According to the Arrhenius equation a straight line is to be obtained by plotting the logarithm of the rate constant of a chemical reaction `(log k)` against

Options

A. `T`
B. `log T`
C. `1//T`
D. `log 1//T`

Explanation

To solve the question regarding the Arrhenius equation and the relationship between the logarithm of the rate constant (log k) and temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Arrhenius Equation**:
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
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 absolute temperature.

2. **Take the Logarithm of Both Sides**:
To analyze the equation, we take the logarithm of both sides:
\[ \log k = \log A - \frac{E_a}{RT \cdot 2.303} \]
Here, we have used the change of base formula for logarithms.

3. **Rearrange the Equation**:
We can rearrange the equation to express it in a linear form:
\[ \log k = \log A - \left(\frac{E_a}{2.303R}\right) \cdot \frac{1}{T} \]
This can be compared to the linear equation \( y = mx + c \), where:
- \( y = \log k \)
- \( m = -\frac{E_a}{2.303R} \) (the slope)
- \( x = \frac{1}{T} \)
- \( c = \log A \) (the y-intercept)

4. **Identify the Variables for Plotting**:
From the rearranged equation, we see that if we plot \( \log k \) (y-axis) against \( \frac{1}{T} \) (x-axis), we will obtain a straight line.

5. **Conclusion**:
Therefore, according to the Arrhenius equation, a straight line is obtained by plotting the logarithm of the rate constant \( (\log k) \) against \( \frac{1}{T} \).

### Final Answer:
The correct answer is that a straight line is obtained by plotting \( \log k \) against \( \frac{1}{T} \).