Step 1: Understanding the Concept:
Since the temperature remains constant, we use Boyle's Law.
Boyle's Law states that for a fixed mass of an ideal gas at constant temperature, the volume is inversely proportional to the pressure.
\[ P \propto \frac{1}{V} \implies PV = \text{constant} \]
Key Formula or Approach:
\[ P_1 V_1 = P_2 V_2 \]
NTP (Normal Temperature and Pressure) corresponds to a pressure of \(1\text{ atm}\).
Step 2: Detailed Explanation:
Given:
Initial Pressure (\(P_1\)) = \(1\text{ atm}\) (at NTP).
Initial Volume (\(V_1\)) = \(2.5\text{ dm}^3\).
Final Pressure (\(P_2\)) = \(1.25\text{ atm}\).
1. Calculate Final Volume (\(V_2\)):
\[ 1 \times 2.5 = 1.25 \times V_2 \]
\[ V_2 = \frac{2.5}{1.25} = 2.0\text{ dm}^3 \]
2. Calculate Change in Volume (\(\Delta V\)):
The question asks for the **change** in volume, not the final volume.
\[ \Delta V = V_1 - V_2 = 2.5\text{ dm}^3 - 2.0\text{ dm}^3 = 0.5\text{ dm}^3 \]
Since the pressure increased, the volume decreased, resulting in a change of \(0.5\text{ dm}^3\).
Step 3: Final Answer:
The change in volume is \(0.5\text{ dm}^3\).