This reaction was monitored as a function of time: A → B + C A plot of ln[A] versus time yields a straight line with slope -0.0045/s. c. What is the half-life?

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Identify that the reaction is first-order because a plot of \( \ln[A] \) versus time yields a straight line.

Recall the formula for the half-life of a first-order reaction: \( t_{1/2} = \frac{0.693}{k} \), where \( k \) is the rate constant.

Recognize that the slope of the line in a plot of \( \ln[A] \) versus time for a first-order reaction is equal to \(-k\).

Given that the slope is \(-0.0045/s\), determine that \( k = 0.0045/s \).

Substitute \( k = 0.0045/s \) into the half-life formula \( t_{1/2} = \frac{0.693}{0.0045/s} \) to find the half-life.

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First-Order Reactions

In chemistry, a first-order reaction is one where the rate of reaction 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 relationship can be expressed mathematically, and for first-order reactions, the natural logarithm of the concentration of the reactant versus time yields a straight line.

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. It can be calculated using the formula t1/2 = 0.693/k, where k is the rate constant derived from the slope of the ln[A] versus time plot.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate equation that relates the rate of a reaction to the concentration of reactants. For first-order reactions, k can be determined from the slope of the ln[A] versus time plot, which is negative. In this case, the slope is -0.0045/s, indicating the rate at which the concentration of A decreases over time.