To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas. The combined gas law states:
(P1 × V1) ÷ T1 = (P2 × V2) ÷ T2
where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
We can use this formula to find the final volume V2 of the gas at a pressure of 2.5 atm:
(P1 × V1) ÷ T1 = (P2 × V2) ÷ T2
We are given:
P1 = 1 atm
V1 = 3.6 L
T1 = 25 °C = 298 K (we need to convert Celsius to Kelvin by adding 273.15)
P2 = 2.5 atm
T2 = T1 (assuming the temperature remains constant)
Substituting these values into the formula, we get:
(1 atm × 3.6 L) ÷ 298 K = (2.5 atm × V2) ÷ 298 K
Simplifying and solving for V2, we get:
V2 = (1 atm × 3.6 L × 298 K) ÷ (2.5 atm × 298 K)
V2 = 1.296 L
Therefore, the volume of the gas at a pressure of 2.5 atm would be 1.296 L.