The rate of reaction becomes two times for every `10^(@)C` rise in temperature. If the rate of reaction increases by 32 times when the temperature is increased from `30^(@)C` to `10x^(@)`C`. Then X=

Explanation

To solve the problem, we need to determine the value of \( x \) given the conditions of the reaction rate and temperature changes.

### Step-by-Step Solution:

1. **Understanding the Rate of Reaction**:
The problem states that the rate of reaction doubles for every \( 10^\circ C \) rise in temperature. This means that the temperature coefficient \( \mu \) is equal to 2.

2. **Setting Up the Equation**:
The rate of reaction at the final temperature divided by the rate at the initial temperature can be expressed as:
\[ \frac{R_f}{R_i} = \mu^n \]
where \( n \) is the number of \( 10^\circ C \) intervals between the initial and final temperatures.

3. **Identifying the Initial and Final Temperatures**:
The initial temperature \( T_i \) is \( 30^\circ C \) and the final temperature \( T_f \) is \( 10x^\circ C \). Thus, the change in temperature \( \Delta T \) is:
\[ \Delta T = T_f - T_i = 10x - 30 \]

4. **Calculating \( n \)**:
Since \( n \) is the number of \( 10^\circ C \) intervals, we can express it as:
\[ n = \frac{\Delta T}{10} = \frac{10x - 30}{10} = x - 3 \]

5. **Using the Given Rate Increase**:
According to the problem, the rate of reaction increases by 32 times when the temperature is increased:
\[ \frac{R_f}{R_i} = 32 \]

6. **Setting Up the Equation**:
Now we can set up the equation:
\[ 32 = 2^{(x - 3)} \]

7. **Expressing 32 as a Power of 2**:
We know that \( 32 = 2^5 \). Therefore, we can equate the exponents:
\[ x - 3 = 5 \]

8. **Solving for \( x \)**:
Adding 3 to both sides gives:
\[ x = 5 + 3 = 8 \]

### Final Answer:
The value of \( x \) is \( 8 \).

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