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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 \(378 \mathrm{~kJ} .\)

Short Answer

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Question: Draw and label a reaction-energy diagram for the chemical reaction $$\mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{R}+\mathrm{Z}$$ with its enthalpy change (\(\Delta H\)) equal to \(+295 \mathrm{~kJ}\) and activation energy (\(E_a\)) equal to \(378 \mathrm{~kJ}\). Answer: To draw a reaction-energy diagram for the given reaction, follow these steps: 1. Draw the axes for the reaction-energy diagram, labeling the x-axis as "Reaction Progress" and the y-axis as "Energy." 2. Indicate the initial energy state of the reactants (point A) and the final energy state of the products (point B), with B being higher on the y-axis than A due to the positive enthalpy change. 3. Mark the point representing the activation energy (point C), which is \(378 \mathrm{~kJ}\) higher on the y-axis than point A. 4. Indicate the enthalpy change (295 kJ) between A and B. 5. Connect points A, C, and B with a smooth curve to create the reaction-energy diagram, showing the energy changes during the reaction.

Step by step solution

01

Draw the axes for the reaction-energy diagram

Begin by drawing the axes for the reaction-energy diagram. Label the x-axis as "Reaction Progress" and the y-axis as "Energy".
02

Indicate the initial and final energy states

On the y-axis, mark a point to represent the initial energy state of the reactants X and Y (let's call this point A). Similarly, mark a point to represent the final energy state of the products R and Z (let's call this point B). Since the enthalpy change, \(\Delta H\), is positive, the final energy state (B) will be higher on the y-axis than the initial energy state (A).
03

Indicate the activation energy

The activation energy, \(E_a\), is the energy required to initiate the reaction. This can be represented by a higher energy state compared to A. Measure up from point A and mark a point \(378 \mathrm{~kJ}\) higher on the y-axis (let's call this point C). This point represents the energy level of the activated complex or transition state.
04

Indicate the enthalpy change

The enthalpy change, \(\Delta H\), represents the difference in energy between the reactants and products. From the initial energy state A, measure up and mark the point that is \(295 \mathrm{~kJ}\) higher on the y-axis, which should correspond to point B.
05

Connect the points to form the reaction-energy diagram

Now, connect the points A, C, and B with a smooth curve to create the reaction-energy diagram. The curve should go from the initial energy state A to the transition state C, and then back down to the final energy state B. This represents the energy changes during the reaction. You now have a complete reaction-energy diagram for the given reaction.

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Most popular questions from this chapter

At low temperatures, the rate law for the reaction $$\mathrm{CO}(\mathrm{g})+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{NO}(g)$$ is as follows: rate \(=\) constant \(\times\left[\mathrm{NO}_{2}\right]^{2}\). Which of the following mechanisms is consistent with the rate law? (a) \(\mathrm{CO}+\mathrm{NO}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{NO}\) (b) \(2 \mathrm{NO}_{2} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4} \quad\) (fast) \(\mathrm{N}_{2} \mathrm{O}_{4}+2 \mathrm{CO} \longrightarrow 2 \mathrm{CO}_{2}+2 \mathrm{NO} \quad\) (slow) (c) \(2 \mathrm{NO}_{2} \longrightarrow \mathrm{NO}_{3}+\) NO \(\quad\) (slow) \(\mathrm{NO}_{3}+\mathrm{CO} \longrightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2} \quad\) (fast) (d) \(2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2} \quad\) (slow) \(\mathrm{O}_{2}+2 \mathrm{CO} \longrightarrow 2 \mathrm{CO}_{2} \quad\) (fast)

For the reaction $$2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ the experimental rate expression is rate \(=k[\mathrm{NO}]^{2} \times\left[\mathrm{H}_{2}\right] .\) The following mechanism is proposed: $$\begin{array}{cc}2 \mathrm{NO} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2} & \text { (fast) } \\ \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{N}_{2} \mathrm{O} & \text { (slow) } \\ \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O} & \text { (fast) } \end{array}$$ Is this mechanism consistent with the rate expression?

For the first-order thermal decomposition of ozone $$\mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)$$ \(k=3 \times 10^{-26} \mathrm{~s}^{-1}\) at \(25^{\circ} \mathrm{C}\). What is the half-life for this reaction in years? Comment on the likelihood that this reaction contributes to the depletion of the ozone layer.

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.

Express the rate of the reaction $$2 \mathrm{~N}_{2} \mathrm{H}_{4}(l)+\mathrm{N}_{2} \mathrm{O}_{4}(l) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$$ in terms of (a) \(\Delta\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]\) (b) \(\Delta\left[\mathrm{N}_{2}\right]\)
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