Question

Determine the molecularity, and write the rate law for each of the following elementary steps: (a) \(\mathrm{X} \longrightarrow\) products (b) \(\mathrm{X}+\mathrm{Y} \longrightarrow\) products (c) \(\mathrm{X}+\mathrm{Y}+\mathrm{Z} \longrightarrow\) products (d) \(\mathrm{X}+\mathrm{X} \longrightarrow\) products (e) \(\mathrm{X}+2 \mathrm{Y} \longrightarrow\) products

Short answer

(a) Unimolecular: Rate = k[X]; (b) Bimolecular: Rate = k[X][Y]; (c) Termolecular: Rate = k[X][Y][Z]; (d) Bimolecular: Rate = k[X]^2; (e) Termolecular: Rate = k[X][Y]^2.

Step-by-step solution

Determine Molecularity of Each Step

The molecularity of an elementary step is determined by the number of reactant molecules involved in the reaction. (a) One X molecule, which means unimolecular. (b) One X and one Y, which means bimolecular. (c) One X, one Y, and one Z, which means termolecular. (d) Two X molecules, which means bimolecular. (e) One X and two Y molecules, which means termolecular.

Write the Rate Law for Each Step

The rate law for an elementary reaction is based directly on the reactants involved:(a) The rate law: \( ext{Rate} = k[ ext{X}] \)(b) The rate law: \( ext{Rate} = k[ ext{X}][ ext{Y}] \)(c) The rate law: \( ext{Rate} = k[ ext{X}][ ext{Y}][ ext{Z}] \)(d) The rate law: \( ext{Rate} = k[ ext{X}]^2 \)(e) The rate law: \( ext{Rate} = k[ ext{X}][ ext{Y}]^2 \)

Key concepts

Molecularity

Molecularity refers to the number of reactant molecules that come together to generate a reaction. It's a crucial concept in understanding chemical reactions, particularly elementary reactions. This idea helps to categorize the reactions into different types based on how many molecules collide and interact to form products. For instance, if a reaction step involves a single molecule decomposing, it is a unimolecular reaction. On the other hand, if two molecules are involved, it's bimolecular, and if three come together, it's termed as termolecular. Understanding molecularity is essential because it directly influences the reaction's rate law, which dictates how the reaction rate changes with concentrations of reactants. It's important to note that molecularity is only determined in elementary reactions, meaning reactions that occur in a single step.

Rate Law

The rate law of a reaction relates the rate of reaction to the concentrations of its reactants, each raised to a power called the reaction order. In the context of elementary reactions, the rate law can be directly deduced from the molecularity of the reaction.

• For a unimolecular reaction, the rate is proportional to the concentration of the single reactant.
• In a bimolecular reaction, it depends on the product of the concentrations of the two reactants.
• For a termolecular reaction, the rate law becomes even more complex, involving a product of the concentrations of three reactants.

These relationships allow chemists to predict how changes in concentrations could affect the reaction speed and ultimately control the reaction environment accordingly.

Unimolecular Reaction

A unimolecular reaction involves a single reactant molecule undergoing rearrangement or decomposition to form products. These reactions are relatively simple in mechanism. For example, in step (a) of the exercise, only one molecule of \(X\) is involved. The rate law for a unimolecular reaction is straightforward: \(\text{Rate} = k[X]\), where \(k\) is the rate constant and \(X\) is the concentration of the reactant. Unimolecular reactions can typically occur spontaneously under the right conditions because they require only the energy within the molecule itself to proceed. Understanding this concept helps in comprehending how certain reactions happen with minimal external influence.

Bimolecular Reaction

Bimolecular reactions are characterized by the interaction between two reactant molecules. This can include two different reactants or two molecules of the same reactant. For a bimolecular reaction, such as in step (b) where \(X\) and \(Y\) react, the rate law is given by \(\text{Rate} = k[X][Y]\). Another example is step (d), where two \(X\) molecules collide: the rate law becomes \(\text{Rate} = k[X]^2\). These reactions are common and crucial in understanding many biochemical processes as they involve simple yet effective interactions between molecules. Bimolecular reactions depend not only on the concentration of each reactant but also on factors like temperature and collision frequency.

Termolecular Reaction

Termolecular reactions are less common than unimolecular and bimolecular reactions due to the complexity of three particles coming together simultaneously to react. Their importance lies in their unique requirement for a simultaneous collision of three molecules. As seen in step (c) involving \(X\), \(Y\), and \(Z\), the rate law is \(\text{Rate} = k[X][Y][Z]\). In cases like step (e), where \(X\) and two \(Y\) molecules react, the rate law becomes \(\text{Rate} = k[X][Y]^2\). The rarity of these reactions is due to the low probability that three molecules will collide with the precise alignment and energy required to react. Thus, understanding termolecular reactions involves appreciating their complex nature and the specific conditions that may contribute to their occurrence.