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 step by step, we will use the concept of the temperature coefficient (denoted as \( Q \)) of a reaction, which indicates how much the rate of a reaction increases with a 10°C rise in temperature.

### Step-by-Step Solution:

1. **Understand the Temperature Coefficient**:
The temperature coefficient \( Q \) is given as 2. This means that for every increase of 10°C in temperature, the rate of reaction doubles.

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

3. **Determine the Number of 10°C Increments**:
Since the temperature change is \( 60°C \), we can find how many 10°C increments are there:
\[ n = \frac{\Delta T}{10°C} = \frac{60°C}{10°C} = 6 \]

4. **Calculate the Rate Increase**:
The rate of reaction increases by a factor of \( Q^n \). Therefore, we calculate:
\[ \text{Rate Increase} = Q^n = 2^6 \]

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

6. **Conclusion**:
Thus, when the temperature is increased from \( 30°C \) to \( 90°C \), the rate of reaction increases by a factor of 64.

### Final Answer:
The rate of reaction is increased by **64 times**.

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