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Chapter 12: Problem 67

Which of the following reactions would you expect to proceed at a faster rate at room temperature? Why? (Hint: Think about which reaction would have the lower activation energy.) \(\begin{aligned} 2 \mathrm{Ce}^{4+}(a q)+\mathrm{Hg}_{2}^{2+}(a q) & \longrightarrow 2 \mathrm{Ce}^{3+}(a q)+2 \mathrm{Hg}^{2+}(a q) \\\ \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned}\)

Short Answer

Expert verified
At room temperature, the acid-base reaction, \(H_{3}O^{+}(aq) + OH^{-}(aq) \longrightarrow 2 H_{2}O(l)\), is expected to proceed at a faster rate than the redox reaction, \(2 Ce^{4+}(aq) + Hg_{2}^{2+}(aq) \longrightarrow 2 Ce^{3+}(aq) + 2 Hg^{2+}(aq)\). This is because acid-base reactions generally have lower activation energies compared to redox reactions, as the transfer of protons requires less energy than the transfer of electrons.

Step by step solution

01

Identify reaction types

In order to compare the activation energies of the reactions, it will be helpful to first identify the reaction types. Reaction 1 involves the transfer of electrons between ions (a redox reaction). Specifically, the Ce^4+ ions are reduced to Ce^3+ ions, while the Hg_2^2+ ion is oxidized to two Hg^2+ ions. Reaction 2 involves the transfer of a proton (a Bronsted-Lowry acid-base reaction). The H_3O^+ ion (hydronium ion, a strong Bronsted-Lowry acid) donates a proton to the OH^- ion (hydroxide ion, a strong Bronsted-Lowry base), resulting in the formation of two water molecules.
02

Compare activation energies

In general, acid-base reactions (such as Reaction 2) have lower activation energies compared to redox reactions (such as Reaction 1). This is because acid-base reactions typically involve the transfer of protons which are generally faster and require lesser energy than the transfer of electrons in redox reactions.
03

Determine the faster reaction

Based on the comparison of activation energies, we can expect Reaction 2, the acid-base reaction, to have a lower activation energy and thus proceed at a faster rate at room temperature: \( H_{3}O^{+}(aq) + OH^{-}(aq) \longrightarrow 2 H_{2}O(l) \) This reaction should proceed faster compared to Reaction 1: \( 2 Ce^{4+}(aq) + Hg_{2}^{2+}(aq) \longrightarrow 2 Ce^{3+}(aq) + 2 Hg^{2+}(aq) \)

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Most popular questions from this chapter

The initial rate of a reaction doubles as the concentration of one of the reactants is quadrupled. What is the order of this reactant? If a reactant has a \(-1\) order, what happens to the initial rate when the concentration of that reactant increases by a factor of two?

The rate constant \((k)\) depends on which of the following (there may be more than one answer)? a. the concentration of the reactants b. the nature of the reactants c. the temperature d. the order of the reaction Explain.

Experiments have shown the average frequency of chirping of individual snowy tree crickets (Oecanthus fultoni) to be \(178 \mathrm{~min}^{-1}\) at \(25.0^{\circ} \mathrm{C}, 126 \mathrm{~min}^{-1}\) at \(20.3^{\circ} \mathrm{C}\), and \(100 . \mathrm{min}^{-1}\) at \(17.3^{\circ} \mathrm{C}\). a. What is the apparent activation energy of the reaction that controls the chirping? b. What chirping rate would be expected at \(15.0^{\circ} \mathrm{C}\) ? c. Compare the observed rates and your calculated rate from part b to the rule of thumb that the Fahrenheit temperature is 42 plus \(0.80\) times the number of chirps in \(15 \mathrm{~s}\).

Each of the statements given below is false. Explain why. a. The activation energy of a reaction depends on the overall energy change \((\Delta E)\) for the reaction. b. The rate law for a reaction can be deduced from examination of the overall balanced equation for the reaction. c. Most reactions occur by one-step mechanisms.

The following data were obtained for the reaction \(2 \mathrm{ClO}_{2}(a q)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{ClO}_{3}^{-}(a q)+\mathrm{ClO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) where \(\quad\) Rate \(=-\frac{\Delta\left[\mathrm{ClO}_{2}\right]}{\Delta t}\)
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