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.