Define the-half of a reaction. Explain on the molecular level why the half- life of a first-order reaction is constant
The half-life of a reaction refers to the amount of time it takes for half of the reactant to be converted into the product. In other words, it is the time required for the concentration of the reactant to decrease by 50%.
A half-reaction represents the conversion of one mole of a reactant to its corresponding product. It is often used to balance chemical equations or determine the stoichiometry of a reaction.
Now, let's discuss the molecular-level explanation for why the half-life of a first-order reaction is constant. First-order reactions are those where the rate of reaction is directly proportional to the concentration of the reactant. Mathematically, this can be expressed as:
Rate = k[A]
Where:
- Rate is the rate of the reaction,
- k is the rate constant, and
- [A] is the concentration of the reactant.
To understand why the half-life is constant, we have to consider that the rate of a reaction at any given moment is determined by the number of reactant molecules present. In a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant.
As the reaction proceeds, the concentration of the reactant decreases, resulting in a lower number of molecules available for the reaction. However, the rate constant remains constant throughout the reaction, given that it is a characteristic of the reaction itself and does not depend on the concentration of the reactant.
Based on the exponential nature of first-order reactions, the concentration of the reactant decreases by a fixed fraction with each successive half-life. This means that after one half-life, half of the initial reactant concentration will be consumed, and the remaining half will still take the same amount of time to reach the next half. This pattern continues throughout the reaction, resulting in a constant half-life.
Essentially, the constant half-life of a first-order reaction is a consequence of the exponential decay of reactant concentration, where the rate of reaction is directly proportional to the concentration of the reactant but independent of its initial amount.