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Chapter 14: Problem 67

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) \(\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)\) (b) \(\mathrm{OCl}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HOCl}(a q)+\mathrm{OH}^{-}(a q)\) (c) \(\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g)\)

Short Answer

Expert verified
(a) Molecularity: 1 (unimolecular). Rate law: Rate = k[\(Cl_{2}\)] (b) Molecularity: 2 (bimolecular). Rate law: Rate = k[\(OCl^-\)][\(H_2O\)] (c) Molecularity: 2 (bimolecular). Rate law: Rate = k[\(NO\)][\(Cl_{2}\)]

Step by step solution

01

(a) Determine the molecularity of reaction (a)

For reaction (a), \(\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)\) There is only 1 reactant, which is Cl鈧�. The molecularity of this reaction is 1 since only one molecule is involved in the elementary reaction step. This reaction is also called a unimolecular reaction.
02

(a) Write the rate law for reaction (a)

The rate law of any elementary reaction depends on the concentrations of the reactants involved. Since reaction (a) is unimolecular, the rate law is written as follows: Rate = k[\(Cl_{2}\)] where k is the rate constant and [\(Cl_{2}\)] represents the concentration of \(Cl_{2}\).
03

(b) Determine the molecularity of reaction (b)

For reaction (b), \(\mathrm{OCl}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HOCl}(a q)+\mathrm{OH}^{-}(a q)\) This reaction involves 2 reactant particles: \(OCl^-\) and \(H_2O\). The molecularity of this reaction is 2 since there are two molecules involved in the elementary reaction step. This reaction is also called a bimolecular reaction.
04

(b) Write the rate law for reaction (b)

Since reaction (b) is bimolecular, the rate law is written as follows: Rate = k[\(OCl^-\)][\(H_2O\)] where k is the rate constant, [\(OCl^-\)] represents the concentration of \(OCl^-\), and [\(H_2O\)] represents the concentration of \(H_2O\).
05

(c) Determine the molecularity of reaction (c)

For reaction (c), \(\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g)\) This reaction involves 2 reactant particles: \(NO\) and \(Cl_{2}\). The molecularity of this reaction is 2 since there are two molecules involved in the elementary reaction step. This reaction is also called a bimolecular reaction.
06

(c) Write the rate law for reaction (c)

Since reaction (c) is bimolecular, the rate law is written as follows: Rate = k[\(NO\)][\(Cl_{2}\)] where k is the rate constant, [\(NO\)] represents the concentration of \(NO\), and [\(Cl_{2}\)] represents the concentration of \(Cl_{2}\).

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Most popular questions from this chapter

Which of the following linear plots do you expect for a reaction \(A \longrightarrow\) products if the kinetics are (a) zero order, (b) first order, or (c) second order? [Section 14.4]

The reaction \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)\) was performed and the following data obtained under conditions of constant \(\left[\mathrm{Cl}_{2}\right]\) : (a) Is the following mechanism consistent with the data? $$ \begin{aligned} \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) & \longrightarrow \mathrm{NOCl}_{2}(g) \text { (fast) } \\ \mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) & \longrightarrow 2 \mathrm{NOCl}(g) \text { (slow) } \end{aligned} $$ (b) Does the linear plot guarantee that the overall rate law is second order?

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 \(\mathrm{NO}, \mathrm{NO}_{2}\), and \(\mathrm{N}_{2}\) - (b) Using a resource such as Table \(8.4\), 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.

Consider the reaction \(A+B \longrightarrow C+D\). Is each of the following statements true or false? (a) The rate law for the reaction must be Rate \(=k[\mathrm{~A}][\mathrm{B}]\). (b) If the reaction is an elementary reaction, the rate law is second order. (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 greater than that for the forward reaction.

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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