Given the following diagrams at t = 0 min and t = 30 min

After four half-life periods for a first-order reaction, what fraction of reactant remains? [Section 14.4]

검증된 단계별 안내

Identify that the problem involves a first-order reaction and the concept of half-life.

Recall that for a first-order reaction, the half-life (t_1/2) is the time required for the concentration of the reactant to decrease by half.

Understand that after one half-life, the concentration of the reactant is reduced to 1/2 of its initial value.

After two half-lives, the concentration is reduced to (1/2)^2 = 1/4 of its initial value.

After four half-lives, the concentration is reduced to (1/2)^4 = 1/16 of its initial value.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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58s

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

First-Order Reaction

A first-order reaction is a type of chemical reaction where the rate is directly proportional to the concentration of one reactant. This means that as the concentration of the reactant decreases, the rate of the reaction also decreases. The mathematical representation of a first-order reaction is given by the equation: rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Half-Life

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. For first-order reactions, the half-life is constant and does not depend on the initial concentration. This property allows for easy calculations of remaining reactant concentration over multiple half-lives, making it a crucial concept in kinetics.

Fraction of Reactant Remaining

The fraction of reactant remaining after a certain number of half-lives can be calculated using the formula: (1/2)^n, where n is the number of half-lives that have passed. For example, after four half-lives, the fraction remaining would be (1/2)^4 = 1/16. This concept is essential for understanding how reactant concentrations change over time in a first-order reaction.

Given the following diagrams at t = 0 min and t = 30 minAfter four half-life periods for a first-order reaction, what fraction of reactant remains? [Section 14.4]