CHEM201 - Celebration of Knowledge \( 3 / 7 / 2022 \) 13. Activation Energy! Consider the reaction... \[ \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{NO}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{~g}) \] Draw an energy diagram for the reaction, using the following information: \( E_{a}=125 \mathrm{~kJ} / \mathrm{mol} \) and \( \Delta E \) for the reaction is \( -216 \mathrm{~kJ} / \mathrm{mol} \). Use your diagram to indicate (and calculate) the activation energy for the reverse reaction. Draw a second energy diagram assuming a catalyst is added which reduces the activation energy to \( 75 \mathrm{~kJ} / \mathrm{mol} \). (Hint... your reactants and products should be at the same energy level on both diagrams!) Catalyzed 14. Rate Constants and Temperature! For a certain reaction, the activation energy is \( 186 \mathrm{~kJ} / \mathrm{mol} \). If the rate constant at \( 282{ }^{\circ} \mathrm{C} \) is \( 3.52 \times 10^{-7} \mathrm{~L} / \mathrm{mol} \cdot \mathrm{s} \), what is the rate constant at \( 372{ }^{\circ} \mathrm{C} \) ?
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The activation energy for the reaction, $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g) $$ is $E_{a}=940 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ (a) Use this and the data from Table $14.3$ to calculate the activation energy of the reverse reaction. (b) Make a sketch of the activation energy diagram for this reaction. Label the reactants, products, $E_{1}$ (forward), $E_{\mathrm{a}}$ (reverse), and $\Delta H_{\mathrm{rxn}}$ on your sketch. What does the top of the hump in your diagram represent? Is this an exothermic or endothermic reaction? (c) This reaction is catalyzed in the presence of an iron surface, which lowers the forward activation energy to about $80 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} .$ Add a dashed line representing the overall pathway for the catalyzed reaction to your diagram. What is the magnitude of the activation energy for the catalyzed reaction in the reverse direction (going from products to reactants)?
1. The activation energy for the reaction between $\mathrm{O}_{3}$ and $\mathrm{NO}$ is $9.6 \mathrm{~kJ} / \mathrm{mol}$. $$ \mathrm{O}_{3}(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) $$ (a) Use the thermodynamic quantities in Appendix $\mathrm{K}$ to calculate $\Delta H^{0}$ for this reaction. (b) Prepare an activation energy plot similar to that in Figure 16-10 for this reaction. (Hint: How does $\Delta H^{0}$ compare with $\Delta E^{0}$ for this reaction?)
For a chemical reaction $\mathrm{A} \longrightarrow$ product, the mechanism of the reaction postulated was as follows. $$ \mathrm{A} \stackrel{\mathrm{k}_{1}}{\mathrm{~g}_{2}} 3 \mathrm{~B} \frac{\mathrm{k}_{\mathrm{s}}}{\text { R.D. }}{\mathrm{\longrightarrow}} \mathrm{C}_{\mathrm{g}} $$ If the reaction occurred with individual rate constants $\mathrm{k}_{1}, \mathrm{k}_{2}$ and $\mathrm{k}_{3}$, determine activation energy for the overall reaction if the activation energies associated with these rate constants are $\mathrm{E}_{a_{1}}=180 \mathrm{~kJ} \mathrm{~mol}^{-1}, \mathrm{E}_{a_{2}}=90 \mathrm{~kJ}$ $\mathrm{mol}^{-1}$ and $\mathrm{E}_{a_{3}}=40 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (a) $70 \mathrm{~kJ}$ (b) $-10 \mathrm{~kJ}$ (c) $310 \mathrm{~kJ}$ (d) $130 \mathrm{~kJ}$
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