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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: (a) $\mathrm{O}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{O}_{2}(g)+\mathrm{H}_{2}(g)$ (b) $4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$ (c) $2 \mathrm{C}_{2} \mathrm{H}_{2}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ (d) $\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2}(g) \longrightarrow \mathrm{C}_{3} \mathrm{H}_{6}(g)+\mathrm{NH}_{3}(g)$

Short Answer

Expert verified
The rate expressions for the given reactions are: (a) Rate = -\(\frac{d[O_3]}{dt}\) = -\(\frac{d[H_2O]}{dt}\) = \(\frac{1}{2}\) \(\frac{d[O_2]}{dt}\) = \(\frac{d[H_2]}{dt}\) (b) Rate = -\(\frac{1}{4}\) \(\frac{d[NH_3]}{dt}\) = -\(\frac{1}{5}\) \(\frac{d[O_2]}{dt}\) = \(\frac{1}{4}\) \(\frac{d[NO]}{dt}\) = \(\frac{1}{6}\) \(\frac{d[H_2O]}{dt}\) (c) Rate = -\(\frac{1}{2}\) \(\frac{d[C_2H_2]}{dt}\) = -\(\frac{1}{5}\) \(\frac{d[O_2]}{dt}\) = \(\frac{1}{4}\) \(\frac{d[CO_2]}{dt}\) = \(\frac{1}{2}\) \(\frac{d[H_2O]}{dt}\) (d) Rate = -\(\frac{d[C_3H_7NH_2]}{dt}\) = \(\frac{d[C_3H_6]}{dt}\) = \(\frac{d[NH_3]}{dt}\)

Step by step solution

01

Analyzing Coefficients

In this reaction, all reactants and products have a coefficient of 1, except for O2 which has a coefficient of 2.
02

Rates of Appearance and Disappearance

Using the coefficients, the rate expression can be written as: Rate = -\(\frac{1}{1}\) \(\frac{d[O_3]}{dt}\) = -\(\frac{1}{1}\) \(\frac{d[H_2O]}{dt}\) = \(\frac{1}{2}\) \(\frac{d[O_2]}{dt}\) = \(\frac{1}{1}\) \(\frac{d[H_2]}{dt}\) (b) \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)
03

Analyzing Coefficients

The coefficients for this reaction are 4 for NH3, 5 for O2, 4 for NO, and 6 for H2O.
04

Rates of Appearance and Disappearance

Using the coefficients, the rate expression can be written as: Rate = -\(\frac{1}{4}\) \(\frac{d[NH_3]}{dt}\) = -\(\frac{1}{5}\) \(\frac{d[O_2]}{dt}\) = \(\frac{1}{4}\) \(\frac{d[NO]}{dt}\) = \(\frac{1}{6}\) \(\frac{d[H_2O]}{dt}\) (c) \(2 \mathrm{C}_{2} \mathrm{H}_{2}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)
05

Analyzing Coefficients

The coefficients for this reaction are 2 for C2H2, 5 for O2, 4 for CO2, and 2 for H2O.
06

Rates of Appearance and Disappearance

Using the coefficients, the rate expression can be written as: Rate = -\(\frac{1}{2}\) \(\frac{d[C_2H_2]}{dt}\) = -\(\frac{1}{5}\) \(\frac{d[O_2]}{dt}\) = \(\frac{1}{4}\) \(\frac{d[CO_2]}{dt}\) = \(\frac{1}{2}\) \(\frac{d[H_2O]}{dt}\) (d) \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2}(g) \longrightarrow \mathrm{C}_{3} \mathrm{H}_{6}(g)+\mathrm{NH}_{3}(g)\)
07

Analyzing Coefficients

In this reaction, all of the substances have a coefficient of 1.
08

Rates of Appearance and Disappearance

Using the coefficients, the rate expression can be written as: Rate = -\(\frac{1}{1}\) \(\frac{d[C_3H_7NH_2]}{dt}\) = \(\frac{1}{1}\) \(\frac{d[C_3H_6]}{dt}\) = \(\frac{1}{1}\) \(\frac{d[NH_3]}{dt}\)

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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?

Consider the reaction \(2 \mathrm{~A} \longrightarrow \mathrm{B}\). Is each of the following statements true or false? (a) The rate law for the reaction must be, Rate \(=k[\mathrm{~A}]^{2} .(\mathbf{b})\) If the reaction is an elementary reaction, the rate law is second order. \((\mathbf{c})\) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order. (d) The activation energy for the reverse reaction must be smaller than that for the forward reaction.

In solution, chemical species as simple as \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\) can serve as catalysts for reactions. Imagine you could measure the \(\left[\mathrm{H}^{+}\right]\) of a solution containing an acidcatalyzed reaction as it occurs. Assume the reactants and products themselves are neither acids nor bases. Sketch the \(\left[\mathrm{H}^{+}\right]\) concentration profile you would measure as a function of time for the reaction, assuming \(t=0\) is when you add a drop of acid to the reaction.

The following mechanism has been proposed for the gasphase reaction of \(\mathrm{H}_{2}\) with ICl: $$ \begin{array}{l} \mathrm{H}_{2}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{HI}(g)+\mathrm{HCl}(g) \\ \mathrm{HI}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{I}_{2}(g)+\mathrm{HCl}(g) \end{array} $$ (a) Write the balanced equation for the overall reaction. (b) Identify any intermediates in the mechanism. (c) If the first step is slow and the second one is fast, which rate law do you expect to be observed for the overall reaction?

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}\(. (a) If we begin with an initial \)\mathrm{SO}_{2} \mathrm{Cl}_{2}\( pressure of \)60 \mathrm{kPa}$, what is the partial pressure of this substance after 60 s? (b) At what time will the partial pressure of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) decline to one-tenth its initial value?
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