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Chapter 14: Problem 60

Indicate whether each statement is true or false. If it is false, rewrite it so that it is true. (a) If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction. (b) Exothermic reactions are faster than endothermic reactions. (c) If you double the temperature for a reaction, you cut the activation energy in half.

Short Answer

Expert verified
(a) False. If you measure the rate constant for a reaction at different temperatures, you can calculate the activation energy for the reaction, which can then be used, along with reaction enthalpies, to calculate the overall enthalpy change for the reaction. (b) False. Exothermic reactions can be faster than endothermic reactions under certain conditions, but the speed of a reaction depends on multiple factors, including activation energy, reaction mechanism, temperature, and concentration of reactants. (c) False. The relationship between temperature and activation energy is defined by the Arrhenius equation, which shows that increasing the temperature can increase the reaction rate. However, doubling the temperature does not directly cause the activation energy to be cut in half.

Step by step solution

01

Statement (a) Analysis

The statement says that the rate constant for a reaction at different temperatures can be used to calculate the overall enthalpy change for the reaction. This statement is false because the rate constant can't be directly used to find the overall enthalpy change. However, using the Arrhenius equation, a relationship between rate constants at different temperatures and activation energy can be obtained. Once we have the activation energy, we can use it along with the reaction enthalpies to calculate the overall enthalpy change.
02

Rewrite Statement (a)

If you measure the rate constant for a reaction at different temperatures, you can calculate the activation energy for the reaction, which can then be used, along with reaction enthalpies, to calculate the overall enthalpy change for the reaction.
03

Statement (b) Analysis

The statement says that exothermic reactions are faster than endothermic reactions. This is a false statement because the speed of a reaction depends on many factors like activation energy, reaction mechanism, temperature, and concentration of reactants. While it is generally believed that exothermic reactions can be faster due to the release of energy, it's not always the case.
04

Rewrite Statement (b)

Exothermic reactions can be faster than endothermic reactions under certain conditions, but the speed of a reaction depends on multiple factors, including activation energy, reaction mechanism, temperature, and concentration of reactants.
05

Statement (c) Analysis

The statement says that if you double the temperature for a reaction, you cut the activation energy in half. This statement is false. Temperature and activation energy have a complex relationship defined by the Arrhenius equation, and doubling the temperature does not necessarily cut the activation energy in half.
06

Rewrite Statement (c)

The relationship between temperature and activation energy is defined by the Arrhenius equation, which shows that increasing the temperature can increase the reaction rate. However, doubling the temperature does not directly cause the activation energy to be cut in half.

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Most popular questions from this chapter

For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product and disappearance of each reactant: (a) \(2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)\)

Sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),\) commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} .\) At \(23{ }^{\circ} \mathrm{C}\) and in \(0.5 \mathrm{M} \mathrm{HCl}\), the following data were obtained for the disappearance of sucrose: $$ \begin{array}{rl} \hline \text { Time }(\mathrm{min}) & {\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right](M)} \\ \hline 0 & 0.316 \\ 39 & 0.274 \\ 80 & 0.238 \\ 140 & 0.190 \\ 210 & 0.146 \\ \hline \end{array} $$ (a) Is the reaction first order or second order with respect to \(\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right] ?(\mathbf{b})\) What is the rate constant? (c) Using this rate constant, calculate the concentration of sucrose at 39,80,140 , and 210 min if the initial sucrose concentration was \(0.316 \mathrm{M}\) and the reaction was zero order in sucrose.

What are the differences between an intermediate and a transition state?

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 . [Section 14.3\(]\)

The reaction $$ \mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) $$ is first order in \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\). Using the following kinetic data, determine the magnitude and units of the first order rate constant: $$ \begin{array}{rl} \hline \text { Time (s) } & \text { Pressure } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { (atm) } \\ \hline 0 & 1.000 \\ 2,500 & 0.947 \\ 5,000 & 0.895 \\ 7,500 & 0.848 \\ 10,000 & 0.803 \\ \hline \end{array} $$
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