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To find the volume of the gas at STP, we can use the ideal gas law equation:
PV = nRT
Where:
P = initial pressure = 0.817 atm
V = initial volume = 4.00 L
n = number of moles of gas
R = ideal gas constant = 0.0821 L.atm/mol.K
T = initial temperature = 39.0 C = 312.15 K
First, we need to find the number of moles of gas in the initial conditions:
PV = nRT
n = (PV) / (RT)
n = (0.817 atm)(4.00 L) / (0.0821 L.atm/mol.K)(312.15 K)
n = 0.1634 mol
Now that we have the number of moles of gas, we can use the ideal gas law at STP (T = 273.15 K, P = 1 atm) to find the volume of the gas at STP:
PV = nRT
V = nRT / P
V = (0.1634 mol)(0.0821 L.atm/mol.K)(273.15 K) / (1 atm)
V = 3.505 L
Therefore, the volume of the gas at STP is 3.505 L.