Arrhenius equation is:

Options

A. `d(Ink)/(dT) = (DeltaE^(+))/(RT)`
B. `(dInK)/(dT)=(DeltaE^(+))/(RT)^2`
C. `(dInK)/(dT)=-(DeltaE^(+))/(RT)^2`
D. `(dInK)/(dT)=-(DeltaE^(+))/(RT)`

Answer

To answer the question regarding the Arrhenius equation, we will break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Arrhenius Equation**:
The Arrhenius equation describes how the rate constant \( k \) of a reaction depends on temperature \( T \) and activation energy \( E \). The equation is given by:
\[ k = A e^{-\frac{E}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (also known as frequency factor)
- \( E \) = activation energy
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

2. **Taking the Natural Logarithm**:
To linearize the Arrhenius equation, we take the natural logarithm of both sides:
\[ \ln k = \ln A - \frac{E}{RT} \]
This equation shows a linear relationship between \( \ln k \) and \( \frac{1}{T} \).

3. **Identifying Variables**:
From the equation \( \ln k = \ln A - \frac{E}{RT} \), we can identify:
- The slope of the line when plotting \( \ln k \) versus \( \frac{1}{T} \) is \( -\frac{E}{R} \).
- The intercept of the line is \( \ln A \).

4. **Differentiating the Equation**:
If we want to find how the rate constant \( k \) changes with temperature \( T \), we can differentiate the equation:
\[ \frac{d \ln k}{dT} = \frac{E}{RT^2} \]
This shows how the natural logarithm of the rate constant changes with temperature.

5. **Conclusion**:
The Arrhenius equation is fundamental in chemical kinetics as it quantifies the effect of temperature on reaction rates. The activation energy \( E \) is a crucial parameter that indicates how much energy is needed for the reaction to occur.