ (a) Determine the order of the reaction. (b) Calculate the rate constant. (c) Suggest a plausible mechanism that is consistent with the rate law. (Hint: Assume that the oxygen atom is the intermediate.)
The rate law for the reaction $$ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g) $$ is given by rate \(=k[\mathrm{NO}]\left[\mathrm{Cl}_{2}\right] .\) (a) What is the order of the reaction? (b) A mechanism involving the following steps has been proposed for the reaction: $$ \begin{array}{c} \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g) \\ \mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \longrightarrow 2 \mathrm{NOCl}(g) \end{array} $$ If this mechanism is correct, what does it imply about the relative rates of these two steps?
For a first-order reaction, how long will it take for the concentration of reactant to fall to one-eighth its original value? Express your answer in terms of the half-life \(\left(t_{1}\right)\) and in terms of the rate constant \(k\).
The decomposition of dinitrogen pentoxide has been studied in carbon tetrachloride solvent \(\left(\mathrm{CCl}_{4}\right)\) at a certain temperature: $$ 2 \mathrm{~N}_{2} \mathrm{O}_{5} \longrightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2} $$ $$ \begin{array}{cc} \hline\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] & \text { Initial Rate }(M / \mathrm{s}) \\ \hline 0.92 & 0.95 \times 10^{-5} \\ 1.23 & 1.20 \times 10^{-5} \\ 1.79 & 1.93 \times 10^{-5} \\ 2.00 & 2.10 \times 10^{-5} \\ 2.21 & 2.26 \times 10^{-5} \\ \hline \end{array} $$ Determine graphically the rate law for the reaction and calculate the rate constant.
A protein molecule, \(\mathrm{P}\), of molar mass \(\mathscr{A}\) dimerizes when it is allowed to stand in solution at room temperature. A plausible mechanism is that the protein molecule is first denatured (that is, loses its activity due to a change in overall structure) before it dimerizes: $$ \begin{array}{rlr} \mathrm{P} & \stackrel{k}{\longrightarrow} \mathrm{P}^{*}(\text { denatured }) & \text { slow } \\ 2 \mathrm{P}^{*} \longrightarrow \mathrm{P}_{2} & \text { fast } \end{array} $$ where the asterisk denotes a denatured protein molecule. Derive an expression for the average molar mass (of \(\mathrm{P}\) and \(\mathrm{P}_{2}\) ), \(, \overline{\mathscr{M}}\), in terms of the initial protein concentration \([\mathrm{P}]_{0}\) and the concentration at time \(t,\) \([\mathrm{P}]_{,}\) and \(\mathscr{A} .\) Describe how you would determine \(k\) from molar mass measurements.
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