Temperature remaining constant, the pressure of gas is decreased by 20%. The percentage change in volume

Options

A. increases by 20%
B. decreases by 20%
C. increases by 25%
D. decreases by 25%

Explanation

To solve the problem of finding the percentage change in volume when the pressure of a gas is decreased by 20% at constant temperature, we can use Boyle's Law. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understand Boyle's Law**: Boyle's Law states that for a given mass of gas at constant temperature, the pressure (P) of the gas is inversely proportional to its volume (V). This can be expressed as:
\[ P_1 V_1 = P_2 V_2 \]

2. **Define Initial and Final Pressures**: Let the initial pressure be \( P_1 \) and the final pressure after a decrease of 20% be \( P_2 \). Since the pressure decreases by 20%, we can express \( P_2 \) as:
\[ P_2 = P_1 - 0.20 P_1 = 0.80 P_1 \]

3. **Substitute into Boyle's Law**: Substitute \( P_2 \) into the Boyle's Law equation:
\[ P_1 V_1 = (0.80 P_1) V_2 \]

4. **Cancel \( P_1 \)**: Since \( P_1 \) is common on both sides, we can cancel it out (assuming \( P_1 \neq 0 \)):
\[ V_1 = 0.80 V_2 \]

5. **Rearrange to Find \( V_2 \)**: Rearranging the equation gives us:
\[ V_2 = \frac{V_1}{0.80} = 1.25 V_1 \]

6. **Calculate the Change in Volume**: The change in volume can be calculated as:
\[ \Delta V = V_2 - V_1 = 1.25 V_1 - V_1 = 0.25 V_1 \]

7. **Find the Percentage Change in Volume**: The percentage change in volume is given by:
\[ \text{Percentage Change} = \left( \frac{\Delta V}{V_1} \right) \times 100 = \left( \frac{0.25 V_1}{V_1} \right) \times 100 = 25\% \]

### Final Answer:
The percentage change in volume when the pressure of the gas is decreased by 20% at constant temperature is **25% increase**.

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