Problem 101 - Chemistry: An Atoms-Focused Approach

Question

Write the rate laws for the following elementary steps and identify them as uni-, bi-, or termolecular steps: a. \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g)\) c. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}_{3}(g)+\mathrm{NO}(g)\)

Step-by-Step Solution

Answer

Question: Determine the order of each reaction, write the rate laws, and identify them as uni-, bi-, or termolecular steps for the following reactions: a. \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g)\) c. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}_{3}(g)+\mathrm{NO}(g)\) Answer: a. Unimolecular step; Rate = k[\(\mathrm{SO}_{2} \mathrm{Cl}_{2}\)] b. Bimolecular step; Rate = k[\(\mathrm{NO}_{2}\)][\(\mathrm{CO}\)] c. Termolecular step; Rate = k[\(\mathrm{NO}_{2}\)]^2

Step 1: Determine the order of each reaction

Look at the stoichiometric coefficients (the numbers before the molecules) of the reactants in each equation. The sum of these coefficients determines the order (uni, bi, or termolecular), which refers to the number of molecules that collide simultaneously in the reaction. a. \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g)\) c. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}_{3}(g)+\mathrm{NO}(g)\) Reaction a: coefficient of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is 1; Reaction b: coefficients of \(\mathrm{NO}_{2}\) and \(\mathrm{CO}\) are 1 and 1 (sum of coefficients = 2); Reaction c: coefficient of \(\mathrm{NO}_{2}\) is 2; So, Reaction a is a unimolecular step, Reaction b is a bimolecular step, and Reaction c is a termolecular step.

Step 2: Write the rate laws for each reaction

For each reaction, the rate law can be written as follows: a. For unimolecular reactions, the rate law is: Rate = k[A], where k is the rate constant and [A] is the concentration of the reactant. b. For bimolecular reactions, the rate law is: Rate = k[A][B], where k is the rate constant, [A] is the concentration of the first reactant and [B] is the concentration of the second reactant. c. For termolecular reactions, the rate law is: Rate = k[A]^2, where k is the rate constant and [A] is the concentration of the reactant. Now substituting the appropriate reactants into the rate laws: a. Rate = k[\(\mathrm{SO}_{2} \mathrm{Cl}_{2}\)] b. Rate = k[\(\mathrm{NO}_{2}\)][\(\mathrm{CO}\)] c. Rate = k[\(\mathrm{NO}_{2}\)]^2

Step 3: Identify each reaction as uni-, bi-, or termolecular steps

We have already determined the order of each reaction in Step 1. a. Unimolecular step b. Bimolecular step c. Termolecular step In conclusion, we have determined the order of each reaction, written the rate laws, and identified them as uni-, bi-, or termolecular steps.

Key Concepts

Rate Laws

Rate laws are crucial for understanding how fast a chemical reaction proceeds. In essence, a rate law expresses the rate of a reaction as a function of the concentration of the reactants. The general form of a rate law is \( ext{Rate} = k[A]^x[B]^y \ldots \), where \( k \) is the rate constant and \( [A], [B] \) are the concentrations of the reactants raised to the power of their respective reaction orders.
- For a unimolecular reaction, the rate depends only on the concentration of one reactant, and the rate law is \( ext{Rate} = k[A] \).
- For a bimolecular reaction, the rate depends on the product of the concentrations of two reactants, with a rate law like \( ext{Rate} = k[A][B] \).
- For a termolecular reaction, rarely occurring due to the complexity of three molecules colliding simultaneously, the rate law could be represented as \( ext{Rate} = k[A]^2 \) or a variation depending on the specific reaction mechanism.
Understanding rate laws allows chemists to predict how the concentration of reactants will affect the speed of the reaction.

Molecularity

Molecularity refers to the number of reactant molecules involved in an elementary reaction step. This concept helps classify reactions as unimolecular, bimolecular, or termolecular based on the number of reacting species.

• **Unimolecular reactions** involve one molecule reacting to form products. This could be a simple decomposition or a rearrangement, like \( ext{SO}_{2} ext{Cl}_{2}(g) \rightarrow ext{SO}_{2}(g) + ext{Cl}_{2}(g) \).
• **Bimolecular reactions** occur when two different molecules collide and react to form products. An example is \( ext{NO}_{2}(g) + ext{CO}(g) \rightarrow ext{NO}(g) + ext{CO}_{2}(g) \).
• **Termolecular reactions** are much less common because they require the simultaneous collision of three molecules — a near-impossible feat in the chaotic world of reactions. Example: \( 2 ext{NO}_{2}(g) \rightarrow ext{NO}_{3}(g) + ext{NO}(g) \).

In practice, termolecular reactions are often broken down into a series of bimolecular steps for easier analysis.

Reaction Order

The concept of reaction order relates to the power to which the concentration of a reactant is raised in the rate law. It is separate from molecularity, which concerns the stoichiometry of a reaction. Reaction orders can be determined from experimental data and may not necessarily match the stoichiometric coefficients in the balanced chemical equation.
- **Unimolecular reactions** typically have a first-order rate law, where the rate depends linearly on the concentration of one reactant (e.g., \( ext{Rate} = k[ ext{SO}_{2} ext{Cl}_{2}] \)).
- **Bimolecular reactions** usually result in second-order rate laws, involving two reactants' concentrations (e.g., \( ext{Rate} = k[ ext{NO}_{2}][ ext{CO}] \)).
- **Termolecular reactions** have a complex third-order or combined rate law, like \( ext{Rate} = k[ ext{NO}_{2}]^2 \), reflecting the unusual requirement of three molecules colliding effectively. Reaction order is thus essential to understanding reaction dynamics and predicting how changes in concentration influence reaction rates.

Elementary Reactions

Elementary reactions are the simplest type of chemical reactions, presenting as individual steps that directly lead to products. Unlike a complex reaction, which may consist of multiple steps or stages, an elementary reaction occurs in a single event. This simplicity allows for direct correlation between the stoichiometric coefficients of the reactants and their reaction orders.
Each elementary step has its molecularity defined by the number of molecules involved, simplifying the deduction of its rate law. For example:

• **Unimolecular step**: Involves the transformation of a single molecule, like the decomposition of \( ext{SO}_{2} ext{Cl}_{2} \).
• **Bimolecular step**: Involving a collision between two molecules, such as \( ext{NO}_{2} + ext{CO} \).
• **Termolecular step**: Although rare, if three molecules are involved, like \( 2 ext{NO}_{2} \)'s transformation, it is still considered an elementary reaction in such a context.

Elementary reactions are fundamental because they offer insights into reaction mechanisms, helping to unravel the detailed pathway through which reactants turn into products. Recognizing these reactions supports the understanding of broader chemical processes.