Understanding the Arrhenius Equation and Rate Constant Plots

The Arrhenius equation describes how the rate constant (k) of a chemical reaction depends on temperature (T). It is given by:

$k=A{e}^{-\frac{E_a}{RT}}$

where:

• $k$ is the rate constant
• $A$ is the pre-exponential factor (frequency factor)
• $E_a$ is the activation energy
• $R$ is the universal gas constant
• $T$ is the absolute temperature (in Kelvin)

Step 1: Linear Form of the Arrhenius Equation

To understand the graphical relationship, we take the natural logarithm of both sides of the equation:

$\ln k=\ln A-\frac{E_a}{RT}$

This equation has the form of a straight line, $y=mx+c$, where:

• $y=\ln k$
• $x=\frac{1}{T}$
• $m=-\frac{E_a}{R}$ (slope)
• $c=\ln A$ (y-intercept)

Step 2: Identifying the Correct Plot

Therefore, a plot that follows the Arrhenius equation must be a graph of $\ln k$ vs. $\frac{1}{T}$. This plot will yield a straight line with a negative slope.

Looking at the provided options, the correct plot is the one where the y-axis is $\ln k$ and the x-axis is $\frac{1}{T}$, showing a straight line decreasing from left to right.

Final Answer

The plot that follows the Arrhenius equation is the one where ln k is plotted against 1/T, resulting in a straight line with a negative slope. Based on the standard representation of these options, this is most likely the second image from the top.

Related Topics

• Chemical Kinetics
• Activation Energy
• Temperature Dependence of Reaction Rates
• Collision Theory

Key Formulae and Theory

Arrhenius Equation: $k=A{e}^{-\frac{E_a}{RT}}$

Linear Form: $\ln k=\ln A-\frac{E_a}{RT}$

Slope and Intercept: The slope of the line $\ln k vs \frac{1}{T}$ is $-\frac{E_a}{R}$, from which the activation energy $E_a$ can be calculated. The y-intercept is equal to $\ln A$.