practical 8: unit conversions, eqbm, fick’s law
1. Your company generates LNG from coal-seam gas piped to a Gladstone processing plant. The molar composition of the LNG produced is:
methane, CH4 93.5 %
ethane, C2H6 4.6 %
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propane, C5H8 1.2 %
carbon dioxide, CO2 0.7 %
Determine:
a) the average molecular weight of the LNG mixture;
b) the mass fraction of ethane, mETH ;
c) the density of the gas mixture when heated to 207 K and at 132 kPa;
d) the partial pressure of methane when the total pressure is 132 kPa; and
e) the mass fraction of CO2 in parts per million, by weight.
2. Consider an ideal gas mixture of n species. Deriving the following equations will provide you with the tools to make quick unit conversions.
a) Derive an equation for determining the mass fraction of species i from knowledge of the mole fraction and molecular weight of each of the n species.
b) Derive an equation for determining the partial pressure of species i from the total pressure, and the mass fraction and molecular weight of each of the n species.
c) In a mixture containing equal mole fractions of O2, N2 ad CO2, what is the mass fraction of each species?
d) In a mixture containing equal mass fractions of O2, N2 ad CO2, what is the molar ratio of O2 on an O2 –free basis? And similarly for N2 and CO2?
3. A tank contains a 50L mixture of ethanol in water and is open to the atmosphere ( 25C, 1 atm) where the relative humidity is 0 %, but in a location where the air above the tank can be considered stagnant. Density of ethanol is 789 kg/m3.
a) If the mole fraction of ethanol in the tank is 5 %, what is the concentration of ethanol on the air side of the interface?
b) If the mole fraction of ethanol in the tank is 20 %, what is the concentration of ethanol on the air side of the interface?
c) How do your answers to (a) and (b) change if the relative humidity is 90 %?
4. Gaseous hydrogen is stored at elevated pressure in a rectangular container having steel walls 10 mm think. The molar concentration of hydrogen in the steel at the inner surface is 1 kmol/m3, while the concentration of hydrogen at the outer surface is negligible. The binary diffusion coefficient for hydrogen in steel is 0.26 x 10-12 m2/s.
a) Draw a diagram of the system, identify the direction of mass transfer and sketch the concentration gradient across the steel wall.
b) If you were not given the concentration of hydrogen in the steel at the inner surface describe how you would estimate it.
c) Determine both the mass and molar flux of hydrogen through the wall.
(Answer: 2.6×10-11 kmol.s-1.m-2)
d) Determine and explain the effect of halving the wall thickness on the molar and mass flux.
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