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. b. Write the rate law for the reaction.

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Identify the order of the reaction: Since a plot of \( \ln[A] \) versus time yields a straight line, the reaction follows first-order kinetics.

Write the general form of the rate law for a first-order reaction: The rate law for a first-order reaction is \( \text{Rate} = k[A] \), where \( k \) is the rate constant.

Determine the rate constant: 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 \(-0.0045/s\), the rate constant \( k \) is 0.0045/s.

Combine the information to write the rate law: Substitute the rate constant into the rate law expression to get \( \text{Rate} = 0.0045[A] \).

Conclude with the rate law: The rate law for the reaction is \( \text{Rate} = 0.0045[A] \), indicating that the reaction is first-order with respect to \( A \).

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주요 개념

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

First-Order Reactions

A first-order reaction is one where the rate of reaction is directly proportional to the concentration of one reactant. In this case, the linear plot of ln[A] versus time indicates that the reaction follows first-order kinetics, as the natural logarithm of the concentration decreases linearly over time.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. For a first-order reaction, the rate law can be written as rate = k[A], where k is the rate constant. This law allows us to predict how changes in concentration will affect the reaction rate.

Slope of the Line

In the context of a first-order reaction, the slope of the ln[A] versus time plot is equal to -k, where k is the rate constant. The given slope of -0.0045/s indicates the rate constant for the reaction, which is crucial for calculating the rate of reaction at different concentrations.