Arrhenius studies the effect of temperature on the rate of a reaction and postulted that rate constant varies with temperature exponentially as `k=Ae^(E_(a)//RT)` . Thuis method is generally used for finding the activation energy of a reaction. Keeping temperature constant, the effect of catalyst on the activation energy has also been studied.
The pre-exponetial factor in the Arrhenius equation of a first order reaction has the unit :

Options

A. mol `L^(-1)s^(-1)`
B. L `mol^(1)s^(-1)`
C. `s^(-1)`
D. `dimensionaless

Answer

To determine the unit of the pre-exponential factor (A) in the Arrhenius equation for a first-order reaction, we can follow these steps:

### Step 1: Understand the Arrhenius Equation
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (frequency factor)
- \( E_a \) = activation energy
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

### Step 2: Identify the Unit of the Rate Constant (k)
For a first-order reaction, the unit of the rate constant \( k \) is:
\[ \text{Unit of } k = \text{s}^{-1} \]
This is because the rate of a first-order reaction is given in terms of concentration per unit time (e.g., mol/L/s).

### Step 3: Analyze the Arrhenius Equation
In the Arrhenius equation, since \( e^{-\frac{E_a}{RT}} \) is a dimensionless quantity (as it is an exponential function), the unit of \( A \) must match the unit of \( k \) to maintain dimensional consistency.

### Step 4: Determine the Unit of the Pre-exponential Factor (A)
Since we established that the unit of \( k \) for a first-order reaction is \( \text{s}^{-1} \), the unit of the pre-exponential factor \( A \) must also be:
\[ \text{Unit of } A = \text{s}^{-1} \]

### Conclusion
Thus, the unit of the pre-exponential factor in the Arrhenius equation for a first-order reaction is:
\[ \text{s}^{-1} \text{ or } \text{reciprocal of time} \]