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Chapter 14: Problem 23

For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product: \(\begin{array}{l}{\text { (a) } \mathrm{H}_{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)} \\ {\text { (b) } 2 \mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)} \\ {\text { (c) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (d) } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{NH}_{3}(g)}\end{array}\)

Short Answer

Expert verified
For each of the given gas-phase reactions: (a) -1 * d[H2O2]/dt = +1 * d[H2]/dt = +1 * d[O2]/dt (b) -2 * d[N2O]/dt = +2 * d[N2]/dt = +1 * d[O2]/dt (c) -1 * d[N2]/dt = -3 * d[H2]/dt = +2 * d[NH3]/dt (d) -1 * d[C2H5NH2]/dt = +1 * d[C2H4]/dt = +1 * d[NH3]/dt

Step by step solution

01

(a) Reaction H2O2(g) → H2(g) + O2(g)

In this reaction, we have: 1 mole of H2O2(g) → 1 mole of H2(g) + 1 mole of O2(g). The rate of disappearance of H2O2 is equal to the rate of appearance of H2 and O2, since they are in a 1-to-1 ratio. Therefore, we can write: Rate of disappearance of H2O2 = -d[H2O2]/dt Rate of appearance of H2 = +d[H2]/dt Rate of appearance of O2 = +d[O2]/dt Since they are in a 1-to-1 ratio: -1 * d[H2O2]/dt = +1 * d[H2]/dt = +1 * d[O2]/dt
02

(b) Reaction 2 N2O(g) → 2 N2(g) + O2(g)

In this reaction, we have: 2 moles of N2O(g) → 2 moles of N2(g) + 1 mole of O2(g). The stoichiometric coefficients indicate the relationship between the disappearance of N2O and the appearance of N2 and O2. We can write: Rate of disappearance of N2O = -d[N2O]/dt Rate of appearance of N2 = +d[N2]/dt Rate of appearance of O2 = +d[O2]/dt Since they are in a 2-to-2-to-1 ratio: -2 * d[N2O]/dt = +2 * d[N2]/dt = +1 * d[O2]/dt
03

(c) Reaction N2(g) + 3 H2(g) → 2 NH3(g)

In this reaction, we have: 1 mole of N2(g) + 3 moles of H2(g) → 2 moles of NH3(g). The stoichiometric coefficients indicate the relationship between the disappearance of N2 and H2, and the appearance of NH3. We can write: Rate of disappearance of N2 = -d[N2]/dt Rate of disappearance of H2 = -d[H2]/dt Rate of appearance of NH3 = +d[NH3]/dt Since they are in a 1-to-3-to-2 ratio: -1 * d[N2]/dt = -3 * d[H2]/dt = +2 * d[NH3]/dt
04

(d) Reaction C2H5NH2(g) → C2H4(g) + NH3(g)

In this reaction, we have: 1 mole of C2H5NH2(g) → 1 mole of C2H4(g) + 1 mole of NH3(g). The rate of disappearance of C2H5NH2 is equal to the rate of appearance of C2H4 and NH3, since they are also in a 1-to-1 ratio. We can write: Rate of disappearance of C2H5NH2 = -d[C2H5NH2]/dt Rate of appearance of C2H4 = +d[C2H4]/dt Rate of appearance of NH3 = +d[NH3]/dt Since they are in a 1-to-1-to-1 ratio: -1 * d[C2H5NH2]/dt = +1 * d[C2H4]/dt = +1 * d[NH3]/dt

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Most popular questions from this chapter

As described in Exercise 14.41 , the decomposition of sulfuryl chloride \(\left(\mathrm{SO}_{2} \mathrm{Cl}_{2}\right)\) is a first-order process. The rate constant for the decomposition at 660 \(\mathrm{K}\) is \(4.5 \times 10^{-2} \mathrm{s}^{-1}\) .half-life for this reaction? (b) If you start with 0.050\(M \mathrm{I}_{2}\) at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form \(\mathrm{I}_{2}\) ?

Hydrogen sulfide \(\left(\mathrm{H}_{2} \mathrm{S}\right)\) is a common and troublesome pollutant in industrial wastewaters. One way to remove \(\mathrm{H}_{2} \mathrm{S}\) is to treat the water with chlorine, in which case the following reaction occurs: $$ \mathrm{H}_{2} \mathrm{S}(a q)+\mathrm{Cl}_{2}(a q) \longrightarrow \mathrm{S}(s)+2 \mathrm{H}^{+}(a q)+2 \mathrm{Cl}^{-}(a q)$$ The rate of this reaction is first order in each reactant. The rate constant for the disappearance of \(\mathrm{H}_{2} \mathrm{S}\) at \(28^{\circ} \mathrm{C}\) is \(3.5 \times 10^{-2} \mathrm{M}^{-1} \mathrm{s}^{-1}\) . If at a given time the concentration of \(\mathrm{H}_{2} \mathrm{S}\) is \(2.0 \times 10^{-4} \mathrm{M}\) and that of \(\mathrm{Cl}_{2}\) is \(0.025 \mathrm{M},\) what is the rate of formation of \(\mathrm{Cl}^{-} ?\)

The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism: $$ \begin{array}{c}{\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{I}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{IO}^{-}(a q) \text { (slow) }} \\ {\mathrm{IO}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(\mathrm{g})+\mathrm{I}^{-}(a q) \text { (fast) }}\end{array} $$ \(\begin{array}{l}{\text { (a) Write the chemical equation for the overall process. }} \\ {\text { (b) Identify the intermediate, if any, in the mechanism. }} \\ {\text { (c) Assuming that the first step of the mechanism is rate }} \\ {\text { determining, predict the rate law for the overall process. }}\end{array}\)

Platinum nanoparticles of diameter \(\sim 2 \mathrm{nm}\) are important catalysts in carbon monoxide oxidation to carbondioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 A. (a) Estimate how many platinum atoms would fit into a 2.0 -nm sphere; the volume of a sphere is \((4 / 3) \pi r^{3} .\) Recall that \(1 \hat{\mathrm{A}}=1 \times 10^{-10} \mathrm{m}\) and \(1 \mathrm{nm}=1 \times 10^{-9} \mathrm{m} .\) (b) Estimate how many platinum atoms are on the surface of a \(2.0-\mathrm{nm}\) Pt sphere, using the surface area of a sphere \(\left(4 \pi r^{2}\right)\) and assuming that the "footprint" of one Pt atom can be estimated from its atomic diameter of 2.8 A. (c) Using your results from (a) and (b), calculate the percentage of Pt atoms that are on the surface of a 2.0 -nm nanoparticle. (d) Repeat these calculations for a 5.0 -nm platinum nanoparticle. (e) Which size of nanoparticle would you expect to be more catalytically active and why?

\(\begin{array}{l}{\text { (a) What is meant by the term elementary reaction? }} \\ {\text { (b) What is the difference between a unimolecular }} \\\ {\text { and a bimolecular elementary reaction? (c) What is a }}\end{array}\) \(\begin{array}{l}{\text {reaction mechanism?}(\mathbf{d}) \text { What is meant by the term rate- }} \\ {\text { determining step? }}\end{array}\)
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