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Chapter 14: Problem 58

Indicate whether each statement is true or false. (a) If you measure the rate constant for a reaction al 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) True - By using the Arrhenius and van 't Hoff equations, we can determine the overall enthalpy change (\(\Delta H\)) for the reaction. (b) False - The rate of a reaction is determined by its activation energy, not whether it is exothermic or endothermic. (c) False - Doubling the temperature affects the rate constant, not the activation energy, which is a characteristic property of the reaction.

Step by step solution

01

a) Enthalpy change calculation from rate constants at different temperatures

The statement is true. By measuring the rate constants for a reaction at different temperatures, we can use the Arrhenius equation to calculate the activation energy and then apply the van 't Hoff equation to determine the overall enthalpy change (\(\Delta H\)) for the reaction.
02

b) Exothermic vs. Endothermic reaction rates

The statement is false. The rate of a reaction is determined by its activation energy and not by whether the reaction is exothermic or endothermic. Lower activation energy usually results in faster reactions; however, both exothermic and endothermic reactions can have a range of activation energies.
03

c) Doubling the temperature and its effect on activation energy

The statement is false. Doubling the temperature of a reaction does not necessarily cut the activation energy in half. The relationship between temperature and the rate constant is given by the Arrhenius equation: \(k = Ae^{-\frac{Ea}{RT}}\), where \(k\) is the rate constant, \(A\) is the pre-exponential factor, \(Ea\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. Doubling the temperature will affect the rate constant but not the activation energy itself, as it is a characteristic property of the reaction.

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Most popular questions from this chapter

Urea \(\left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right)\) is the end product in protein metabolism in animals. The decomposition of urea in $0.1 \mathrm{M} \mathrm{HCl}$ occurs according to the reaction $$ \mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}^{+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NH}_{4}^{+}(a q)+\mathrm{HCO}_{3}^{-}(a q) $$ The reaction is first order in urea and first order overall. When \(\left[\mathrm{NH}_{2} \mathrm{CONH}_{2}\right]=0.200 \mathrm{M},\) the rate at \(61.05^{\circ} \mathrm{C}\) $$ \text { is } 8.56 \times 10^{-5} \mathrm{M} / \mathrm{s} $$ (a) What is the rate constant, \(k\) ? (b) What is the concentration of urea in this solution after $4.00 \times 10^{3} \mathrm{~s}\( if the starting concentration is \)0.500 \mathrm{M}$ ? (c) What is the half-life for this reaction at \(61.05^{\circ} \mathrm{C}\) ?

The gas-phase decomposition of ozone is thought to occur by the following two- step mechanism. Step $1: \quad \mathrm{O}_{3}(g) \rightleftharpoons \mathrm{O}_{2}(g)+\mathrm{O}(g)$ (fast) Step $2: \quad \mathrm{O}(g)+\mathrm{O}_{3}(\mathrm{~g}) \longrightarrow 2 \mathrm{O}_{2}(g)$ (slow) (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 \(\mathrm{O}\) 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?

Consider the following hypothetical aqueous reaction: $\mathrm{A}(a q) \rightarrow \mathrm{B}(a q)\(. A flask is charged with \)0.065 \mathrm{~mol}$ of \(\mathrm{A}\) in a total volume of \(100.0 \mathrm{~mL}\). The following data are collected: $$ \begin{array}{lccccc} \hline \text { Time (min) } & 0 & 10 & 20 & 30 & 40 \\ \hline \text { Moles of A } & 0.065 & 0.051 & 0.042 & 0.036 & 0.031 \\ \hline \end{array} $$ (a) Calculate the number of moles of \(\mathrm{B}\) at each time in the table, assuming that there are no molecules of \(\mathrm{B}\) at time zero and that A cleanly converts to B with no intermediates. (b) Calculate the average rate of disappearance of A for each 10 -min interval in units of \(M /\) s. (c) Between \(t=0 \mathrm{~min}\) and \(t=30 \mathrm{~min},\) what is the average rate of appearance of \(\mathrm{B}\) in units of \(\mathrm{M} / \mathrm{s}\) ? Assume that the volume of the solution is constant.

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) $\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CN}^{-}(a q) \longrightarrow \mathrm{HCN}(a q)$ (b) \(\mathrm{CH}_{3} \mathrm{Cl}(\) solv \()+\mathrm{OH}^{-}(\) solv $) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(\( solv \))+\mathrm{Cl}^{-}($ solv \()\) (c) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightarrow 2 \mathrm{NO}_{2}\)

(a) The activation energy for the reaction $\mathrm{A}(g) \longrightarrow \mathrm{B}(g)\( is \)100 \mathrm{~kJ} / \mathrm{mol}$. Calculate the fraction of the molecule A that has an energy equal to or greater than the activation energy at \(400 \mathrm{~K} .(\mathbf{b})\) Calculate this fraction for a temperature of \(500 \mathrm{~K}\). What is the ratio of the fraction at $500 \mathrm{~K}\( to that at \)400 \mathrm{~K}$ ?
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