A tank contains 0.5 m3 of nitrogen (N2) at 2718C and 1356 kPa. Determine the mass of nitrogen, in kg, using (a) the ideal gas model. (b) data from the compressibility chart. Comment on the applicability of the ideal gas model for nitrogen at this state.

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04-02-2020
Chemistry

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A tank contains 0.5 m3 of nitrogen (N2) at 2718C and 1356 kPa. Determine the mass of nitrogen, in kg, using (a) the ideal gas model. (b) data from the compressibility chart. Comment on the applicability of the ideal gas model for nitrogen at this state.

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cristoshiwa cristoshiwa · Answer 1 · 2020-02-05T20:43:24+01:00

Answer: (a) m=7.64kg (b)m=7.64kg

Explanation: (a) Calculating the mass of nitrogen using the ideal gas model:

P.V=n.R.T

Note: as pressure is in Pascal and volume is in m³, the constant R will be 8,31J/K.mol.

Totransform kPa in Pa: P=1356kPa → P=1356.10³ Pa

To use the temperature, it has to be in Kelvin: T=2718°C → T = 2718 + 273 = 2991K

P.V=n.R.T

n=(P.V) / (R.T)

n= (1356.10³. 0.5) / (8.31.2991)

n= 27,28 mols

For nitrogen, 1 mol = 28,014 g so m=764,22g or, in this case, m=764220kg.

(b) To calculate the mass with the compressibility chart, use a compatibility factor Z, which is Z=(p.v) / (R.T). If the factor Z=1, the gas behaves ideally.

This means that, in general, gases behaves almost ideally. So, in this case, calculating the mass of nitrogen by the ideal gas law or the Z factor will result in the same quantity.