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Ch.14 - Chemical Kinetics
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 14, Problema 10b

The accompanying graph shows plots of ln k versus 1>T for two different reactions. The plots have been extrapolated to the y-intercepts. Which reaction (red or blue) has (b) the larger value for the frequency factor, A? [Section 14.5]
Graph showing ln k vs 1/T for two reactions, indicating their frequency factors.

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Identify the Arrhenius equation in its linear form: \( \ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T} \).
Recognize that the y-intercept of the plot of \( \ln k \) versus \( \frac{1}{T} \) corresponds to \( \ln A \).
Observe the graph and note the y-intercepts for both Reaction 1 (blue) and Reaction 2 (red).
Determine which reaction has the higher y-intercept value, as this indicates a larger \( \ln A \) value.
Conclude that the reaction with the higher y-intercept has the larger frequency factor, \( A \).

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Arrhenius Equation

The Arrhenius equation relates the rate constant (k) of a reaction to temperature (T) and the frequency factor (A). It is expressed as k = A * e^(-Ea/RT), where Ea is the activation energy and R is the gas constant. The frequency factor A represents the number of collisions that result in a reaction, and it is influenced by factors such as molecular orientation and collision frequency.
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Arrhenius Equation

Graphical Interpretation of ln k vs. 1/T

In a plot of ln k versus 1/T, the slope of the line is equal to -Ea/R, where Ea is the activation energy. The y-intercept of this plot corresponds to ln A, allowing for the determination of the frequency factor A. A higher y-intercept indicates a larger frequency factor, suggesting that the reaction has a greater likelihood of occurring due to more effective collisions.
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Extrapolation of Graphs

Extrapolation involves extending the plotted lines of the graph to find values outside the measured data range. In this context, extrapolating the lines to the y-intercept allows for the determination of the frequency factors for both reactions. By comparing the y-intercepts of the two reactions, one can ascertain which reaction has the larger frequency factor, A.
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