A gas is heated from 252 K to 296 K while its volume is increased from 23.5 L to 30.5 L by moving a large piston within a cylinder. If the original pressure was 0.96 atm, what would be the final pressure?
(P1V1/T1) = (P2V2/T2)
To find the final pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature (in Kelvin)
In this case, we know the initial pressure (P1 = 0.96 atm), the initial volume (V1 = 23.5 L), the final volume (V2 = 30.5 L), and the initial temperature (T1 = 252 K).
Step 1: Calculate the number of moles (n) using the ideal gas law equation for the initial state:
P1V1 = nRT1
n = (P1V1) / (RT1)
Step 2: Calculate the final pressure (P2) using the ideal gas law equation for the final state:
P2 = (nRT2) / V2
Let's substitute the known values and solve the equations:
Step 1:
n = (0.96 atm * 23.5 L) / (0.0821 L·atm/(mol·K) * 252 K)
≈ 0.9445 mol
Step 2:
P2 = (0.9445 mol * 0.0821 L·atm/(mol·K) * 296 K) / 30.5 L
≈ 0.989 atm
Therefore, the final pressure of the gas would be approximately 0.989 atm.