To solve this problem, we need to first calculate the new density of oxygen at the given conditions (25 atm and 27°C) and then use that density to find the mass of oxygen in the cylinder.
Calculate the new density of oxygen at the given conditions:
Using the ideal gas law, we can calculate the new density of oxygen at the given conditions:
P1V1/T1 = P2V2/T2
Where:
P1 = Initial pressure = 1 atm
V1 = Initial volume = 20 liters
T1 = Initial temperature = 0°C = 273K
P2 = Final pressure = 25 atm
V2 = Final volume = 20 liters
T2 = Final temperature = 27°C = 300K
(1 atm)(20L)/(273K) = (25 atm)(20L)/(300K)
20/273 = 500/300
Density at 25 atm and 27°C = (20/273)(500/300) = 0.3037 g/l
Calculate the mass of oxygen in the cylinder:
Mass = Density x Volume
Mass = 0.3037 g/l x 20 L
Mass = 6.074 g
Therefore, the mass of oxygen in the cylinder is 6.074 grams.