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Chapter 14: Problem 20

For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product or disappearance of each reactant: (a) \(2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

Short Answer

Expert verified
For the given gas-phase reactions, the rate expressions are: (a) \(Rate = -\frac{1}{2}\frac{鈭哰H_2O]}{鈭唗} = \frac{1}{2}\frac{鈭哰H_2]}{鈭唗} = \frac{鈭哰O_2]}{鈭唗}\) (b) \(Rate = -\frac{1}{2}\frac{鈭哰SO_2]}{鈭唗} = -\frac{鈭哰O_2]}{鈭唗} = \frac{1}{2}\frac{鈭哰SO_3]}{鈭唗}\) (c) \(Rate = -\frac{1}{2}\frac{鈭哰NO]}{鈭唗} = -\frac{1}{2}\frac{鈭哰H_2]}{鈭唗} = \frac{鈭哰N_2]}{鈭唗} = \frac{1}{2}\frac{鈭哰H_2O]}{鈭唗}\)

Step by step solution

01

Reaction (a) Rate Expression

For reaction (a): \(2 H_2O(g) \longrightarrow 2 H_2(g) + O_2(g)\) Step 1: Write the rate expressions for the disappearance of reactants and the appearance of products: \(Rate = -\frac{1}{2}\frac{鈭哰H_2O]}{鈭唗} = \frac{1}{2}\frac{鈭哰H_2]}{鈭唗} = \frac{鈭哰O_2]}{鈭唗}\).
02

Reaction (b) Rate Expression

For reaction (b): \(2 SO_2(g) + O_2(g) \longrightarrow 2 SO_3(g)\) Step 1: Write the rate expressions for the disappearance of reactants and the appearance of products: \(Rate = -\frac{1}{2}\frac{鈭哰SO_2]}{鈭唗} = -\frac{鈭哰O_2]}{鈭唗} = \frac{1}{2}\frac{鈭哰SO_3]}{鈭唗}\)
03

Reaction (c) Rate Expression

For reaction (c): \(2 NO(g) + 2 H_2(g) \longrightarrow N_2(g) + 2 H_2O(g)\) Step 1: Write the rate expressions for the disappearance of reactants and the appearance of products: \(Rate = -\frac{1}{2}\frac{鈭哰NO]}{鈭唗} = -\frac{1}{2}\frac{鈭哰H_2]}{鈭唗} = \frac{鈭哰N_2]}{鈭唗} = \frac{1}{2}\frac{鈭哰H_2O]}{鈭唗}\) These rate expressions show the relationship between the rate of appearance of products and the rate of disappearance of reactants for each of the given gas-phase reactions.

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Most popular questions from this chapter

Zinc metal dissolves in hydrochloric acid according to the reaction $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q)-\ldots \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ Suppose you are asked to study the kinetics of this reaction by monitoring the rate of production of \(\mathrm{H}_{2}(g)\). (a) By using a reaction flask, a manometer, and any other common laboratory equipment, design an experimental apparatus that would allow you to monitor the partial pressure of \(\mathrm{H}_{2}(g)\) produced as a function of time. (b) Explain how you would use the apparatus to determine the rate law of the reaction. (c) Explain how you would use the apparatus to determine the reaction order for \(\left[\mathrm{H}^{+}\right]\) for the reaction. (d) How could you use the apparatus to determine the activation energy of the reaction? (e) Explain how you would use the apparatus to determine the effects of changing the form of \(\mathrm{Zn}(s)\) from metal strips to granules.

(a) Consider the combustion of ethylene, \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\) \(3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) .\) If the concentration of \(\mathrm{C}_{2} \mathrm{H}_{4}\) is decreasing at the rate of \(0.025 \mathrm{M} / \mathrm{s}\), what are the rates of change in the concentrations of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} ?\) (b) The rate of decrease in \(\mathrm{N}_{2} \mathrm{H}_{4}\) partial pressure in a closed reaction vessel from the reaction \(\mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) is 63 torr \(/ \mathrm{h}\). What are the rates of change of \(\mathrm{NH}_{3}\) partial pressure and total pressure in the vessel?

The first-order rate constant for reaction of a particular organic compound with water varies with temperature as follows: $$ \begin{array}{ll} \hline \text { Temperature (K) } & \text { Rate Constant (s }^{-1} \text { ) } \\\ \hline 300 & 3.2 \times 10^{-11} \\ 320 & 1.0 \times 10^{-9} \\ 340 & 3.0 \times 10^{-8} \\ 355 & 2.4 \times 10^{-7} \\ \hline \end{array} $$ From these data, calculate the activation energy in units of \(\mathrm{kJ} / \mathrm{mol}\).

Consider the following reaction: $$ \mathrm{CH}_{3} \mathrm{Br}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(a q)+\mathrm{Br}^{-}(a q) $$ The rate law for this reaction is first order in \(\mathrm{CH}_{3} \mathrm{Br}\) and first order in \(\mathrm{OH}^{-}\). When \(\left[\mathrm{CH}_{3} \mathrm{Br}\right]\) is \(5.0 \times 10^{-3} \mathrm{M}\) and \(\left[\mathrm{OH}^{-}\right]\) is \(0.050 \mathrm{M}\), the reaction rate at \(298 \mathrm{~K}\) is \(0.0432 \mathrm{M} / \mathrm{s}\). (a) What is the value of the rate constant? (b) What are the units of the rate constant? (c) What would happen to the rate if the concentration of \(\mathrm{OH}^{-}\) were tripled?

The first-order rate constant for the decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}, 2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\), at \(70^{\circ} \mathrm{C}\) is \(6.82 \times 10^{-3} \mathrm{~s}^{-1}\). Suppose we start with \(0.0250 \mathrm{~mol}\) of \(\mathrm{N}_{2} \mathrm{O}_{5}(g)\) in a volume of \(2.0 \mathrm{~L}\). (a) How many moles of \(\mathrm{N}_{2} \mathrm{O}_{5}\) will remain after \(5.0\) min? (b) How many minutes will it take for the quantity of \(\mathrm{N}_{2} \mathrm{O}_{5}\) to drop to \(0.010\) mol? (c) What is the half- life of \(\mathrm{N}_{2} \mathrm{O}_{5}\) at \(70^{\circ} \mathrm{C}\) ?
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