For a certain reaction the variation of rate constant with temperature is given by the equation
`ln k_(t) = lnk_(0) + ((ln 3)t)/(10) (t ge 0^(@)C)`
The value of temperature coefficient of the reaction is

Options

A. 0.1
B. 1
C. 10
D. 3

Answer

To find the temperature coefficient of the reaction based on the given equation for the variation of the rate constant with temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Equation**:
The equation provided is:
\[ \ln k_T = \ln k_0 + \frac{\ln 3}{10} T \]
where \( k_T \) is the rate constant at temperature \( T \) and \( k_0 \) is the rate constant at a reference temperature (usually 0°C).

2. **Identify the Temperature Coefficient Formula**:
The temperature coefficient \( \mu \) is defined as:
\[ \frac{k_T}{k_0} = \mu^{(T - 0)} \]
This can be rearranged to:
\[ \ln k_T - \ln k_0 = (T - 0) \ln \mu \]

3. **Rewrite the Given Equation**:
From the given equation, we can express the left-hand side:
\[ \ln k_T - \ln k_0 = \frac{\ln 3}{10} T \]

4. **Set the Two Equations Equal**:
Now we can equate the two expressions we have for \( \ln k_T - \ln k_0 \):
\[ \frac{\ln 3}{10} T = T \ln \mu \]

5. **Cancel \( T \) from Both Sides**:
Assuming \( T \) is not zero (since \( T \geq 0 \)), we can divide both sides by \( T \):
\[ \frac{\ln 3}{10} = \ln \mu \]

6. **Solve for \( \mu \)**:
To find \( \mu \), we exponentiate both sides:
\[ \mu = e^{\frac{\ln 3}{10}} = 3^{\frac{1}{10}} \]

7. **Final Result**:
The temperature coefficient \( \mu \) is:
\[ \mu = 3^{0.1} \]

### Conclusion:
The value of the temperature coefficient of the reaction is \( 3^{0.1} \).