The rate constant for the first-order decomposition of N2O5(g) to NO2(g) and O2(g) is 7.48 * 10-3 s-1 at a given temperature. a. Find the length of time required for the total pressure in a system containing N2O5 at an initial pressure of 0.100 atm to rise to 0.145 atm. b. Find the length of time required for the total pressure in a system containing N2O5 at an initial pressure of 0.100 atm to rise to 0.200 atm. c. Find the total pressure after 100 s of reaction.

In chemistry, the rate constant is a fundamental component in the study of reaction kinetics, representing the speed at which a chemical reaction proceeds. For a first-order reaction, such as the decomposition of N₂O₅(g), the rate constant, denoted as 'k', has units of s^-1, indicating it's a measure of the reaction rate per second.

The rate constant can be understood as a proportionality factor that connects the rate of reaction with the concentration (or in the case of gases, pressure) of the reactants involved. For a first-order reaction, the reaction rate is directly proportional to the concentration of a single reactant. Mathematically, this relationship is expressed as Rate = k [Reactant], where [Reactant] signifies the molar concentration of the reactant. In our case of N₂O₅ decomposition, since the reaction is carried out in a closed container, the concentration is directly related to the gas pressure.

Experimentally determining the rate constant is crucial because it allows for the prediction of how long it will take for reactants to convert into products under certain conditions, like the ones presented in our exercise. The rate constant can vary with temperature and the presence of a catalyst, hence knowing 'k' under the given conditions is essential for calculations.

Chemical kinetics is the branch of chemistry that deals with the study of the speed or rate of chemical reactions and the factors that affect this rate. It provides insights into the steps of reaction mechanisms and the behavior of reactants during transformations. A key aspect of chemical kinetics is understanding how different conditions, such as concentration, temperature, and catalysts, can influence the reaction rate.

In the context of our exercise on N₂O₅ decomposition, kinetics helps us predict how different initial pressures and time intervals affect the system's total pressure. It's the kinetics principles that underpin the use of the rate equation and the calculation of the time required for pressures to change in the system. Learning about kinetics is fundamental as it not only explains how quickly a reaction takes place but also provides explanations for the underlying molecular-level events involved in a reaction.

The reaction order is a term used to indicate the power to which the concentration of a reactant is raised in the rate law, which is an equation that links the reaction rate with the concentrations of reactants. For a first-order reaction, the reaction order is one, indicating that the rate is directly proportional to the concentration of a single reactant.

Reactants in a first-order reaction, such as the decomposition of N₂O₅, can be represented by the rate law: Rate = k [N₂O₅]¹. This means that if the concentration of N₂O₅ doubles, the rate of reaction will also double. Understanding the reaction order is vital for solving kinetics problems because it determines the form of the mathematical equations used to calculate reaction rates and the necessary time for a reaction to reach a certain stage, as showcased in the steps of our exercise. Recognizing the order of a reaction is essential for the effective design of chemical processes and in industries where controlling reaction speed is critical.