The temperature coefficient of a reaction is 2. When the temperature is increased from `30^(@)C` to `90^(@)C`, the rate of reaction is increased by x times. Value of x is ?

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Temperature Coefficient**:
The temperature coefficient (μ) indicates how much the rate of reaction increases for every 10°C rise in temperature. Here, μ = 2 means that for every 10°C increase, the rate of reaction doubles.

2. **Calculate the Temperature Change**:
We need to find the total temperature change (ΔT) when the temperature is increased from 30°C to 90°C.
\[ \Delta T = T_2 - T_1 = 90°C - 30°C = 60°C \]

3. **Determine the Number of 10°C Increments**:
Since the temperature coefficient applies to every 10°C increase, we need to find out how many 10°C increments are in a 60°C change.
\[ \text{Number of increments} = \frac{\Delta T}{10°C} = \frac{60°C}{10°C} = 6 \]

4. **Calculate the Rate Increase**:
The rate of reaction increases by a factor of 2 for each 10°C rise. Therefore, for 6 increments, the rate increases by:
\[ \text{Rate increase} = 2^{\text{Number of increments}} = 2^6 = 64 \]

5. **Conclusion**:
The rate of reaction at 90°C is 64 times the rate of reaction at 30°C. Therefore, the value of \( x \) is:
\[ x = 64 \]

### Final Answer:
The value of \( x \) is 64.