The volume of a given mass of a gas is reduced to `1/4`th of its initial value of at constant temperature. Calculate the percentage change in the pressure of the gas.

Explanation

To solve the problem, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. This can be mathematically expressed as:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume

### Step-by-Step Solution:

1. **Identify Initial and Final Volumes**:
- Let the initial volume \( V_1 \) be \( V \).
- The final volume \( V_2 \) is given as \( \frac{1}{4} V_1 \), so \( V_2 = \frac{1}{4} V \).

2. **Apply Boyle's Law**:
- According to Boyle's Law:
\[ P_1 V_1 = P_2 V_2 \]
- Substitute \( V_2 \):
\[ P_1 V = P_2 \left(\frac{1}{4} V\right) \]

3. **Solve for Final Pressure \( P_2 \)**:
- Rearranging the equation gives:
\[ P_2 = \frac{P_1 V}{\frac{1}{4} V} = P_1 \cdot 4 \]
- Thus, \( P_2 = 4 P_1 \).

4. **Calculate the Change in Pressure**:
- The change in pressure \( \Delta P \) is given by:
\[ \Delta P = P_2 - P_1 = 4 P_1 - P_1 = 3 P_1 \]

5. **Calculate the Percentage Change in Pressure**:
- The percentage change in pressure is calculated as:
\[ \text{Percentage Change} = \left(\frac{\Delta P}{P_1}\right) \times 100 \]
- Substitute \( \Delta P \):
\[ \text{Percentage Change} = \left(\frac{3 P_1}{P_1}\right) \times 100 = 3 \times 100 = 300\% \]

### Final Answer:
The percentage change in the pressure of the gas is **300%**.