The rate constant for a first order reaction is 60 s^-1. How much time will it take to reduce t

step 1 Hello, good evening student. In this question, we have to find the time taken to reduce the init

The rate constant for a first order reaction is 60 s^-1....

Key Concepts

Exponential Decay and Natural Logarithms

Exponential decay in the context of kinetics implies that the reactant concentration decreases exponentially over time. Taking the natural logarithm of the concentration ratio linearizes the exponential relationship, making it easier to solve for time, especially when determining the duration needed to reach a given fraction of the original concentration.

Half-Life

Although not explicitly required in every problem, the concept of half-life—the time required for the concentration of a reactant to decrease by half—is an important characteristic of first-order reactions. It provides an intuitive means of understanding the time scales involved in the decay process, particularly when the target fraction can be expressed as repeated halvings.

First?Order Reaction Kinetics

In first?order reactions, the rate depends linearly on the concentration of a single reactant. This means that the decrease in concentration over time follows an exponential decay law, providing a predictable relationship between the concentration and time based on the rate constant.

Integrated Rate Law

The integrated rate law for a first?order reaction, given by ln([A]_t/[A]_0) = –kt, relates the natural logarithm of the ratio of the reactant's concentration at time t to its initial concentration to the product of the rate constant and time. This equation is fundamental for calculating the time required for a specified fraction of the reactant to be consumed.

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