For a first order reaction the units of A in Arrhenius equation will be

Options

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

Explanation

To determine the units of the Arrhenius constant \( A \) in the Arrhenius equation for a first-order reaction, we can follow these steps:

### Step 1: Write down 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 Arrhenius constant,
- \( E_a \) 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 first-order reaction
For a first-order reaction, the rate of reaction can be expressed as:
\[ \text{Rate} = k \cdot [\text{Reactant}] \]
The unit of the rate of reaction is typically expressed as:
\[ \text{mole} \, \text{L}^{-1} \, \text{s}^{-1} \]
Since the concentration of the reactant is in moles per liter (\( \text{mol} \, \text{L}^{-1} \)), we can rearrange the equation to find the units of \( k \):
\[ k = \frac{\text{Rate}}{[\text{Reactant}]} = \frac{\text{mole} \, \text{L}^{-1} \, \text{s}^{-1}}{\text{mol} \, \text{L}^{-1}} = \text{s}^{-1} \]
Thus, the unit of \( k \) for a first-order reaction is \( \text{s}^{-1} \).

### Step 3: Conclude the units of the Arrhenius constant \( A \)
Since the Arrhenius constant \( A \) has the same units as the rate constant \( k \) for a first-order reaction, we conclude that:
\[ \text{Units of } A = \text{s}^{-1} \]

### Final Answer:
The units of \( A \) in the Arrhenius equation for a first-order reaction are \( \text{s}^{-1} \).

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