Thermal decomposition of a compound is of first order. If \(50 \%\) sample of the compound is decomposed in 120 minute, how long will it take for \(90 \%\) of the compound to decompose?

Chemical kinetics is the study of the rates of chemical processes, the factors that affect these rates, and the mechanisms by which reactions occur. Understanding kinetics is key to predicting the behavior of chemicals over time and can help in designing reactions for industrial, laboratory, and everyday applications.

For instance, in the exercise, we're examining a first-order reaction, which means the reaction rate is directly proportional to the concentration of the reactant. Hence, as the reactant concentration decreases, so does the rate of reaction. This relationship is described mathematically through rate equations, which allow us to determine the time required for a certain percentage of reactant to decompose. By studying kinetics, we not only understand the speed at which a product is formed but also gain valuable insights into the reaction mechanism itself.

The reaction rate constant, represented by the symbol 'k,' is a crucial number in chemical kinetics that describes the speed of a chemical reaction. For a first-order reaction, the rate constant provides the link between the concentration of the reactants and the rate at which they are consumed.

This constant is determined experimentally and varies with temperature, as depicted by the Arrhenius equation. In the given exercise, once the half-life for a decomposing sample is known, we can calculate the rate constant, which then can be utilized to find out how long it will take for a different percentage of the compound to decompose. Importantly, 'k' remains the same regardless of concentration, which underpins the predictability of reaction outcomes under constant conditions.

The half-life of a reaction, often denoted as 't_{1/2}', is the time required for half of the reactant to be used up in a chemical reaction. For first-order reactions, the half-life is constant because it does not depend on the reactant's initial concentration.

In the context of our problem, knowing that the half-life of the reaction is 120 minutes allows us to calculate the rate constant 'k.' This value can then be used to determine the time it will take for 90% of the sample to decompose, simply by applying the first-order reaction equation. The concept of half-life is not only essential in chemical kinetics but also in various fields such as pharmacology, radioactive dating, and environmental science, highlighting its universal significance.