Calculate the volume of nitrogen weighing 4 kg at a pressure of 400 kPa and a temperature of 27 C.

univerkov | February 10, 2021 | education

Data: m (mass of nitrogen) = 4 kg; P (pressure) = 400 kPa (400 * 10 ^ 3 Pa); T (absolute temperature of nitrogen) = 27 ºС (300 K).

Constants: M (molar mass of nitrogen (diatomic gas)) = 0.028 kg / mol; R (universal gas constant) = 8.31 J / (mol * K).

The volume that 4 kg of nitrogen occupies can be determined by the formula (Mendeleev-Clapeyron’s law): P * V = (m / M) * R * T, whence V = m * R * T / (P * M).

Calculation: V = 4 * 8.31 * 300 / (400 * 10 ^ 3 * 0.028) = 0.89 m3.

Answer: Nitrogen occupies a volume of 0.89 m3.

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