The rate of a reaction becomes 2 times for every `10^@C` rise in temperature . How many times rate of reaction will be increased when temperature is increased from `30^@ C " to " 80^@C` ?

Options

A. 16
B. 32
C. 64
D. 128

Answer

To solve the problem, we need to determine how many times the rate of reaction increases when the temperature is raised from 30°C to 80°C, given that the rate doubles for every 10°C increase in temperature.

### Step-by-Step Solution:

1. **Identify the Temperature Change**:
- The initial temperature (T1) is 30°C.
- The final temperature (T2) is 80°C.
- The change in temperature (ΔT) is calculated as:
\[ ΔT = T2 - T1 = 80°C - 30°C = 50°C \]

2. **Determine the Number of 10°C Increments**:
- Since the rate of reaction doubles for every 10°C increase, we need to find out how many 10°C increments fit into the total temperature change of 50°C.
- The number of increments (n) is given by:
\[ n = \frac{ΔT}{10°C} = \frac{50°C}{10°C} = 5 \]

3. **Calculate the Rate Increase**:
- The rate of reaction increases by a factor of 2 for each 10°C increment. Therefore, after 5 increments, the increase in rate can be calculated using the formula:
\[ \text{Rate Increase} = 2^n = 2^5 \]
- Calculating \(2^5\):
\[ 2^5 = 32 \]

4. **Conclusion**:
- Therefore, the rate of reaction will increase by a factor of 32 when the temperature is increased from 30°C to 80°C.

### Final Answer:
The rate of reaction will increase by **32 times** when the temperature is increased from 30°C to 80°C.

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