To find the mass of oxygen in the cylinder, we first need to calculate the number of moles of oxygen in the cylinder at the given conditions and then convert it to mass using the molar mass of oxygen.
Given data:
Density of oxygen at 0°C and pressure of 1 atm = 1.43 g/L
Volume of the cylinder = 20 L
Pressure of oxygen in the cylinder = 25 atm
Temperature of the oxygen in the cylinder = 27°C
Step 1: Calculate the number of moles of oxygen in the cylinder.
First, we need to calculate the density of oxygen at the new conditions (25 atm and 27°C). This can be done by using the ideal gas law:
PV = nRT
Convert the temperature to Kelvin:
27°C + 273 = 300 K
Now we can calculate the density using the ideal gas law:
P1V1/T1 = P2V2/T2
(1 atm) * (1 L) / (273 K) = (25 atm) * (20 L) / (300 K)
1/273 = 500/300
1/273 = 5/3
Density at new conditions = (5/3) * (1.43 g/L) ≈ 2.38 g/L
Step 2: Calculate the number of moles of oxygen in the cylinder.
Density = mass/volume
Mass = density * volume
Mass of oxygen in the cylinder = 2.38 g/L * 20 L = 47.6 g
Step 3: Convert the mass of oxygen to moles.
To convert mass to moles we need the molar mass of oxygen. The molar mass of oxygen (O2) is approximately 32 g/mol.
Number of moles = Mass / Molar mass
Number of moles = 47.6 g / 32 g/mol ≈ 1.49 moles
Therefore, the mass of oxygen in the cylinder is approximately 47.6 grams.