The initial condition of the gas can be expressed using the combined gas law:
P1V1 / T1 = P2V2 / T2
where P1 = 2.0 atm, V1 = 20 L, and T1 is the initial temperature (which we will assume remains constant).
If the volume is decreased to 10 L and the pressure is increased to 4.0 atm, the new conditions can be expressed as:
P2 = 4.0 atm, V2 = ?, and T2 = T1
We can rearrange the combined gas law to solve for V2:
V2 = (P1V1T2) / (P2T1)
Plugging in the given values, we get:
V2 = (2.0 atm x 20 L x T1) / (4.0 atm x T1) = 10 L
Therefore, the final volume of the gas is 10 liters.