Arrhenius equation may be written as

Options

A. `(d ln K)/(dT) = E_(a)/RT`
B. `(d ln K)/(dT)= E_(a)/(RT)^(2)`
C. `(d ln K)/(dT) = - (E_(a)/RT)`
D. `(d ln K)/(dT) = - (E_(a)/(RT)^(2))`

Explanation

To write the Arrhenius equation, we start with the relationship between the rate constant (k) and temperature (T). The Arrhenius equation can be expressed in a standard form as follows:

1. **Understanding the Rate Constant (k)**:
The rate constant (k) is a crucial part of chemical kinetics, representing the speed of a reaction at a given temperature.

2. **Starting with the Fundamental Relationship**:
The fundamental relationship can be derived from the change in the natural logarithm of the rate constant with respect to time:
\[ \frac{d \ln k}{dt} = \frac{E_a}{RT^2} \]
Here, \(E_a\) is the activation energy, \(R\) is the universal gas constant, and \(T\) is the absolute temperature.

3. **Integrating the Equation**:
To derive the Arrhenius equation, we integrate this expression. However, we can directly write the Arrhenius equation in its exponential form:
\[ k = A \cdot e^{-\frac{E_a}{RT}} \]
where \(A\) is the pre-exponential factor, which is a constant that represents the frequency of collisions and the orientation of reactant molecules.

4. **Understanding the Components**:
- \(k\): Rate constant
- \(A\): Pre-exponential factor
- \(E_a\): Activation energy
- \(R\): Universal gas constant (8.314 J/(mol·K))
- \(T\): Absolute temperature in Kelvin

5. **Final Formulation**:
The Arrhenius equation is therefore expressed as:
\[ k = A \cdot e^{-\frac{E_a}{RT}} \]