If you initially have 7.9 L of a gas at a pressure of 3.2 atm, and you increase the pressure to 6.9 atm, the volume will decrease to 2.5 L.
This is because the pressure and volume of a gas are inversely proportional, according to Boyle's law. Boyle's law states that for a fixed mass of an ideal gas kept at a fixed temperature, the pressure and volume are inversely proportional. This means that if the pressure is increased, the volume will decrease, and vice versa.
In this case, the temperature and the number of moles are held constant, so the only thing that can change is the pressure and the volume. When the pressure is increased from 3.2 atm to 6.9 atm, the volume must decrease in order to keep the product of the pressure and the volume constant.
The final volume can be calculated using the following equation:
V2 = V1 * (P1 / P2)
where:
V1 is the initial volume (7.9 L)
V2 is the final volume
P1 is the initial pressure (3.2 atm)
P2 is the final pressure (6.9 atm)
Substituting these values into the equation, we get:
V2 = 7.9 L * (3.2 atm / 6.9 atm)
V2 = 2.5 L
Therefore, the final volume of the gas will be 2.5 L.