The temperature coefficient of a certain reaction is found to be 3. If temperature changes from `25^@ " to " 55^@` , the new rate of reaction will be

Options

A. 8 times
B. 9 times
C. 16 times
D. 27 times

Answer

To solve the problem, we need to determine the new rate of reaction when the temperature is increased from \(25^\circ C\) to \(55^\circ C\), given that the temperature coefficient (\( \mu \)) of the reaction is 3.

### Step-by-Step Solution:

1. **Understand the Temperature Coefficient**:
The temperature coefficient (\( \mu \)) indicates how much the rate of reaction increases with a rise in temperature. A \( \mu \) of 3 means that for every 10°C increase in temperature, the rate of reaction increases by a factor of 3.

2. **Identify Initial and Final Temperatures**:
- Initial temperature (\( T_1 \)) = \( 25^\circ C \)
- Final temperature (\( T_2 \)) = \( 55^\circ C \)

3. **Calculate the Temperature Change**:
\[ \Delta T = T_2 - T_1 = 55^\circ C - 25^\circ C = 30^\circ C \]

4. **Determine the Number of 10°C Increments**:
Since the temperature coefficient is based on increments of 10°C, we need to find out how many 10°C increments are in the 30°C change:
\[ \text{Number of increments} = \frac{\Delta T}{10} = \frac{30}{10} = 3 \]

5. **Apply the Temperature Coefficient**:
The new rate of reaction (\( k_2 \)) can be calculated using the formula:
\[ \frac{k_2}{k_1} = \mu^{\text{number of increments}} = 3^3 \]

6. **Calculate \( 3^3 \)**:
\[ 3^3 = 27 \]

7. **Conclusion**:
The new rate of reaction (\( k_2 \)) will be:
\[ k_2 = 27 \times k_1 \]
Therefore, the new rate of reaction is 27 times the original rate.

### Final Answer:
The new rate of reaction will be **27 times** the original rate.

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