What amount of a substance is contained in oxygen if, at a pressure of 100 kPa

What amount of a substance is contained in oxygen if, at a pressure of 100 kPa and a mass of 0.02 kg, its volume is 50 cm3, what is the gas temperature?

Data: P – oxygen pressure (P = 100 kPa = 10 ^ 5 Pa); m – mass (m = 0.02 kg); V is the volume occupied by oxygen (V = 50 cm3; in the SI system V = 5 * 10 ^ -5 m3).

Const: MO2 – molar mass of oxygen (MO2 = 0.032 kg / mol); R – universal gas constant (R = 8.31 J / (mol * K)).

1) The amount of oxygen substance: νO2 = m / MO2 = 0.02 / 0.032 = 0.625 mol.

2) Oxygen temperature: P * V = νO2 * R * T, from where we express: T = P * V / (νO2 * R) = 10 ^ 5 * 5 * 10 ^ -5 / (0.625 * 8.31) ≈ 0 , 96 K = -272.19 ºС.

Answer: The amount of the substance is 0.625 mol, the oxygen temperature is 0.96 K (-272.19 ºС).