Arrhenius studied the effect of temperature on the rate of a reaction and postulated that rate constant varies with temperature exponentially as `k=Ae^(-E_(a)//RT)`. For most of the reactions, it was found that the temperature coefficient of the reaction lies between 2 to 3. The 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 by studying how much the rate of reaction changes in the presence of catalyst. In most of the cases, it is observed that catalyst lowers the activation energy barrier and increases the rate of reaction.
The pre-exponential factor in the Arrhenus equation of second order reaction has the units

Options

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

Explanation

To find the units of the pre-exponential factor \( A \) in the Arrhenius equation for a second-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:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

### Step 2: Identify the Units of the Rate Constant \( k \)
For a second-order reaction, the units of the rate constant \( k \) are:
\[ \text{Units of } k = \text{(concentration)}^{-1} \times \text{(time)}^{-1} = \text{mol L}^{-1} \text{s}^{-1} \]

### Step 3: Relate the Units of \( A \) to the Units of \( k \)
Since the pre-exponential factor \( A \) is multiplied by the exponential term (which is dimensionless), the units of \( A \) must be the same as the units of \( k \). Therefore:
\[ \text{Units of } A = \text{Units of } k = \text{mol L}^{-1} \text{s}^{-1} \]

### Step 4: Write the Final Answer
Thus, the units of the pre-exponential factor \( A \) for a second-order reaction are:
\[ \text{mol L}^{-1} \text{s}^{-1} \]