A gas sample contained in a cylinder equipped with a moveable piston occupied 300.0 mL at a pressure of 2.00 atm. What would be the final pressure if the volume were increased to 500.0 mL at constant temperature? Answer should include units.
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law equation: P1V1 = P2V2
Given:
P1 = 2.00 atm (initial pressure)
V1 = 300.0 mL (initial volume)
V2 = 500.0 mL (final volume)
Rearranging the equation, we can solve for P2:
P2 = (P1 * V1) / V2
Substituting the given values:
P2 = (2.00 atm * 300.0 mL) / (500.0 mL)
P2 = 1.20 atm
Therefore, the final pressure if the volume is increased to 500.0 mL at constant temperature would be 1.20 atm.
To find the final pressure when the volume is changed at constant temperature, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law can be expressed as: P1 * V1 = P2 * V2
Where:
P1 = initial pressure of the gas in the cylinder (2.00 atm)
V1 = initial volume of the gas in the cylinder (300.0 mL)
P2 = final pressure of the gas after the volume change (unknown)
V2 = final volume of the gas after the volume change (500.0 mL)
We can rearrange the equation to solve for P2:
P2 = (P1 * V1) / V2
Substituting the values:
P2 = (2.00 atm * 300.0 mL) / 500.0 mL
Now we can solve for P2:
P2 = (600.0 atm * mL) / 500.0 mL
The milliliter units cancel out, leaving us with the final pressure in atm:
P2 = 1.20 atm
Therefore, the final pressure when the volume is increased to 500.0 mL at constant temperature would be 1.20 atm.