91Ó°ÊÓ

First-order reactions are an important part of chemical kinetics, which is the study of the rates of chemical processes. In these types of reactions, the rate at which the reaction proceeds is directly proportional to the concentration of a single reactant. This means that if you increase the concentration of the reactant, the rate of the reaction will increase as well, as long as other conditions remain the same.

Mathematically, for a reaction where the reactant A is converting to products, the rate can be expressed as:

• \[ \text{Rate} = k [A] \]

Here,

• "Rate" is how fast the reaction is happening.
• "k" is the rate constant, an important term that provides insights into how quickly the reaction occurs.
• "[A]" denotes the concentration of reactant A.

In our exercise, we're dealing with a first-order reaction involving \(\mathrm{N}_2\mathrm{O}_5\). Understanding this concept will help us solve problems involving reaction rates and concentrations.

The rate constant, often denoted as "k", is a crucial part of the rate law for a reaction. It provides important information about the reaction rate at a given temperature. For different reactions, the rate constant can vary significantly, and it is usually determined experimentally. In the context of first-order reactions, the units of the rate constant are typically inverse seconds \( (\text{s}^{-1}) \).

In our given problem, the rate constant k for the decomposition of \( \mathrm{N}_2\mathrm{O}_5 \) is \( 3.0 \times 10^{-5} \text{s}^{-1} \). This means as the concentration of \( \mathrm{N}_2\mathrm{O}_5 \) changes, the rate at which it disappears is directly tied to this constant. Understanding the rate constant helps in predicting how fast a reaction will occur under certain conditions.

Calculating concentrations is a key part of solving rate law problems. For first-order reactions, once you know the rate law and the rate constant, calculating the concentration of a reactant becomes straightforward. This is done by rearranging the rate law to solve for the concentration of the reactant.

In the exercise at hand, we are given the rate of reaction as \( 2.40 \times 10^{-5} \text{mol L}^{-1} \text{s}^{-1} \) and the rate constant as \( 3.0 \times 10^{-5} \text{s}^{-1} \). To find the concentration \( [\mathrm{N}_2\mathrm{O}_5] \), we rearrange the rate law equation:

• \[ [\mathrm{N}_2\mathrm{O}_5] = \frac{\text{Rate}}{k} \]

Substitute the given numbers into the equation:

• \[ [\mathrm{N}_2\mathrm{O}_5] = \frac{2.40 \times 10^{-5}}{3.0 \times 10^{-5}} = 0.8 \text{ mol L}^{-1} \]

This gives us the concentration of\( \mathrm{N}_2\mathrm{O}_5 \), illustrating how changes in concentration affect the rate of reaction.

Chemical kinetics is the field of chemistry that deals with the rate of reactions and the factors affecting them. It helps chemists predict how quickly a chemical process will occur, providing important insights for industries, laboratories, and more.

Understanding kinetics involves studying how different conditions like temperature, concentration, and the presence of catalysts influence the speed of reactions. Key concepts in kinetics include reaction order, rate laws, and the Arrhenius equation.

In our example, we specifically look at a decomposition reaction of \( \mathrm{N}_2\mathrm{O}_5 \), applying the concept of first-order reactions. The field of kinetics uses such knowledge to determine the best conditions for reactions to proceed efficiently and safely. This information is vital in many real-world applications, from manufacturing to environmental science.