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]

Verified step by step guidance

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

Key Concepts

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.

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.

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.