The temperature coefficient of a reaction is 2. When the temperature is increases from `30 ^@C " to " 90^@C` , the rate of reaction is increased by

Options

A. 150 times
B. 410 times
C. 72 times
D. 64 times

Answer

To solve the problem, we need to determine how much the rate of a reaction increases when the temperature is raised from 30 °C to 90 °C, given that the temperature coefficient (Q10) of the reaction is 2.

### Step-by-Step Solution:

1. **Understand the Temperature Coefficient**:
The temperature coefficient (Q10) indicates how much the rate of a reaction increases when the temperature is raised by 10 °C. In this case, Q10 = 2 means that for every increase of 10 °C, the rate of the reaction doubles.

2. **Calculate the Temperature Change**:
The temperature change (ΔT) from 30 °C to 90 °C is:
\[ \Delta T = 90 °C - 30 °C = 60 °C \]

3. **Determine the Number of 10 °C Intervals**:
Since the temperature increases by 60 °C, we can find out how many 10 °C intervals are in this change:
\[ \text{Number of intervals} = \frac{\Delta T}{10 °C} = \frac{60 °C}{10 °C} = 6 \]

4. **Calculate the Rate Increase**:
Since the rate doubles for each 10 °C increase, we can express the rate increase after 6 intervals as:
\[ \text{Rate increase} = 2^6 \]
This is because the rate doubles for each interval.

5. **Calculate \(2^6\)**:
\[ 2^6 = 64 \]

6. **Final Result**:
Therefore, the rate of the reaction at 90 °C (R2) is 64 times the rate at 30 °C (R1):
\[ R2 = 64 \times R1 \]

### Conclusion:
The rate of reaction increases by a factor of 64 when the temperature is raised from 30 °C to 90 °C.