Question

A scuba diver's tank contains 0.240 kg of o2 compressed into a volume of 3.10 l. what volume (in liters) would this oxygen occupy at 27.0 ºc and 0.910 atm?

Answer 1

Given:
m = 0.240 kg = 240 g, the mass of O₂
V = 3.10 L = 3.10 x 10⁻³ m³, the volume

Because the molar mass of oxygen is 16, the number of moles of O₂ is
n = (240 g)/(2*16 g/mol) = 7.5 mol

As an ideal gas,
p*V = nRT
or
V = (nRT)/p
where R = 8.314 J/(mol-K)

When
p = 0.910 atm = (0.910 atm) * (101325Pa/atm) = 92205.75 Pa
T = 27 °C = (27 + 273) K = 300 K
then the volume is

`V= ((7.5 \, mol)*(8.314 \, J/(mol-K))*(300 \, K))/((92205.75 \, Pa)) =0.2029 \, m^(3)`

V = (0.2029 m³)*(10³ L/m³) = 202.9 L

Answer: 203 liters