  The mass fractions of a mixture of gases are 10 percent nitrogen, 3 percent helium, 55 percent methane, and 32 percent ethane. Determine the mole fractions of each constituent, the mixture’s apparent molecular weight, the partial pressure of each constituent when the mixture pressure is 1200 kPa, and the apparent specific heats of the mixture when the mixture is at the room temperature. The universal gas constant is Ru = 8.314 kJ/kmol·K. Use the table containing the molar mass, gas constant, and critical-point properties and the table containing the ideal-gas specific heats of various common gases. The mole fraction of nitrogen is _______. The mole fraction of helium is _____. The mole fraction of methane is ._______ The mole fraction of ethane is ______. The apparent molecular weight of the mixture is ______kg/kmol. The partial pressure of nitrogen is ______kPa. The partial pressure of helium is _____kPa. The partial pressure of methane is _____kPa. The partial pressure of ethane is ______kPa. The constant-pressure specific heat of the mixture is_____ kJ/kg·K. The constant-volume specific heat of the mixture is _____kJ/kg·K.

Question

The mass fractions of a mixture of gases are 10 percent nitrogen, 3 percent helium, 55 percent methane, and 32 percent ethane. Determine the mole fractions of each constituent, the mixture’s apparent molecular weight, the partial pressure of each constituent when the mixture pressure is 1200 kPa, and the apparent specific heats of the mixture when the mixture is at the room temperature. The universal gas constant is Ru = 8.314 kJ/kmol·K. Use the table containing the molar mass, gas constant, and critical-point properties and the table containing the ideal-gas specific heats of various common gases.

The mole fraction of nitrogen is _______.

The mole fraction of helium is _____.

The mole fraction of methane is ._______

The mole fraction of ethane is ______.

The apparent molecular weight of the mixture is ______kg/kmol.

The partial pressure of nitrogen is ______kPa.

The partial pressure of helium is _____kPa.

The partial pressure of methane is _____kPa.

The partial pressure of ethane is ______kPa.

The constant-pressure specific heat of the mixture is_____ kJ/kg·K.

The constant-volume specific heat of the mixture is _____kJ/kg·K.

Step 1

Assume the mass of the mixture as 100 grams.

Given mass of Nitrogen is 10% of mixture which equals 10g

Given mass of Helium is    3% of mixture which equals 3g

Given mass of Methane is 55% of mixture which equals 55g

Given mass of ethane is 32% of mixture which equals 32g

Step 2

Total no. of moles N in the mixture is sum of no. of moles of each component in the mixture.

N = 0.3571 moles of Nitrogen + 0.75 moles of Helium + 3.4375 moles of Methane + 1.0667   moles of Ethane.

N = 5.6113 moles

Now calculate the molar fraction of each of the component.

Step 3

Molecular weight of the mixture is,

∑ (mole fraction of component) (molar weight of that componen...

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