A certain amount of chlorine gas was placed inside a cylinder with a movable piston at one end. The initial volume was 3.00 and the initial pressure of chlorine was 1.75 . The piston was pushed down to change the volume to 1.00 . Calculate the final pressure of the gas if the temperature and number of moles of chlorine remain constant
To find the final pressure of the gas with a constant temperature and number of moles of chlorine, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional at constant temperature and number of moles.
Mathematically, Boyle's Law is represented as:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure
V2 = Final volume
Let's calculate the final pressure:
P1 * V1 = P2 * V2
1.75 * 3.00 = P2 * 1.00
5.25 = P2
Therefore, the final pressure of the gas would be 5.25 units.
To calculate the final pressure of the gas, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
Since the temperature and number of moles of chlorine remain constant, they can be considered as fixed values in this situation. Therefore, we can rewrite the equation as:
P1V1 = P2V2
where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
P2 = final pressure of the gas
V2 = final volume of the gas
Substituting the given values into the equation, we have:
(1.75)(3.00) = P2(1.00)
To solve for P2, divide both sides by 1.00:
P2 = (1.75)(3.00) / 1.00
P2 = 5.25
Therefore, the final pressure of the gas is 5.25 units.
Use P1V1 = P2V2
P2 is the only unknown.