Question

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

Short answer

(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

Reaction (a) Molecularity

In this reaction, a Cl₂ molecule dissociates into two Cl atoms. Only one molecule is involved in the rate-determining step, so the molecularity is 1, also known as a unimolecular reaction.

Reaction (a) Rate Law

The rate of the reaction is directly proportional to the concentration of the reactant Cl₂. Thus, the rate law can be written as: Rate = k[Cl₂], where k is the rate constant.

Reaction (b) Molecularity

In this reaction, OCl⁻ reacts with H₂O to form HOCl and OH⁻. Two molecules are involved in the rate-determining step, so the molecularity is 2, also known as a bimolecular reaction.

Reaction (b) Rate Law

The rate of the reaction is directly proportional to the concentration of the reactants OCl⁻ and H₂O. Thus, the rate law can be written as: Rate = k[OCl⁻][H₂O], where k is the rate constant.

Reaction (c) Molecularity

In this reaction, NO and Cl₂ react to form NOCl₂. Two molecules are involved in the rate-determining step, making this another bimolecular reaction.

Reaction (c) Rate Law

The rate of the reaction is directly proportional to the concentration of the reactants NO and Cl₂. Thus, the rate law can be written as: Rate = k[NO][Cl₂], where k is the rate constant.

Key concepts

Molecularity of Reaction

The molecularity of a reaction refers to the number of reactant molecules that collide and participate in a single elementary step. Understanding the molecularity is vital because it provides insights into the reaction mechanism, which is the step-by-step sequence of elementary reactions that make up the overall reaction.

Molecularity is always an integer and can be unimolecular, involving a single molecule, bimolecular, involving two molecules, or termolecular, involving three molecules. It's important to note that molecularity is defined only for elementary reactions - these are reactions that occur in a single step and represent the actual physical process at the molecular level.

For instance, in the example reaction \(\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{Cl}(g)\), we determined the molecularity to be unimolecular because only one molecule of \(\mathrm{Cl}_{2}\) is involved in the rate-determining step.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is derived empirically, meaning it is based on experimental observations rather than theoretical predictions.

A typical rate law takes the form of \(\text{Rate} = k[\text{Reactant}_1]^{n_1}[\text{Reactant}_2]^{n_2}...\), where \(k\) is the rate constant and \(n_1\), \(n_2\), etc., are the reaction orders with respect to each reactant. These orders can be integers, fractions, or even zero which indicate that the reaction rate is independent of the concentration of that particular reactant.

In the case of the reaction \((b)\), \(\mathrm{OCl}^{-} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{HOCl} + \mathrm{OH}^{-}\), the rate law was found to be \(\text{Rate} = k[\mathrm{OCl}^{-}][\mathrm{H}_{2}O]\), suggesting a first order dependence on each reactant.

Unimolecular Reaction

A unimolecular reaction involves a single reactant molecule undergoing a chemical change to transform into products. This type of reaction is characterized by its molecularity of one, indicating that the reaction proceeds when just one reactant molecule is activated or has enough energy to undergo the change.

An example includes the decomposition of \(\mathrm{Cl}_{2}\) into chlorine atoms, as seen in reaction \(\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{Cl}(g)\). Since it is an elementary reaction, the rate at which it occurs depends solely on the concentration of \(\mathrm{Cl}_{2}\), which fits with the rate law \(\text{Rate} = k[\mathrm{Cl}_{2}]\). The simplicity of unimolecular reactions makes them important conceptual tools in understanding chemical kinetics.

Bimolecular Reaction

In contrast to unimolecular reactions, bimolecular reactions involve the collision between two reactant molecules. The molecularity for these reactions is two. The reactions are governed by the kinetic theory of gases, which suggests that the frequency and energy of collisions between molecules greatly influence reaction rates.

Examples of bimolecular reactions include \((b)\) \(\mathrm{OCl}^{-} + \mathrm{H}_{2} \mathrm{O}\) and \((c)\) \(\mathrm{NO} + \mathrm{Cl}_{2}\), both of which require the interaction of two reactant molecules for the reaction to occur. The corresponding rate laws are \(\text{Rate} = k[\mathrm{OCl}^{-}][\mathrm{H}_{2}O]\) and \(\text{Rate} = k[\mathrm{NO}][\mathrm{Cl}_{2}]\), respectively, which indicate that the reaction rate is proportional to the product of the concentrations of both reactants involved in the elementary step.