To determine the amount of oxygen gas in the cylinder, we can use the ideal gas law equation:
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)
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
So, for a temperature of 30 degrees Celsius:
T = 30 + 273.15 = 303.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (20 atm) * (30 L) / (0.0821 L·atm/(mol·K) * 303.15 K)
n ≈ 0.775 moles
Therefore, the amount of oxygen gas in the cylinder is approximately 0.775 moles.