An ideal gas mixture contains 40.0% helium, 20.0% methane, and 40.0% nitrogen by

Question

An ideal gas mixture contains 40.0% helium, 20.0% methane, and 40.0% nitrogen by volume at 2.50 atm absolute and 80.0°C.

Problem 5.34 Gas Composition An ideal gas mixture contains 40.0% helium, 20.0% methane, and 40.0% nitrogen by volume at 2.50 atm absolute and 80.0°C. (a) Calculate the partial pressure of each component. Helium: atm Methane: atm Nitrogen: atm (b) Calculate the mass fractions of methane and nitrogen Methane: Nitrogen: (c) Calculate the average molecular weight of the gas. 9/mol (d) Calculate the density of the gas. kg/m3

Explanation / Answer

Basis 100 mol of gas

Mol% = volume %

Part a

Partial pressure of Helium = mol fraction of He x Total Pressure

= 0.4 x 2.5 = 1 atm

Partial pressure of methane = mol fraction of methane x Total Pressure

= 0.2 x 2.5 = 0.5 atm

Partial pressure of nitrogen = mol fraction of nitrogen x Total Pressure

= 0.4 x 2.5 = 1 atm

Part b

Mass of methane = moles x molecular weight

= 20 x 16 = 320 g

Mass of nitrogen = 40 x 28 = 1120 g

Mass of He = 40 x 4 = 160 g

Total mass = 320 + 1120 + 160 = 1600 g

Mass fraction of methane = mass of methane/total mass

= 320/1600 = 0.20

Mass fraction of nitrogen = mass of nitrogen/total mass

= 1120/1600 = 0.70

Part C

Average molecular weight

= M1*X1 + M2*X2 + M3*X3

= 4*0.4 + 16*0.2 + 0.4*28

= 16 g/mol

Part d

From the ideal gas equation

PM = density x RT

Density of gas = PM/RT

= 2.5 atm *16g/mol /0.0821L-atm/mol·K *353K

= 1.38 g/L x 10^-3kg/g x 10^3L/m3

= 1.38 kg/m3

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