To calculate the number of moles of nitrogen gas required, we can use the Ideal Gas Law formula:
PV = nRT
Where:
P = Pressure (in atmospheres)
V = Volume (in liters)
n = Number of moles
R = Ideal Gas Constant (0.0821 L atm/mol K)
T = Temperature (in Kelvin)
We are given the volume (V) as 30.0 liters, pressure (P) as 3.5 atmospheres, and temperature (T) as 50 degrees Celsius. First, we need to convert the temperature to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 50 + 273.15
T(K) = 323.15 K
Now, we can plug the given values into the Ideal Gas Law formula and solve for the number of moles (n):
(3.5 atm) * (30.0 L) = n * (0.0821 L atm/mol K) * (323.15 K)
105 atm * L = n * (0.0821 L atm/mol K) * (323.15 K)
Now, we can cancel out the units and solve for n:
n = (105 L atm) / (0.0821 L atm/mol K * 323.15 K)
n ≈ 4.62 moles
So, approximately 4.62 moles of nitrogen gas are required to produce a volume of 30.0 liters at 50 degrees Celsius and 3.5 atmospheres of pressure.
