The rate of a chemical reaction doubles for every `10^(@)C` rise of temperature. If the temperature is raised by `50^(@)C`, the rate of the reaction increases by about

Options

A. `10` times
B. `24` times
C. `32` times
D. `64` 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 50°C, given that the rate doubles for every 10°C rise in temperature.

### Step-by-Step Solution:

1. **Understand the Doubling Rate**: We know that for every increase of 10°C, the rate of reaction doubles. This means that if we start with a rate \( R \) at a certain temperature, after a 10°C increase, the new rate will be \( 2R \).

2. **Calculate the Number of 10°C Increments in 50°C**: Since we are increasing the temperature by 50°C, we can determine how many 10°C increments fit into this increase:
\[ \text{Number of increments} = \frac{50°C}{10°C} = 5 \]

3. **Determine the Rate Increase**: Since the rate doubles with each 10°C increase, we can express the increase in rate after 5 increments as:
\[ \text{New Rate} = R \times 2^5 \]
Here, \( 2^5 \) accounts for the rate doubling 5 times.

4. **Calculate \( 2^5 \)**:
\[ 2^5 = 32 \]
Therefore, the new rate of reaction after a 50°C increase is:
\[ \text{New Rate} = R \times 32 \]

5. **Conclusion**: The rate of the reaction increases by a factor of 32 when the temperature is raised by 50°C.

### Final Answer:
The rate of the reaction increases by about **32 times** when the temperature is raised by 50°C.

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