The percentage change in the pressure of a given mass of a gas at constant temperature is 50% (increases). Calculate the percentage in the pressure of the gas.

Answer

To solve the problem, we need to determine the percentage change in the volume of a gas when the pressure increases by 50% at constant temperature. We'll use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant (P1V1 = P2V2).

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Initial pressure (P1) and final pressure (P2) are related by a 50% increase in pressure.
- This means P2 = P1 + 0.5P1 = 1.5P1.

2. **Apply Boyle's Law**:
- According to Boyle's Law: P1V1 = P2V2.
- Rearranging gives us V2 = (P1/P2) * V1.

3. **Substitute P2**:
- We know P2 = 1.5P1, so we can substitute this into the equation for V2:
\[ V2 = \left(\frac{P1}{1.5P1}\right) * V1 = \frac{1}{1.5} * V1 = \frac{2}{3} V1. \]

4. **Calculate the Change in Volume**:
- The change in volume (ΔV) is given by:
\[ ΔV = V2 - V1 = \frac{2}{3}V1 - V1 = \frac{2}{3}V1 - \frac{3}{3}V1 = -\frac{1}{3}V1. \]

5. **Calculate the Percentage Change in Volume**:
- The percentage change in volume is calculated as:
\[ \text{Percentage Change} = \left(\frac{ΔV}{V1}\right) * 100 = \left(-\frac{1/3 V1}{V1}\right) * 100 = -\frac{1}{3} * 100 = -33.33\%. \]

### Final Result:
The volume of the gas decreases by 33.33%.