A gas is confined in a cylinder fitted with a movable piston. At 27 °C, the gas occupies a volume of 2.0 L under a pressure of 3.0 atm. The gas is heated to 47 °C and compressed to 5.0 atm. What volume does the gas occupy in its final state?
O 21 L
O 0.48 L
O 0.78
O 1.3 L
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
First, we need to calculate the initial number of moles of gas using the initial conditions:
P1 = 3.0 atm
V1 = 2.0 L
T1 = 27 °C = 27 + 273 = 300 K
n = (P1 * V1) / (R * T1)
n = (3.0 atm * 2.0 L) / (0.0821 L.atm/mol.K * 300 K)
n = 0.2 moles
Now, we can use the final conditions and the number of moles to find the final volume:
P2 = 5.0 atm
T2 = 47 °C = 47 + 273 = 320 K
V2 = (n * R * T2) / P2
V2 = (0.2 moles * 0.0821 L.atm/mol.K * 320 K) / 5.0 atm
V2 = 0.787 L or 0.78 L
Therefore, the gas occupies a volume of 0.78 L in its final state. So the correct answer is O 0.78 L.