Question

Enzyme activation energy \((E_{a})\) for thermal decomposition of glucose in a first-order reaction is calculated by

• A. The x-axis intercept of the Arrhenius plot
• B. The y-axis intercept of the Arrhenius plot
• C. Slope of the Arrhenius plot
• D. Rate constant at room temperature

Hint:

Arrhenius plot is a valuable tool to determine kinetic parameters such as activation energy and frequency factor from temperature-dependent rate constant data.

Answer 1

The Correct Option is C

The activation energy \( E_a \) of a reaction is a fundamental parameter in chemical kinetics that indicates the minimum energy required for reactants to undergo a successful transformation into products. It can be calculated using the \textit{Arrhenius equation}: \[ k = A e^{-E_a / RT} \] Taking the natural logarithm of both sides: \[ \ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T} \] This is the equation of a straight line: \[ y = mx + c \] Where: - \( y = \ln k \)
- \( x = \frac{1}{T} \)
- Slope \( m = -\frac{E_a}{R} \)
- \( R \) = gas constant (8.314 \, \text{J/mol·K})
Hence, the \textit{activation energy} is calculated from the \textit{slope of the Arrhenius plot} (which is a plot of \( \ln k \) versus \( \frac{1}{T} \)). The slope gives \( -\frac{E_a}{R} \), and multiplying this by \( -R \) yields the value of \( E_a \).