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Chapter 14: Problem 24

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: \(\begin{array}{l}{\text { (a) } 2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)} \\ {\text { (b) } 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)} \\\ {\text { (c) } 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (d) } \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)}\end{array}\)

Short Answer

Expert verified
\(a)\) Rate = -\(\frac{1}{2}\) × (rate of disappearance of \(H_2O\)) = \(\frac{1}{2}\) × (rate of appearance of \(H_2\)) = (rate of appearance of \(O_2\)) \(b)\) Rate = -\(\frac{1}{2}\) × (rate of disappearance of \(SO_2\)) = - (rate of disappearance of \(O_2\)) = \(\frac{1}{2}\) × (rate of appearance of \(SO_3\)) \(c)\) Rate = -\(\frac{1}{2}\) × (rate of disappearance of \(NO\)) = -\(\frac{1}{2}\) × (rate of disappearance of \(H_2\)) = (rate of appearance of \(N_2\)) = \(\frac{1}{2}\) × (rate of appearance of \(H_2O\)) \(d)\) Rate = - (rate of disappearance of \(N_2\)) = -\(\frac{1}{2}\) × (rate of disappearance of \(H_2\)) = (rate of appearance of \(N_2H_4\))

Step by step solution

01

(a) Reaction and rate expression for H2O -> H2 + O2

Given reaction: \(2 H_2O(g) \longrightarrow 2 H_2(g) + O_2(g)\) Rate expression: Rate = -\(\frac{1}{2}\) × (rate of disappearance of \(H_2O\)) = \(\frac{1}{2}\) × (rate of appearance of \(H_2\)) = (rate of appearance of \(O_2\))
02

(b) Reaction and rate expression for SO2 + O2 -> SO3

Given reaction: \(2 SO_2(g) + O_2(g) \longrightarrow 2 SO_3(g)\) Rate expression: Rate = -\(\frac{1}{2}\) × (rate of disappearance of \(SO_2\)) = - (rate of disappearance of \(O_2\)) = \(\frac{1}{2}\) × (rate of appearance of \(SO_3\))
03

(c) Reaction and rate expression for NO + H2 -> N2 + H2O

Given reaction: \(2 NO(g) + 2 H_2(g) \longrightarrow N_2(g) + 2 H_2O(g)\) Rate expression: Rate = -\(\frac{1}{2}\) × (rate of disappearance of \(NO\)) = -\(\frac{1}{2}\) × (rate of disappearance of \(H_2\)) = (rate of appearance of \(N_2\)) = \(\frac{1}{2}\) × (rate of appearance of \(H_2O\))
04

(d) Reaction and rate expression for N2 + H2 -> N2H4

Given reaction: \(N_2(g) + 2 H_2(g) \longrightarrow N_2H_4(g)\) Rate expression: Rate = - (rate of disappearance of \(N_2\)) = -\(\frac{1}{2}\) × (rate of disappearance of \(H_2\)) = (rate of appearance of \(N_2H_4\))

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Most popular questions from this chapter

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 \(\mathrm{Cl}^{-} ?\)

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 \(\left[\mathrm{NH}_{2} \mathrm{CONH}_{2}\right]=0.200 M,\) the rate at \(61.05^{\circ} \mathrm{C}\) is \(8.56 \times 10^{-5} \mathrm{M} / \mathrm{s}\) , (a) What is the rate constant, \(k ?\) units of \(s^{-1}\) . (c) Calculate the half-life of the reaction. (d) How long does it take for the absorbance to fall to 0.100\(?\)

The \(\mathrm{NO}_{x}\) waste stream from automobile exhaust includes species such as \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) . Catalysts that convert these species to \(\mathrm{N}_{2}\) are desirable to reduce air pollution. (a) Draw the Lewis dot and VSEPR structures of NO, NO \(_{2}\) and \(\mathrm{N}_{2} .(\mathbf{b})\) Using a resource such as Table \(8.3,\) look up the energies of the bonds in these molecules. In what region of the electromagnetic spectrum are these energies? (c) Design a spectroscopic experiment to monitor the conversion of \(\mathrm{NO}_{x}\) into \(\mathrm{N}_{2},\) describing what wavelengths of light need to be monitored as a function of time.

(a) In which of the following reactions would you expect the orientation factor to be least important in leading to reaction: \(\mathrm{NO}+\mathrm{O} \longrightarrow \mathrm{NO}_{2}\) or \(\mathrm{H}+\mathrm{Cl} \longrightarrow \mathrm{HCl}\) ? (b) Does the orientation factor depend on temperature?

The activation energy of an uncatalyzed reaction is 95 \(\mathrm{kJ} / \mathrm{mol} .\) The addition of a catalyst lowers the activation energy to 55 \(\mathrm{kJ} / \mathrm{mol}\) . Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (a) \(25^{\circ} \mathrm{C},\) (b) \(125^{\circ} \mathrm{C} ?\)
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