Question

Given below are graphs showing the variation in velocity constant with temperature on the Kelvin scale. Identify the graph which represents the Arrhenius equation.

• A. D
• B. C
• C. A
• D. B

Hint:

Remember that the Arrhenius equation describes the temperature dependence of the reaction rate constant. A graph of \( \ln k \) versus \( \frac{1}{T} \) should yield a straight line, and the slope of this line is related to the activation energy.

Answer 1

The Correct Option is D

The Arrhenius equation is given by: \[ k = A e^{-\frac{E_a}{RT}} \] where: - \( k \) is the rate constant, - \( A \) is the pre-exponential factor, - \( E_a \) is the activation energy, - \( R \) is the universal gas constant, and - \( T \) is the temperature in Kelvin. Taking the natural logarithm of both sides, we get: \[ \ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T} \] This equation shows a linear relationship between \(\ln k\) and \( \frac{1}{T} \). Therefore, when the graph of \(\ln k\) is plotted against \( \frac{1}{T} \), we expect a straight line with a negative slope proportional to the activation energy \( E_a \). From the given options, the correct graph corresponding to the Arrhenius equation is the one showing a straight-line decrease with increasing \( \frac{1}{T} \), which corresponds to Option (D)