A sample of gas is confined to a cylinder housed with a movable piston. Initially, the gas
occupies a volume of 2.7 L at 6.0 atm and 25°C. Calculate the volume of the gas sample if the
pressure is reduced to 1.8 atm and the temperature decreased to 20°C.
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of the gas sample. The combined gas law equation is as follows:
(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
Given:
P1 = 6.0 atm
V1 = 2.7 L
T1 = 25°C + 273.15 = 298.15 K
P2 = 1.8 atm
T2 = 20°C + 273.15 = 293.15 K
Let's substitute these values into the equation and solve for V2:
(6.0 atm × 2.7 L) / 298.15 K = (1.8 atm × V2) / 293.15 K
Simplifying the equation:
16.2 L / 298.15 K = 1.8 atm × V2 / 293.15 K
Cross-multiplying and rearranging the equation:
(16.2 L × 293.15 K) / (298.15 K × 1.8 atm) = V2
Solving the equation:
V2 = (16.2 L × 293.15 K) / (298.15 K × 1.8 atm)
Calculating the value:
V2 = 8.065 L
Therefore, the volume of the gas sample when the pressure is reduced to 1.8 atm and the temperature decreased to 20°C is approximately 8.065 L.