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Chapter 14: Problem 58

Indicate whether each statement is true or false. \(\begin{array}{l}{\text { (a) If you measure the rate constant for a reaction at different}} \\ {\text { temperatures, you can calculate the overall }} \\ {\text { enthalpy change for the reaction. }} \\ {\text { (b) Exothermic reactions are faster than endothermic }} \\ {\text { reactions. }} \\ {\text { (c) If you double the temperature for a reaction, you cut }} \\ {\text { the activation energy in half. }}\end{array}\)

Short Answer

Expert verified
(a) False - Measuring the rate constant at different temperatures doesn't provide information about the overall enthalpy change for the reaction. (b) False - Reaction speed is primarily determined by the activation energy, not by whether the reaction is exothermic or endothermic. (c) False - Doubling the temperature doesn't directly cut the activation energy in half, though it can increase the rate of reaction by making it easier for molecules to overcome the activation energy barrier.

Step by step solution

01

Statement (a)

If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction. False. The rate constant is related to the activation energy and temperature of the reaction by the Arrhenius equation, but it does not directly provide information about the overall enthalpy change for the reaction. The enthalpy change, which represents the overall energy change in a reaction, is determined experimentally or through computation with chemical equations and thermodynamics.
02

Statement (b)

Exothermic reactions are faster than endothermic reactions. False. The speed of a reaction is not determined solely by whether it is exothermic or endothermic. Reaction speed is primarily determined by the activation energy, not the overall energy change in the reaction. It is possible for an exothermic reaction to have a high activation energy and be slower than an endothermic reaction.
03

Statement (c)

If you double the temperature for a reaction, you cut the activation energy in half. False. The relationship between the temperature and the activation energy is described by the Arrhenius equation: \(k = Ae^{\frac{-E_{a}}{RT}}\), where k is the rate constant, A is the pre-exponential factor, E_a is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Doubling the temperature does not directly cut the activation energy in half. Instead, increasing the temperature can increase the rate of reaction by making it easier for molecules to overcome the activation energy barrier, but it does not directly affect the value of the activation energy.

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Most popular questions from this chapter

The gas-phase decomposition of ozone is thought to occur by the following two- step mechanism. \(\begin{array}{ll}{\text { Step } 1 :} & {\mathrm{O}_{3}(g) \Longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g) \text { (fast) }} \\ {\text { Step } 2 :} & {\mathrm{O}(g)+\mathrm{O}_{3}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(g) \quad(\text { slow })}\end{array}\) (a) Write the balanced equation for the overall reaction. (b) Derive the rate law that is consistent with this mechanism. (Hint: The product appears in the rate law.) (c) Is O a catalyst or an intermediate? (d) If instead the reaction occurred in a single step, would the rate law change? If so, what would it be?

You perform a series of experiments for the reaction \(\mathrm{A} \longrightarrow \mathrm{B}+\mathrm{C}\) and find that the rate law has the form rate \(=k[\mathrm{A}]^{x}\) . Determine the value of \(x\) in each of the following cases: (a) There is no rate change when \([\mathrm{A}]_{0}\) is tripled. (b) The rate increases by a factor of 9 when \([\mathrm{A}]_{0}\) is tripled. (c) When \([\mathrm{A}]_{0}\) is doubled, the rate increases by a factor of \(8 .\)

For the elementary process \(\mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{NO}_{3}(g)\) the activation energy \(\left(E_{a}\right)\) and overall \(\Delta E\) are 154 \(\mathrm{kJ} / \mathrm{mol}\) and 136 \(\mathrm{kJ} / \mathrm{mol}\) , respectively. (a) Sketch the energy profile for this reaction, and label \(E_{a}\) and \(\Delta E\) . (b) What is the activation energy for the reverse reaction?

One of the many remarkable enzymes in the human body is carbonic anhydrase, which catalyzes the interconversion of carbon dioxide and water with bicarbonate ion and protons. If it were not for this enzyme, the body could not rid itself rapidly enough of the \(\mathrm{CO}_{2}\) accumulated by cell metabolism. The enzyme catalyzes the dehydration (release to air) of up to \(10^{7} \mathrm{CO}_{2}\) molecules per second. Which components of this description correspond to the terms enzyme, substrate, and turnover number?

In a hydrocarbon solution, the gold compound \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3}\) decomposes into ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) and a different gold compound, (CH \(_{3} ) \mathrm{AuPH}_{3} .\) The following mechanism has been proposed for the decomposition of \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3} :\) $$ \quad Step \quad1.\left(\mathrm{CH}_{3}\right)_{3} \mathrm{AuPH}_{3} \frac{\mathrm{k}_{1}}{\mathrm{k}_{-1}}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Au}+\mathrm{PH}_{3} $$ $$ Step\quad \quad2.\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Au} \stackrel{k_{2}}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{6}+\left(\mathrm{CH}_{3}\right) \mathrm{Au} \quad$$ $$ Step\quad 3 :\left(\mathrm{CH}_{3}\right) \mathrm{Au}+\mathrm{PH}_{3} \stackrel{k_{3}}{\longrightarrow}\left(\mathrm{CH}_{3}\right) \mathrm{AuPH}_{3}$$ (a) What is the overall reaction? (b) What are the intermediates in the mechanism? (c) What is the molecularity of each of the elementary steps? (d) What is the ratedetermining step? (e) What is the rate law predicted by this mechanism? (f) What would be the effect on the reaction rate of adding \(\mathrm{PH}_{3}\) to the solution of \(\left(\mathrm{CH}_{3}\right)_{3}\) AuPH \(_{3} ?\)
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