Question

A certain mass of a gas occupies a volume of \(2.5\ \text{dm}^3\) at NTP. Calculate the change in volume of gas at the same temperature if pressure of gas is changed to \(1.25\ \text{atm}\).

• A. \(3.0\ \text{dm}^3\)
• B. \(0.5\ \text{dm}^3\)
• C. \(4.5\ \text{dm}^3\)
• D. \(1.5\ \text{dm}^3\)

Hint:

For Boyle's law: \[ P \propto \frac{1}{V} \] This means:
• Increase in pressure causes decrease in volume.
• Decrease in pressure causes increase in volume. Always remember: \[ P_1V_1 = P_2V_2 \] Temperature must remain constant for Boyle's law to be applicable.

Answer 1

The Correct Option is B

Concept: Since temperature remains constant, Boyle's law is applicable. Boyle's law states: \[ P_1V_1 = P_2V_2 \] This law shows that pressure and volume are inversely proportional at constant temperature.

Step 1: Writing the given values.}
At NTP: \[ P_1 = 1\ \text{atm} \] Initial volume: \[ V_1 = 2.5\ \text{dm}^3 \] Final pressure: \[ P_2 = 1.25\ \text{atm} \] Final volume: \[ V_2 = ? \]

Step 2: Applying Boyle's law.}
\[ P_1V_1 = P_2V_2 \] Substituting values: \[ 1 \times 2.5 = 1.25 \times V_2 \] \[ 2.5 = 1.25V_2 \] \[ V_2 = \frac{2.5}{1.25} \] \[ V_2 = 2.0\ \text{dm}^3 \]

Step 3: Calculating change in volume.}
Initial volume: \[ 2.5\ \text{dm}^3 \] Final volume: \[ 2.0\ \text{dm}^3 \] Therefore, \[ \text{Change in volume} = 2.5 - 2.0 \] \[ = 0.5\ \text{dm}^3 \]

Step 4: Final conclusion.}
Hence, the decrease in volume of gas is: \[ \boxed{0.5\ \text{dm}^3} \] Therefore, the correct option is: \[ \boxed{(2)\ 0.5\ \text{dm}^3} \]