The activation energy of a reaction can be determined from the slope of which of the following graphs ?

Options

A. in K Vs T
B. `("in" K)/(T) vs T `
C. ln K vs `(1)/(T)`
D. `(T)/("in"K)vs (I)/(T)`

Explanation

To determine the activation energy of a reaction from the slope of a graph, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The activation energy (EA) is related to the rate constant (k) and temperature (T) through the Arrhenius equation:
\[ k = A e^{-\frac{E_A}{RT}} \]
where A is the pre-exponential factor, R is the universal gas constant, and T is the temperature in Kelvin.

2. **Take the Natural Logarithm**: To linearize the Arrhenius equation, take the natural logarithm of both sides:
\[ \ln k = \ln A - \frac{E_A}{R} \cdot \frac{1}{T} \]

3. **Rearrange the Equation**: This can be rearranged into the form of a straight line:
\[ \ln k = -\frac{E_A}{R} \cdot \frac{1}{T} + \ln A \]
Here, if we let Y = \ln k and X = \frac{1}{T}, we can see that this is in the form of Y = MX + C, where:
- M (slope) = -\frac{E_A}{R}
- C (y-intercept) = \ln A

4. **Identify the Graph**: The graph that plots \(\ln k\) (Y-axis) against \(\frac{1}{T}\) (X-axis) will yield a straight line. The slope of this line is given by:
\[ \text{slope} = -\frac{E_A}{R} \]

5. **Conclusion**: From the slope of the graph of \(\ln k\) vs. \(\frac{1}{T}\), we can determine the activation energy (E_A) of the reaction.

### Final Answer:
The activation energy of a reaction can be determined from the slope of the graph of \(\ln k\) versus \(\frac{1}{T}\).