The pressure of a gas of given mass of constant temperature is reduced to half of its value. Calculate the percentage change in its volume.

Explanation

To solve the problem, we will use Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure (P) and volume (V) are inversely proportional. This means that:

\[ P_1 V_1 = P_2 V_2 \]

### Step-by-Step Solution:

1. **Identify Initial Conditions:**
Let the initial pressure be \( P_1 \) and the initial volume be \( V_1 \).

2. **Determine Final Pressure:**
According to the problem, the pressure is reduced to half its value:
\[ P_2 = \frac{P_1}{2} \]

3. **Apply Boyle's Law:**
Using Boyle's Law:
\[ P_1 V_1 = P_2 V_2 \]
Substitute \( P_2 \) with \( \frac{P_1}{2} \):
\[ P_1 V_1 = \left(\frac{P_1}{2}\right) V_2 \]

4. **Solve for Final Volume \( V_2 \):**
Rearranging the equation to solve for \( V_2 \):
\[ V_2 = \frac{P_1 V_1}{\frac{P_1}{2}} = 2 V_1 \]

5. **Calculate Change in Volume:**
The change in volume \( \Delta V \) is given by:
\[ \Delta V = V_2 - V_1 = 2 V_1 - V_1 = V_1 \]

6. **Calculate Percentage Change in Volume:**
The percentage change in volume can be calculated using the formula:
\[ \text{Percentage Change} = \left(\frac{\Delta V}{V_1}\right) \times 100 \]
Substituting \( \Delta V \):
\[ \text{Percentage Change} = \left(\frac{V_1}{V_1}\right) \times 100 = 100\% \]

### Final Answer:
The percentage change in volume is **100%**.

---