Problem 22 - Chemistry The Molecular Science

Question

Nitrosyl bromide, NOBr, is formed from \(\mathrm{NO}\) and \(\mathrm{Br}_{2}\). $$ 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g}) $$ Experiment shows that the reaction is first-order in \(\mathrm{Br}_{2}\) and second-order in NO. (a) Write the rate law for the reaction. (b) If the concentration of \(\mathrm{Br}_{2}\) is tripled, determine how the reaction rate changes. (c) Determine what happens to the reaction rate when the concentration of \(\mathrm{NO}\) is doubled.

Step-by-Step Solution

Answer

(a) rate = k [NO]^2 [Br2]; (b) Rate is tripled; (c) Rate is quadrupled.

Step 1: Understand the Rate Law

The rate law for a chemical reaction relates the rate of the reaction to the concentrations of the reactants. For a reaction where one reactant is first-order and another is second-order, the rate law takes the form: \[ \text{rate} = k [\text{NO}]^m [\text{Br}_2]^n \] In this case, the reaction is first-order in \( \text{Br}_2 \) (\( n = 1 \)) and second-order in NO (\( m = 2 \)), giving: \[ \text{rate} = k [\text{NO}]^2 [\text{Br}_2] \] where \( k \) is the rate constant.

Step 2: Analyze the Effect of Changing \\(\text{Br}_2\\) Concentration

If the concentration of \( \text{Br}_2 \) is tripled, since the reaction is first-order in \( \text{Br}_2 \), you can substitute into the rate law: \[ \text{rate} = k [\text{NO}]^2 [3\cdot\text{Br}_2] \] The rate increases by a factor of 3. Hence, the overall reaction rate is also tripled.

Step 3: Analyze the Effect of Changing \\(\text{NO}\\) Concentration

If the concentration of NO is doubled, and considering the reaction is second-order with respect to NO, the rate changes as follows: \[ \text{rate} = k [2\cdot\text{NO}]^2 [\text{Br}_2] \] This becomes: \[ \text{rate} = k (2^2)[\text{NO}]^2 [\text{Br}_2] = 4k [\text{NO}]^2 [\text{Br}_2] \] Thus, the rate increases by a factor of 4.

Key Concepts

Order of Reaction

Chemists often explore how the concentration of reactants influences the rate of a chemical reaction. The order of reaction helps us understand this relationship. It shows how the rate depends on the concentration of each reactant.
In our given reaction, the formation of NOBr from NO and Br\(_2\), we look at how changes in concentrations affect the speed of the reaction. The reaction is described as first-order in Br\(_2\) and second-order in NO. This implies:

• First-order in Br\(_2\): The rate changes directly with the concentration of Br\(_2\). If you double the Br\(_2\) concentration, the rate doubles.
• Second-order in NO: The rate is influenced more strongly by changes in NO concentration. If you double the NO concentration, the rate increases by a factor of four (since 2\(^2\) is 4).

These findings allow us to draft the rate law equation, which shows the mathematical relationship of how each reactant concentration affects the reaction rate.

Reaction Rate

Reaction rate is the speed at which reactants are converted into products. It's crucial for understanding how quickly a chemical process progresses.
In chemical equations, reaction rate can vary widely, depending on the conditions and the nature of the reactants involved. For example, we saw that when the concentration of Br\(_2\) is tripled in our NOBr formation, the rate triples due to its first-order nature. Similarly, doubling the concentration of NO, which is second-order, results in a fourfold increase in the rate.
Mathematically, reaction rate for our specific reaction can be expressed using the rate law:\[\text{rate} = k [\text{NO}]^2 [\text{Br}_2]\]Here, \( k \) is the rate constant—a unique value that differs with conditions like temperature. Understanding how the rate changes with concentration helps predict the reaction's behavior under different scenarios.

Chemical Kinetics

Chemical kinetics is the study of reaction rates and the steps involved in reactions. It's like the clock that measures how fast a reaction proceeds. Kinetics doesn’t just help chemists understand how reactions happen; it aids in controlling them to optimize conditions for desired outcomes.
The principles of kinetics are seen clearly in our reaction. By determining the order of the reaction and using the rate law, we predict how changes in concentration affect the rate. For instance:

• Knowing the order of the reaction directs us to how sensitive the rate is to concentration changes.
• The rate law equation provides a clear quantitative relationship between concentrations and rate.
• By understanding kinetics, we can deliberately manipulate reaction conditions like concentration or temperature to control the speed of reactions.

Chemical kinetics thus serves as a powerful tool in both theoretical research and practical applications, allowing for precise control over chemical processes.