The temperature dependence of rate constant (k) of a chemical reaction is written in terms of Arrhenius equation, `k=Ae^(-E_(a)//RT))` Activation energy `(E_(a))` of the reaction can be calculate by plotting

Options

A. `log k vs (1)/(T)`
B. `log k vs (1)/(logT)`
C. `k vs T`
D. `k vs (1)/(logT)`

Explanation

To calculate the activation energy (Ea) of a chemical reaction using the Arrhenius equation, we can follow these steps:

### Step-by-Step Solution:

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

2. **Take the Natural Logarithm**:
To linearize the equation, take the natural logarithm of both sides:
\[ \ln k = \ln A - \frac{E_a}{RT} \]

3. **Rearrange the Equation**:
Rearranging gives us:
\[ \ln k = -\frac{E_a}{R} \cdot \frac{1}{T} + \ln A \]
This is in the form of \( y = mx + c \) where:
- \( y = \ln k \)
- \( m = -\frac{E_a}{R} \)
- \( x = \frac{1}{T} \)
- \( c = \ln A \)

4. **Plot the Graph**:
Plot a graph of \( \ln k \) (y-axis) versus \( \frac{1}{T} \) (x-axis). The slope of this line will be:
\[ \text{slope} = -\frac{E_a}{R} \]

5. **Calculate the Activation Energy**:
From the slope of the graph, you can calculate the activation energy (Ea) using:
\[ E_a = -\text{slope} \cdot R \]
where \( R \) is the gas constant (8.314 J/mol·K).

### Conclusion:
By plotting \( \ln k \) against \( \frac{1}{T} \), the activation energy \( E_a \) can be determined from the slope of the resulting line.

---