For a third order reaction, which plot represents its kinetics?

For a third order reaction, which plot represents its kinetics?

• A. Concentration vs. time
• B. 1/[A] vs. time
• C. 1/(2[A]²) vs. time
• D. Ln[A] vs. time

Answer: (C)

For a third-order reaction, the relationship between the concentration of a reactant and time is represented through a specific plot based on the integrated rate law for third-order kinetics. The integrated rate law for a third-order reaction involving a single reactant A can be expressed as: \[ \frac{1}{2[A]^2} = kt + \text{constant} \] This equation indicates that the plot of \(1/(2[A]^2)\) versus time (where "t" is the time elapsed) will yield a straight line. The slope of this line is \(k\), the rate constant for the reaction. This characteristic behavior arises from the mathematical nature of third-order kinetics, where the rate of reaction is proportional to the square of the concentration of the reactant. In contrast, the other plots do not yield straight lines for third-order reactions. Concentration versus time shows a non-linear decay that does not reflect a simple correlation for third-order behavior. The plot of \(1/[A]\) versus time corresponds to a second-order reaction, while the natural log of concentration versus time represents first-order kinetics. Therefore, the correct choice for a third-order reaction's kinetics is the plot of \(1/(2[A]^2

For a third-order reaction, the relationship between the concentration of a reactant and time is represented through a specific plot based on the integrated rate law for third-order kinetics.

The integrated rate law for a third-order reaction involving a single reactant A can be expressed as:

[

\frac{1}{2[A]^2} = kt + \text{constant}

]

This equation indicates that the plot of (1/(2[A]^2)) versus time (where "t" is the time elapsed) will yield a straight line. The slope of this line is (k), the rate constant for the reaction. This characteristic behavior arises from the mathematical nature of third-order kinetics, where the rate of reaction is proportional to the square of the concentration of the reactant.

In contrast, the other plots do not yield straight lines for third-order reactions. Concentration versus time shows a non-linear decay that does not reflect a simple correlation for third-order behavior. The plot of (1/[A]) versus time corresponds to a second-order reaction, while the natural log of concentration versus time represents first-order kinetics. Therefore, the correct choice for a third-order reaction's kinetics is the plot of (1/(2[A]^2