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Chapter 56: Problem 3

A student obtains data for a second-order reaction at a given temperature, and then makes a graph of \(1 /(\mathrm{R})\) (along the vertical axis) versus \(t\) (along the horizontal axis). He notes that the resulting plot appears to correspond to a straight-line relationship. The student then determines the slope and intercept of the best-fit straight line. Describe how the student could use the slope and/or intercept of the best-fit straight line to determine: a) the rate constant for the reaction at the given temperature. b) the value of \((\mathrm{R})_{\mathrm{o}}\)

Short Answer

Expert verified
The rate constant for the reaction at the given temperature can be determined directly from the slope of the plot of \(1 /(\mathrm{R})\) versus \(t\). The initial reaction rate \((\mathrm{R})_{\mathrm{o}}\) can be obtained by taking the reciprocal of the intercept of the graph.

Step by step solution

01

Determine the rate constant

For a second-order reaction, the slope of a plot of \(1 /(\mathrm{R})\) versus \(t\) is equal to the rate constant (k). Therefore, the student can simply use the numerical value of the slope as the rate constant, k.
02

Determine \((\mathrm{R})_{\mathrm{o}}\)

The intercept on the vertical axis of the graph (at \(t = 0\)) represents \(1 /(\mathrm{R})_{\mathrm{o}}\), where \((\mathrm{R})_{\mathrm{o}}\) is the initial reaction rate. Hence, to find \((\mathrm{R})_{\mathrm{o}}\), one needs to simply take the reciprocal of the intercept.

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Most popular questions from this chapter

Recall that for a first-order reaction: $$ \ln (\mathrm{R})=\ln (\mathrm{R})_{0}-k t $$ a) When \(t=t_{1 / 2}\), what is the value of \((\mathrm{R})\) in terms of \((\mathrm{R})_{0}\) ? b) Show that \(t_{1 / 2}=\frac{\ln 2}{k}=\frac{0.693}{k}\) for a first-order reaction.

Recall that for a second-order reaction: $$ \frac{1}{(\mathrm{R})}=\frac{1}{(\mathrm{R})_{\mathrm{o}}}+k t $$ a) When \(t=t_{1 / 2}\), what is the value of \((\mathrm{R})\) in terms of \((\mathrm{R})_{0}\) ? b) Show that \(t_{1 / 2}=\frac{1}{k(\mathrm{R})_{\mathrm{o}}}\) for a second- order reaction.

A student obtains data for a first-order reaction at a given temperature, and then makes a graph of \(\ln (\mathrm{R})\) (along the vertical axis) versus \(t\) (along the horizontal axis). She notes that the resulting plot appears to correspond to a straight-line relationship. The student then determines the slope and intercept of the best-fit straight line. Describe how the student could use the slope and/or intercept of the best-fit straight line to determine: a) the rate constant for the reaction at the given temperature. b) the value of \((\mathrm{R})_{0}\)
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