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)+InA`
C. In `K="In 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. **Write the Arrhenius Equation**:
The Arrhenius equation is given by:
\[ k = A \cdot e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (Arrhenius constant)
- \( E_a \) = 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:
\[ \ln k = \ln A + \ln\left(e^{-\frac{E_a}{RT}}\right) \]

3. **Simplify the Right Side**:
Using the property of logarithms, \(\ln(e^x) = x\), we can simplify the right side:
\[ \ln k = \ln A - \frac{E_a}{RT} \]

4. **Rearranging the Equation**:
We can rearrange this equation to isolate \(\ln k\):
\[ \ln k - \ln A = -\frac{E_a}{RT} \]

5. **Expressing in Terms of \(k\)**:
We can express this in terms of \(k\) and \(A\):
\[ \frac{\ln k}{A} = -\frac{E_a}{RT} \]

6. **Final Form**:
The final expression we derive from the Arrhenius equation is:
\[ \ln k = \ln A - \frac{E_a}{RT} \]

### Conclusion:
The correct expression for the Arrhenius equation is:
\[ k = A \cdot e^{-\frac{E_a}{RT}} \]