Question

Arrhenius equation represents graphically the variation between the:

• A. Rate constant and temperature
• B. Rate of reaction and temperature
• C. Activation energy and temperature
• D. Frequency factor and temperature

Hint:

Plotting \( \ln k \) vs \( \frac{1}{T} \) gives a straight line — this is the graphical form of the Arrhenius equation, linking rate constant and temperature.

Answer 1

The Correct Option is A

Step 1: Arrhenius Equation
The Arrhenius equation provides a quantitative relationship between the rate constant \( k \) of a reaction and the absolute temperature \( T \): \[ k = A e^{-E_a/RT} \] Taking natural logarithm on both sides: \[ \ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T} \] This is a linear equation of the form \( y = mx + c \), where:
\( y = \ln k \)
\( x = \frac{1}{T} \)
Slope \( m = -\frac{E_a}{R} \)
Intercept \( c = \ln A \) Step 2: What It Graphically Represents
A plot of \( \ln k \) versus \( \frac{1}{T} \) yields a straight line. Therefore, the Arrhenius equation graphically represents the relationship between: - Rate constant \( k \) and - Temperature \( T \) Step 3: Eliminating Incorrect Options
- (B) and (C): Refer to different dependencies, not directly plotted in the Arrhenius form.
- (D): Frequency factor \( A \) is a constant at a given temperature, not plotted against \( T \). Conclusion: The Arrhenius equation graphically shows the variation between the rate constant and temperature.