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:

At constant temperature: \[ P\propto \frac1V \] So, if pressure increases, volume decreases and vice versa.

Answer 1

The Correct Option is B

Concept: At constant temperature, gases obey Boyle’s law: \[ P_1V_1=P_2V_2 \] According to this law, pressure and volume are inversely proportional.

Step 1: Writing the given data.
At NTP: \[ P_1=1\ \text{atm} \] \[ V_1=2.5\ \text{dm}^3 \] New pressure: \[ P_2=1.25\ \text{atm} \] Let the new volume be \(V_2\).

Step 2: Applying Boyle’s law.
\[ P_1V_1=P_2V_2 \] Substitute the values: \[ 1\times2.5=1.25\times V_2 \] \[ V_2=\frac{2.5}{1.25} \] \[ V_2=2.0\ \text{dm}^3 \]

Step 3: Calculating the change in volume.
Initial volume: \[ 2.5\ \text{dm}^3 \] Final volume: \[ 2.0\ \text{dm}^3 \] Therefore, \[ \Delta V=2.5-2.0 \] \[ \Delta V=0.5\ \text{dm}^3 \] Hence, the correct answer is: \[ \boxed{(B)\ 0.5\ \text{dm}^3} \]