Answer:
V = 12 L
Explanation:
In order to know this, we can use the ideal gas equation which is:
PV = nRT (1)
Where:
P: Pressure
V: Volume
n: moles
R: gas constant
T: Temperature
Now, we don't know the temperature or the mole, but the problem states that the temperature is constante, so, T1 = T2 = T.
As is the same gas, we can asume the moles are the same, so n1 = n2 = n. And the gas constant is always the same value, therefore:
P1V1 = nRT
P2V2 = nRT
The general equation would be:
P1V1 = P2V2 (2)
This is known as the Boyle's law which is a relation concerning the compression and expansion of a gas at constant temperature.
So, we use the above expression and replace the data to solve for V2:
V2 = P1V1/P2
V2 = 6 * 2 / 1
V2 = 12 L
This is the new volume, when the gas is compressed.
Taking into account the Boyle's law, the new volume is 12 L.
As the volume increases, the gas particles (atoms or molecules) take longer to reach the walls of the container and therefore collide with them less times per unit of time. This means that the pressure will be lower because it represents the frequency of collisions of the gas against the walls. In this way pressure and volume are related, determining Boyle's law which says:
"The volume occupied by a given gaseous mass at constant temperature is inversely proportional to pressure"
Boyle's law is expressed mathematically as:
Pressure * Volume = constant
or P× V = k
Studying two different states, an initial state 1 and a final state 2, it is satisfied:
P1× V1= P2× V2
In this case, you know:
Replacing:
2 atm× 6 L= 1 atm× V2
Solving:
[tex]V2=\frac{2 atm x 6 L}{1 atm}[/tex]
V2= 12 L
In summary, the new volume is 12 L.
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