If the rate of reaction increases by two times with every `10^@C` rise in temperature, then if we raise the temperature by `40^@C`, the new rate of the reaction will be :-

Options

A. 4 times
B. 8 times
C. 16 times
D. 32 times

Answer

To solve the problem, we need to determine how the rate of a reaction changes with an increase in temperature. The problem states that the rate of reaction doubles (increases by two times) for every 10°C rise in temperature. We are asked to find the new rate of reaction when the temperature is raised by 40°C.

### Step-by-Step Solution:

1. **Identify the Temperature Increase**:
We are given that the temperature is raised by 40°C.

2. **Determine the Number of 10°C Increments in 40°C**:
Since the temperature increases by 40°C, we can calculate how many 10°C increments fit into this increase:
\[ \text{Number of increments} = \frac{40°C}{10°C} = 4 \]

3. **Understand the Rate Change**:
The problem states that the rate of reaction doubles for each 10°C increase. Therefore, for each increment, the rate will be multiplied by 2.

4. **Calculate the Total Rate Increase**:
Since the rate doubles for each of the 4 increments, we can express the total increase in rate mathematically:
\[ \text{New Rate} = \text{Original Rate} \times 2^{\text{Number of increments}} = \text{Original Rate} \times 2^4 \]
Here, \(2^4 = 16\).

5. **Final Expression**:
Therefore, the new rate of the reaction after a 40°C increase in temperature will be:
\[ \text{New Rate} = 16 \times \text{Original Rate} \]

### Conclusion:
The new rate of the reaction will be **16 times the original rate**.

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