Chapter 11: Problem 62
For the reaction $$\mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{R}+\mathrm{Z} \quad \Delta H=+295 \mathrm{~kJ},$$ draw a reaction-energy diagram for the reaction if its activation energy is \(378 \mathrm{~kJ} .\)
Chapter 11: Problem 62
For the reaction $$\mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{R}+\mathrm{Z} \quad \Delta H=+295 \mathrm{~kJ},$$ draw a reaction-energy diagram for the reaction if its activation energy is \(378 \mathrm{~kJ} .\)
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Get started for freeThe decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) to \(\mathrm{NO}_{2}\) and \(\mathrm{NO}_{3}\) is a first-order gas-phase reaction. At \(25^{\circ} \mathrm{C}\), the reaction has a half-life of \(2.81\) s. At \(45^{\circ} \mathrm{C}\), the reaction has a half-life of \(0.313 \mathrm{~s}\). What is the activation energy of the reaction?
Experimental data are listed for the hypothetical reaction $$\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D}$$ $$\begin{array}{lcccccc}\hline \text { Time (s) } & 0 & 10 & 20 & 30 & 40 & 50 \\\\{[\mathrm{~A}]} & 0.32 & 0.24 & 0.20 & 0.16 & 0.14 & 0.12 \\ \hline\end{array}$$ (a) Plot these data as in Figure \(11.2\). (b) Draw a tangent to the curve to find the instantaneous rate at \(30 \mathrm{~s}\). (c) Find the average rate over the 10 to \(40 \mathrm{~s}\) interval. (d) Compare the instantaneous rate at \(30 \mathrm{~s}\) with the average rate over the thirty-second interval.
In the first-order decomposition of acetone at \(500^{\circ} \mathrm{C}\), $$\mathrm{CH}_{3}-\mathrm{CO}-\mathrm{CH}_{3}(g) \longrightarrow \text { products }$$ it is found that the concentration is \(0.0300 \mathrm{M}\) after \(200 \mathrm{~min}\) and \(0.0200 \mathrm{M}\) after 400 min. Calculate the following. (a) the rate constant (b) the half-life (c) the initial concentration
The gas-phase reaction between hydrogen and iodine $$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)$$ proceeds with a rate constant for the forward reaction at \(700^{\circ} \mathrm{C}\) of \(138 \mathrm{~L} / \mathrm{mol} \cdot \mathrm{s}\) and an activation energy of \(165 \mathrm{~kJ} / \mathrm{mol}\). (a) Calculate the activation energy of the reverse reaction given that \(\Delta H_{i}^{\circ}\) for HI is \(26.48 \mathrm{~kJ} / \mathrm{mol}\) and \(\Delta H_{i}^{\circ}\) for \(\mathrm{I}_{2}(\mathrm{~g})\) is \(62.44 \mathrm{~kJ} / \mathrm{mol}\). (b) Calculate the rate constant for the reverse reaction at \(700^{\circ} \mathrm{C}\). (Assume \(\mathrm{A}\) in the equation \(k=\mathrm{Ae}^{-\mathcal{P}_{2} / \mathrm{RT}^{\prime}}\) is the same for both forward and reverse reactions.) (c) Calculate the rate of the reverse reaction if the concentration of HI is \(0.200 M\). The reverse reaction is second-order in HI.
The decomposition of ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}\), is a first-order reaction. It is found that it takes 212 s to decompose \(0.00839 \mathrm{M} \mathrm{C}_{2} \mathrm{H}_{6}\) to \(0.00768 \mathrm{M}\). (a) What is the rate constant for the reaction? (b) What is the rate of decomposition (in \(\mathrm{mol} / \mathrm{L} \cdot \mathrm{h}\) ) when \(\left[\mathrm{C}_{2} \mathrm{H}_{6}\right]=\) \(0.00422 \mathrm{M} ?\) (c) How long (in minutes) will it take to decompose \(\mathrm{C}_{2} \mathrm{H}_{6}\) so that \(27 \%\) remains? (d) What percentage of \(\mathrm{C}_{2} \mathrm{H}_{6}\) is decomposed after \(22 \mathrm{~min}\) ?
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