Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation?

To determine which plot follows the Arrhenius equation, we first need to understand what the Arrhenius equation represents and how it relates the rate constant (k) to temperature (T). The Arrhenius equation is expressed as:

Understanding the Arrhenius Equation

The equation is given by:

k = A * e^(-Ea/(RT))

Where:

• k = rate constant
• A = pre-exponential factor (frequency factor)
• Ea = activation energy
• R = universal gas constant (8.314 J/(mol·K))
• T = absolute temperature in Kelvin

Interpreting the Equation

The Arrhenius equation indicates that the rate constant increases exponentially with an increase in temperature. This means that as temperature rises, the rate constant (k) should also increase, reflecting a higher reaction rate. The plot that follows the Arrhenius equation will typically show a curve that rises steeply as temperature increases.

Identifying the Correct Plot

When examining the plots, look for the following characteristics:

• A plot of ln(k) versus 1/T will yield a straight line with a negative slope, according to the linearized form of the Arrhenius equation: ln(k) = ln(A) - (Ea/R)(1/T).
• If the plot shows a direct exponential increase of k with T, it indicates that the relationship is consistent with the Arrhenius equation.
• Conversely, if the plot shows a decrease in k with increasing T or a non-linear relationship that does not resemble an exponential function, it does not follow the Arrhenius behavior.

Example of Plot Analysis

Imagine you have three plots:

• Plot A shows a linear increase in k with T.
• Plot B shows a curve that flattens out as T increases.
• Plot C shows an exponential rise in k as T increases.

In this case, Plot C would be the one that follows the Arrhenius equation, as it demonstrates the expected exponential relationship between the rate constant and temperature.

Conclusion

In summary, to identify which plot follows the Arrhenius equation, look for a plot that shows an exponential increase in the rate constant with temperature. If you can visualize or analyze the plots based on these criteria, you should be able to determine the correct one effectively.