1. A sample of gas under a pressure of 622 kPa has a volume of 233 cm3. The pressure is increased to 988 kPa, while the temperature remains constant. What volume will the gas occupy at this pressure?
2. The pressure exerted by a gas is 2.0 atm while it has a volume of 350 cm3. What would be the volume of this sample of gas at standard atmospheric pressure?
To solve these questions, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
1. To find the volume of the gas at the increased pressure, we can set up the following equation using Boyle's Law:
(P1)(V1) = (P2)(V2)
where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
Given:
P1 = 622 kPa
V1 = 233 cm^3
P2 = 988 kPa
V2 = ?
Plugging in the values into the equation, we get:
(622 kPa)(233 cm^3) = (988 kPa)(V2)
Now, we can solve for V2:
V2 = (622 kPa)(233 cm^3) / (988 kPa)
≈ 146.71 cm^3
Therefore, the gas will occupy approximately 146.71 cm^3 at the increased pressure.
2. To find the volume of the gas at standard atmospheric pressure, we can use the same equation as before, but this time we know the initial pressure (2.0 atm) and volume (350 cm^3), and we need to find the final volume when the pressure is at standard atmospheric pressure.
Given:
P1 = 2.0 atm
V1 = 350 cm^3
P2 = 1 atm
V2 = ?
Plugging in the values into the equation, we get:
(2.0 atm)(350 cm^3) = (1 atm)(V2)
Now, we can solve for V2:
V2 = (2.0 atm)(350 cm^3) / (1 atm)
= 700 cm^3
Therefore, the volume of the gas at standard atmospheric pressure would be 700 cm^3.