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Chapter 14: Problem 65

We have used the terms order of a reaction and molecularity of an elementary process (that is, unimolecular, bimolecular). What is the relationship, if any, between these two terms?

Short Answer

Expert verified
In elementary reactions, the order and molecularity are the same, indicating the number of molecules participating in the reaction. However, for complex reactions that involve more than a single step, the order of the reaction does not necessarily match the sum of the molecularities of the elementary steps, as it is determined by the slowest (rate-determining) step.

Step by step solution

01

Clarify the terms

Before explaining the relationship, let's define the terms. The order of a reaction is the sum of the powers of the concentrations of the reactants in the rate equation of the reaction and it indicates how the reaction rate is affected by the concentrations of the reactants. On the other hand, molecularity of a reaction is defined as the number of molecules, atoms, or ions that must collide simultaneously to result in a chemical reaction. The terms for molecularity are unimolecular (one molecule), bimolecular (two molecules), and termolecular (three molecules).
02

Identify the correlation

In elementary reactions, which are reactions that occur in a single step, the order of a reaction matches its molecularity. For example, a unimolecular reaction is also first order, a bimolecular reaction is second order and so on.
03

Notice the exception

However, this correlation does not hold true for complex reactions which involve more than one step (known as reaction mechanism). In complex reactions, the overall order of the reaction does not necessarily equate to the sum of the molecularities of the elementary steps, since the order of the reaction is determined by the slowest (rate-determining) step, not the sum of all steps.

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Most popular questions from this chapter

The decomposition of dimethyl ether at \(504^{\circ} \mathrm{C}\) is $$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CH}_{4}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})+\mathrm{CO}(\mathrm{g})$$ The following data are partial pressures of dimethyl ether (DME) as a function of time: \(t=0\) s, \(P_{\text {DME }}=\) \(312 \mathrm{mmHg} ; 390 \mathrm{s}, 264 \mathrm{mmHg} ; 777 \mathrm{s}, 224 \mathrm{mmHg} ; 1195 \mathrm{s},187 \mathrm{mmHg} ; 3155 \mathrm{s}, 78.5 \mathrm{mmHg}.\) (a) Show that the reaction is first order. (b) What is the value of the rate constant, \(k ?\) (c) What is the total gas pressure at 390 s? (d) What is the total gas pressure when the reaction has gone to completion? (e) What is the total gas pressure at \(t=1000\) s?

For the reaction \(A \longrightarrow\) products, the following data give \([\mathrm{A}]\) as a function of time \(t=0 \mathrm{s},[\mathrm{A}]=0.600 \mathrm{M};100 \mathrm{s}, 0.497 \mathrm{M} ; 200 \mathrm{s}, 0.413 \mathrm{M} ; 300 \mathrm{s}, 0.344 \mathrm{M} ; 400 \mathrm{s}\) \(0.285 \mathrm{M} ; 600 \mathrm{s}, 0.198 \mathrm{M} ; 1000 \mathrm{s}, 0.094 \mathrm{M}.\) (a) Show that the reaction is first order. (b) What is the value of the rate constant, \(k ?\) (c) What is \([\mathrm{A}]\) at \(t=750 \mathrm{s} ?\)

Three different sets of data of \([\mathrm{A}]\) versus time are giv the following table for the reaction \(A \longrightarrow\) prod [Hint: There are several ways of arriving at answer each of the following six questions. $$\begin{array}{cccccc} \hline \text { I } & & \text { II } & & \text { III } & \\ \hline \begin{array}{c} \text { Time, } \\ \text { s } \end{array} & \text { [A], M } & \begin{array}{c} \text { Time, } \\ \text { s } \end{array} & \text { [A], M } & \begin{array}{c} \text { Time, } \\ \text { s } \end{array} & \text { [A], M } \\ \hline 0 & 1.00 & 0 & 1.00 & 0 & 1.00 \\ 25 & 0.78 & 25 & 0.75 & 25 & 0.80 \\ 50 & 0.61 & 50 & 0.50 & 50 & 0.67 \\ 75 & 0.47 & 75 & 0.25 & 75 & 0.57 \\ 100 & 0.37 & 100 & 0.00 & 100 & 0.50 \\ 150 & 0.22 & & & 150 & 0.40 \\ 200 & 0.14 & & & 200 & 0.33 \\ 250 & 0.08 & & & 250 & 0.29 \\ \hline \end{array}$$ What is the approximate half-life of the first-order reaction?

The decomposition of nitric oxide occurs through two parallel reactions: $$\mathrm{NO}(\mathrm{g}) \longrightarrow \frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \quad k_{1}=25.7 \mathrm{s}^{-1}$$ $$\mathrm{NO}(\mathrm{g}) \longrightarrow \frac{1}{2} \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+\frac{1}{4} \mathrm{O}_{2}(\mathrm{g}) \quad k_{2}=18.2 \mathrm{s}^{-1}$$ (a) What is the reaction order for these reactions? (b) Which reaction is the slow reaction? (c) If the initial concentration of \(\mathrm{NO}(\mathrm{g})\) is \(2.0 \mathrm{M},\) what is the concentration of \(\mathrm{N}_{2}(\mathrm{g})\) after 0.1 seconds? (d) If the initial concentration of \(\mathrm{NO}(\mathrm{g})\) is \(4.0 \mathrm{M},\) what is the concentration of \(\mathrm{N}_{2} \mathrm{O}(\mathrm{g})\) after 0.025 seconds?

The decomposition of ethylene oxide at \(690 \mathrm{K}\) is monitored by measuring the total gas pressure as a function of time. The data obtained are \(t=10 \mathrm{min}, P_{\text {tot }}= 139.14 \mathrm{mmHg} ; 20 \mathrm{min}, 151.67 \mathrm{mmHg} ; 40 \mathrm{min}, 172.65 \mathrm{mmHg} ; 60 \mathrm{min}, 189.15 \mathrm{mmHg} ;\) \(100 \mathrm{min}, 212.34\) \(\mathrm{mmHg} ; 200 \mathrm{min}, 238.66 \mathrm{mmHg} ; \infty, 249.88 \mathrm{mmHg}\) What is the order of the reaction \(\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) ?\)
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