Define the-half of a reaction. Explain on the molecular level why the half- life of a first-order reaction is constant
The half-reaction refers to a chemical reaction that only involves the oxidation or reduction process of a single reactant. It helps to separate the overall redox reaction into two separate processes.
On the molecular level, in a first-order reaction, the rate of the reaction depends solely on the concentration of one reactant. The reaction follows an exponential decay or exponential growth pattern.
The half-life of a first-order reaction is constant because the rate constant, k, is constant. The rate constant represents the fraction of reactant molecules that undergo the reaction per unit time.
As the reaction proceeds, the concentration of the reactant continuously decreases. However, the rate of the reaction remains constant, as k does not change. Therefore, it takes the same amount of time for the concentration of the reactant to decrease by half, regardless of the initial concentration.
To summarize, the half-life of a first-order reaction is constant because the rate constant remains constant and determines the rate of reaction based on the concentration of one reactant. This behavior leads to an exponential decay or growth pattern, allowing for a predictable and constant halving time.
The half-life of a reaction refers to the time it takes for the concentration of a reactant to decrease by half. It is a useful way to measure the rate of a reaction and provides insights into its kinetics.
To define the half-life of a reaction, we can look at a generic chemical equation:
A → Products
In this equation, A represents the reactant, and "Products" denote the resulting substances formed after the reaction. The half-life of the reaction is denoted as t(1/2).
Now, let's discuss why the half-life of a first-order reaction is constant on a molecular level. In a first-order reaction, the rate of the reaction depends on the concentration of only one reactant, A. According to the rate law equation for a first-order reaction:
Rate = k[A]
where [A] represents the concentration of A and k is the rate constant.
On the molecular level, the concept of half-life can be understood as follows:
At any given time, there are numerous molecules of reactant A present in the system. Some of these molecules will undergo the reaction and transform into products, while others will remain unreacted. As time progresses, the concentration of reactant A decreases.
For a first-order reaction, the rate of the reaction is proportional to the concentration of A. Therefore, if we start with a certain concentration of A, the rate of the reaction will be higher initially, leading to a rapid decrease in concentration. As time goes on, the concentration decreases, resulting in a lower rate of the reaction.
The half-life of a first-order reaction is defined as the time it takes for the concentration of A to reduce by half. Since the rate of the reaction is directly proportional to the concentration of A, the decrease in concentration over time follows an exponential decay pattern.
Mathematically, the relationship between the half-life (t(1/2)) and the rate constant (k) of a first-order reaction can be given by the equation:
t(1/2) = ln(2) / k
From this equation, we can see that the half-life is inversely proportional to the rate constant. Hence, regardless of the initial concentration, the half-life of a first-order reaction remains constant as long as the temperature and other reaction conditions remain constant.
In summary, the half-life of a first-order reaction is constant because the rate of the reaction is directly proportional to the concentration of the reactant. As the concentration decreases over time, the reaction rate decreases, and the time taken for the concentration to reduce by half remains constant.