A gas at a pressure of 2.0 atm is contained in a closed container. Indicate the changes in its volume when the pressure undergoes the following changes at constant temperature. (Assume that the volume of the container changes with the volume of the gas.) The pressure increases to 7.5 atm
P1V1 = P2V2
P1/V2=P2/V1
To determine the change in volume when the pressure of a gas changes at constant temperature, we can use Boyle's law. Boyle's law states that the pressure and volume of a gas are inversely proportional when the temperature is constant.
Mathematically, Boyle's law can be expressed as:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
In this case, we have the initial pressure (P1 = 2.0 atm) and we need to determine the final volume (V2) when the pressure increases to 7.5 atm.
We can rearrange the equation as:
V2 = (P1 * V1) / P2
Substituting the known values:
V2 = (2.0 atm * V1) / 7.5 atm
Simplifying the equation:
V2 = (2/7.5) * V1
Therefore, the volume will change to (2/7.5) times the initial volume.