Which one of the following does not represent Arrhenius equation?

Options

A. `K = Ae^(-E/(RT))`
B. `log_ek = log_eA - E/(RT)`
C. `log_10k = log_10 A - E/(2.303RT)`
D. `k =AE^(-RT)`

Answer

To determine which of the given options does not represent the Arrhenius equation, we first need to recall the standard forms of the Arrhenius equation.

### Step 1: Write the Arrhenius Equation
The Arrhenius equation is given by:

\[ k = A \cdot e^{-\frac{E_a}{RT}} \]

Where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

### Step 2: Identify Different Forms of the Arrhenius Equation
The Arrhenius equation can be expressed in different forms, including:

1. **Exponential Form**:
\[ k = A \cdot e^{-\frac{E_a}{RT}} \]

2. **Logarithmic Form**:
Taking the natural logarithm of both sides, we get:
\[ \ln k = \ln A - \frac{E_a}{RT} \]

3. **Base 10 Logarithm Form**:
Using base 10 logarithm:
\[ \log_{10} k = \log_{10} A - \frac{E_a}{2.303RT} \]

### Step 3: Analyze the Given Options
Now, we need to analyze the options provided in the question to see which one does not conform to the Arrhenius equation.

- **Option 1**: \( k = A \cdot e^{-\frac{E_a}{RT}} \) (This is the standard form of the Arrhenius equation)
- **Option 2**: \( \ln k = \ln A - \frac{E_a}{RT} \) (This is a logarithmic form of the Arrhenius equation)
- **Option 3**: \( \log_{10} k = \log_{10} A - \frac{E_a}{2.303RT} \) (This is also a valid form of the Arrhenius equation)
- **Option 4**: \( k = A \cdot e^{-rT} \) (This does not represent the Arrhenius equation as it incorrectly uses \( rT \) instead of \( \frac{E_a}{RT} \))

### Step 4: Conclusion
Based on the analysis, **Option 4** does not represent the Arrhenius equation.

### Final Answer
The option that does not represent the Arrhenius equation is:
**Option 4: \( k = A \cdot e^{-rT} \)**

---