A(aq) →B (aq) + ( (aq) a plot of In [A] + vs, time gives a straight line with a negative slope, what is the order of the reaction?

Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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A chemical reaction is represented as follows:

\[ A(aq) \rightarrow B(aq) + C(aq) \]

A plot of \(\ln[A]\) versus time gives a straight line with a negative slope. What is the order of the reaction?

**Explanation:**

In chemical kinetics, if a plot of the natural logarithm of the concentration of a reactant (\(\ln[A]\)) versus time yields a straight line with a negative slope, this indicates that the reaction is first-order with respect to the reactant \(A\). The linear relationship suggests that the rate of reaction depends exponentially on the concentration of \(A\). 

**Key Concepts:**

- **First-Order Reaction:** The rate is directly proportional to the concentration of one reactant. For a first-order reaction, the integrated rate law is \(\ln[A] = -kt + \ln[A_0]\), where \(k\) is the rate constant and \([A_0]\) is the initial concentration.
  
- **Graphical Representation:** The straight line on the plot demonstrates a linear relationship as predicted by the first-order kinetics, with the slope being equal to \(-k\).

Understanding these concepts assists in predicting reaction behaviors and calculating reaction rates.
Transcribed Image Text:A chemical reaction is represented as follows: \[ A(aq) \rightarrow B(aq) + C(aq) \] A plot of \(\ln[A]\) versus time gives a straight line with a negative slope. What is the order of the reaction? **Explanation:** In chemical kinetics, if a plot of the natural logarithm of the concentration of a reactant (\(\ln[A]\)) versus time yields a straight line with a negative slope, this indicates that the reaction is first-order with respect to the reactant \(A\). The linear relationship suggests that the rate of reaction depends exponentially on the concentration of \(A\). **Key Concepts:** - **First-Order Reaction:** The rate is directly proportional to the concentration of one reactant. For a first-order reaction, the integrated rate law is \(\ln[A] = -kt + \ln[A_0]\), where \(k\) is the rate constant and \([A_0]\) is the initial concentration. - **Graphical Representation:** The straight line on the plot demonstrates a linear relationship as predicted by the first-order kinetics, with the slope being equal to \(-k\). Understanding these concepts assists in predicting reaction behaviors and calculating reaction rates.
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