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 will use the concept of the temperature coefficient (Q10) and the relationship between the rate of a reaction at two different temperatures.

### Step-by-Step Solution:

1. **Understand the Temperature Coefficient (Q10)**:
The temperature coefficient (Q10) is defined as the factor by which the rate of a reaction increases when the temperature is raised by 10°C. In this case, Q10 = 3 means that for every 10°C increase in temperature, the rate of reaction triples.

2. **Identify the Initial and Final Temperatures**:
- Initial temperature (T1) = 25°C
- Final temperature (T2) = 55°C

3. **Calculate the Change in Temperature (ΔT)**:
ΔT = T2 - T1 = 55°C - 25°C = 30°C

4. **Determine the Number of 10°C Increments in ΔT**:
Since the temperature changes by 30°C, we can find the number of 10°C increments:
Number of increments = ΔT / 10 = 30°C / 10°C = 3

5. **Calculate the New Rate of Reaction**:
If the initial rate of reaction at 25°C is R (R25), then the new rate of reaction at 55°C (R55) can be calculated using the formula:
\[ R_{T2} = R_{T1} \times Q10^{\text{(number of increments)}} \]
Substituting the values:
\[ R_{55} = R_{25} \times 3^3 \]
\[ R_{55} = R_{25} \times 27 \]

6. **Conclusion**:
The new rate of reaction at 55°C will be 27 times the rate of reaction at 25°C.

### Final Answer:
The new rate of reaction at 55°C is **27 times the rate at 25°C**.

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