# A 20 liter cylinder contains a mixture of hydrogen and nitrogen at a temperature of 280 K and a pressure of 1 MPa.

A 20 liter cylinder contains a mixture of hydrogen and nitrogen at a temperature of 280 K and a pressure of 1 MPa. Determine the mass of hydrogen if the mass of the mixture is 150 g.

Initial data: V = 20 l = 0.02 m3, T = 280 K, P = 1 MPa = 10 ^ 6 Pa, m = 150 g, M1 (H2) = 2 g / mol, M2 (N2) = 28 g / mol.

Total pressure: P = P1 + P2.

H2 pressure: P1 = m1 * R * T / (M1 * V).

N2 pressure: P2 = (150 – m1) * R * T / (M2 * V).

P = m1 * R * T / (M1 * V) + (0.15 – m1) * R * T / (M2 * V) = (m1 / M1 + (150 – m1) / M2) / (R * T / V).

m1 / M1 + (150 – m1) / M2 = P * V / (R * T).

m1 / 2 + (150 – m1) / 28 = 8.6.

14m1 + 150 – m1 = 240.8.

13m1 = 90.8.

m1 = 7 g.

Answer: The mass of hydrogen is 7 g.

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