The correct expression for Arrhenius equation is (where K is rate constant)

Options

A. `K=e^(-DeltaH//RT)A`
B. In `K=(DeltaE_a)/(RT)+lnA`
C. In `K="ln A" +E_a/(RT)`
D. In `(A/K)=E_a/(RT)`

Answer

To derive the correct expression for the Arrhenius equation, we start with the fundamental form of the equation and manipulate it step by step.

### Step-by-Step Solution:

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

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

3. **Rearranging the Equation**:
We can rearrange the equation to express \( \ln A \):
\[ \ln A = \ln k + \frac{E_a}{RT} \]

4. **Expressing in Terms of a Ratio**:
From the equation \( \ln k = \ln A - \frac{E_a}{RT} \), we can express it in terms of a ratio:
\[ \ln \left(\frac{A}{k}\right) = \frac{E_a}{RT} \]

5. **Final Form**:
Thus, the final expression derived from the Arrhenius equation is:
\[ \ln A - \ln k = \frac{E_a}{RT} \]
or equivalently,
\[ \ln \left(\frac{A}{k}\right) = \frac{E_a}{RT} \]

6. **Identifying the Correct Option**:
After deriving the above expressions, we compare them with the options provided in the question. The correct expression for the Arrhenius equation is:
\[ \ln k = \ln A - \frac{E_a}{RT} \]