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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: (a) $\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})$ (b) \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)\) (c) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ (d) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\)

Short Answer

Expert verified
For each of the given gas-phase reactions, the rate of disappearance of each reactant is related to the rate of appearance of each product as follows: (a) \(-\frac{d[\mathrm{CO}]}{dt} = +\frac{d[\mathrm{CO}_{2}]}{dt} = -\frac{d[\mathrm{H}_{2} \mathrm{O}]}{dt} = +\frac{d[\mathrm{H}_{2}]}{dt}\) (b) \(-\frac{1}{2} \frac{d[\mathrm{NO}]}{dt} = -\frac{d[\mathrm{Cl}_{2}]}{dt} = +\frac{1}{2} \frac{d[\mathrm{NOCl}]}{dt}\) (c) \(-\frac{d[\mathrm{CH}_{4}]}{dt} = -\frac{1}{2} \frac{d[\mathrm{O}_{2}]}{dt} = +\frac{d[\mathrm{CO}_{2}]}{dt} = +\frac{1}{2} \frac{d[\mathrm{H}_{2} \mathrm{O}]}{dt}\) (d) \(-\frac{1}{2} \frac{d[\mathrm{N}_{2} \mathrm{O}_{4}]}{dt} = +\frac{d[\mathrm{NO}_{2}]}{dt}\)

Step by step solution

01

(a) Reaction: \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\)

The rate of disappearance of reactants CO and H₂O, and rate of appearance of products CO₂ and H₂ can be related as follows: \[ -\frac{d[\mathrm{CO}]}{dt} = +\frac{d[\mathrm{CO}_{2}]}{dt} = -\frac{d[\mathrm{H}_{2} \mathrm{O}]}{dt} = +\frac{d[\mathrm{H}_{2}]}{dt} \]
02

(b) Reaction: \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)\)

The rate of disappearance of reactants NO and Cl₂, and rate of appearance of product NOCl can be related as follows: \[ -\frac{1}{2} \frac{d[\mathrm{NO}]}{dt} = -\frac{d[\mathrm{Cl}_{2}]}{dt} = +\frac{1}{2} \frac{d[\mathrm{NOCl}]}{dt} \]
03

(c) Reaction: \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

The rate of disappearance of reactants CH₄ and O₂, and rate of appearance of products CO₂ and H₂O can be related as follows: \[ -\frac{d[\mathrm{CH}_{4}]}{dt} = -\frac{1}{2} \frac{d[\mathrm{O}_{2}]}{dt} = +\frac{d[\mathrm{CO}_{2}]}{dt} = +\frac{1}{2} \frac{d[\mathrm{H}_{2} \mathrm{O}]}{dt} \]
04

(d) Reaction: \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\)

The rate of disappearance of reactant N₂O₄, and rate of appearance of product NO₂ can be related as follows: \[ -\frac{1}{2} \frac{d[\mathrm{N}_{2} \mathrm{O}_{4}]}{dt} = +\frac{d[\mathrm{NO}_{2}]}{dt} \]

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Most popular questions from this chapter

The oxidation of \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3}\) is accelerated by \(\mathrm{NO}_{2}\). The reaction proceeds according to: $$ \begin{array}{l} \mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g) \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \end{array} $$ (a) Show that, with appropriate coefficients, the two reactions can be summed to give the overall oxidation of \(\mathrm{SO}_{2}\) by \(\mathrm{O}_{2}\) to give \(\mathrm{SO}_{3} .\) (b) Do we consider \(\mathrm{NO}_{2}\) a catalyst or an intermediate in this reaction? (c) Would you classify NO as a catalyst or as an intermediate? (d) Is this an example of homogeneous catalysis or heterogeneous catalysis?

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 $30{ }^{\circ} \mathrm{C}\( is \)4.0 \times 10^{-2} M^{-1} \mathrm{~s}^{-1}$. If at a given time the concentration of \(\mathrm{H}_{2} \mathrm{~S}\) is $2.5 \times 10^{-4} \mathrm{M}\( and that of \)\mathrm{Cl}_{2}\( is \)2.0 \times 10^{-2} \mathrm{M},$ what is the rate of formation of \(\mathrm{H}^{+}\) ?

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)$ was studied with the following results: $$ \begin{array}{lccc} \hline \text { Experiment } & {\left[\mathrm{CIO}_{2}\right](M)} & {\left[\mathrm{OH}^{-}\right](M)} & \text { Initial Rate }(M / s) \\ \hline 1 & 0.060 & 0.030 & 0.0248 \\ 2 & 0.020 & 0.030 & 0.00276 \\ 3 & 0.020 & 0.090 & 0.00828 \\ \hline \end{array} $$ (a) Determine the rate law for the reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when \(\left[\mathrm{ClO}_{2}\right]=0.100 \mathrm{M}\) and \(\left[\mathrm{OH}^{-}\right]=0.050 \mathrm{M}\)

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 \(61.05^{\circ} \mathrm{C}\) ?

(a) The reaction $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+\( \)\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)$ is first order with in \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(a q)\) and zero-order in \(\mathrm{H}_{2} \mathrm{O}\). At \(300 \mathrm{~K}\) the rate constant equals \(3.30 \times 10^{-2} \mathrm{~min}^{-1} .\) Calculate the half- life at this temperature. \((\mathbf{b})\) If the activation energy for this reaction is \(80.0 \mathrm{~kJ} / \mathrm{mol}\), at what temperature would the reaction rate be doubled?
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