The rate of a chemical reaction doubles for every `10^(@)C` rise in temperature. If the temperature is increased by `60^(@)C` the rate of reaction increases by about

Options

A. 20 times
B. 32 times
C. 64 times
D. 128 times

Explanation

To solve the problem, we need to determine how much the rate of a chemical reaction increases when the temperature is raised by 60°C, given that the rate doubles for every 10°C increase in temperature.

### Step-by-Step Solution:

1. **Understand the Doubling Rate**:
The problem states that the rate of reaction doubles for every 10°C rise in temperature. This means that if we denote the initial rate as \( r_1 \), after a 10°C increase, the new rate \( r_2 \) will be:
\[ r_2 = 2 \times r_1 \]

2. **Calculate the Number of 10°C Increments in 60°C**:
We need to find out how many 10°C increments are in a 60°C increase. This can be calculated as:
\[ n = \frac{60°C}{10°C} = 6 \]
This means there are 6 increments of 10°C in a 60°C increase.

3. **Determine the Rate Increase**:
Since the rate doubles with each 10°C increase, after 6 increments, the rate will increase by a factor of \( 2^n \) where \( n \) is the number of increments. Thus, we calculate:
\[ \text{Rate Increase} = 2^6 \]
Calculating \( 2^6 \):
\[ 2^6 = 64 \]

4. **Final Result**:
Therefore, when the temperature is increased by 60°C, the rate of reaction increases by a factor of 64. If the initial rate is \( r_1 \), the new rate \( r_2 \) will be:
\[ r_2 = 64 \times r_1 \]

### Conclusion:
The rate of reaction increases by about **64 times** when the temperature is increased by 60°C.

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