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

Explanation

To solve the problem of calculating the percentage change in the volume of a gas when its pressure is reduced to half, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- Let the initial pressure be \( P_1 \).
- Let the initial volume be \( V_1 \).
- Given that the pressure is reduced to half, the final pressure \( P_2 = \frac{P_1}{2} \).

2. **Use the Ideal Gas Law**:
- According to the ideal gas law, for a given mass of gas at constant temperature, we have:
\[ P_1 V_1 = P_2 V_2 \]
- Substitute \( P_2 \) into the equation:
\[ P_1 V_1 = \left(\frac{P_1}{2}\right) V_2 \]

3. **Rearrange the Equation**:
- To find the relationship between \( V_1 \) and \( V_2 \), rearranging gives:
\[ V_2 = \frac{2 P_1 V_1}{P_1} \]
- Simplifying this, we find:
\[ V_2 = 2 V_1 \]

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

5. **Calculate the 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 the volume of the gas when its pressure is reduced to half is **100%**.