Question

Which one of the following does not represent the Arrhenius equation?

• A. \( \log k = \log A - \frac{E_a}{2.303RT} \)
• B. \( k = A e^{-\frac{E_a}{RT}} \)
• C. \( \ln k = -\frac{E_a}{RT} + \ln A \)
• D. \( k = A e^{\frac{E_a}{RT}} \)

Hint:

The Arrhenius equation shows that higher Ea​ reduces the rate constant, disproving an exponential increase with Ea​.

Answer 1

The Correct Option is D

The Arrhenius equation is fundamental in chemical kinetics and is used to express the temperature dependence of reaction rates. It is defined as:

\(k = A e^{-\frac{E_a}{RT}}\) 

Where:

• \( k \) = Rate constant
• \( A \) = Pre-exponential factor (frequency factor)
• \( E_a \) = Activation energy
• \( R \) = Universal gas constant
• \( T \) = Temperature in Kelvin

Each of the given options is analyzed below:

1. \(\log k = \log A - \frac{E_a}{2.303RT}\)
   This is a logarithmic form of the Arrhenius equation, expressed in base 10 logarithms.
2. \(k = A e^{-\frac{E_a}{RT}}\)
   This is the standard form of the Arrhenius equation, showing the dependency of the rate constant on temperature.
3. \(\ln k = -\frac{E_a}{RT} + \ln A\)
   This is another logarithmic form of the Arrhenius equation, expressed in natural logarithms.
4. \(k = A e^{\frac{E_a}{RT}}\)
   This equation suggests that as the activation energy increases, the rate constant would absurdly increase exponentially, which contradicts the phenomena described by Arrhenius' theory. Hence, it does not represent the Arrhenius equation.

Conclusively, the equation \(k = A e^{\frac{E_a}{RT}}\) does not represent the Arrhenius equation correctly. In the Arrhenius equation, the exponential part of the expression should have a negative exponent to match the physical observation that higher activation energies lead to lower reaction rates at a given temperature.