Solution 3.2

Example 3.3 Problem Statement:

A material balance problem from chapter 4 gives us the following information about streams going in and out of a condenser. Determine the mole fractions of each stream.

To solve Example 3.2:

The condenser has one inlet and two outlets, but only one inlet and one outlet contain mixtures of compounds. The bottom outlet contains only water, so yH2 = 1.0, the mole fraction of water is 1.0. For the other two streams, the mole fraction of each compound can be calculated by knowing the total amount of moles in the system. Remember, yA is the mole fraction of A in the mixture, which is defined as:

    Equation 4:     yA = nA / ntotal

For the two streams the total moles must be calculated first. For the inlet stream:

    nTOTAL = 750 moles O2 + 3760 moles N2 + 150 moles CO2 + 200 moles H2O
    nTOTAL = 4860 moles total

The mole fractions of each compound in the inlet stream can now be calculated:
    yO2 = 750 moles O2 / 4860 moles Total
    yO2 = 0.1543
    yN2 = 3760 moles N2 / 4860 moles Total
    yN2 = 0.7737
    yCO2 = 150 moles CO2 / 4860 moles Total
    yCO2 = 0.0309
    yH2O = 200 moles H2O / 4860 moles Total
    yH2O = 0.0412
To make sure the answer is reasonable, add the mole fractions together to see if the sum is 1.0:
    yTOTAL = 0.1543 + 0.7737 + 0.0309 + 0.0412
    yTOTAL = 1.0001

For the outlet stream, the total number of moles can be calculated:
    nTOTAL = 750 mol O2 + 3760 mole N2 + 150 moles CO2
    nTOTAL = 4660 moles total
The mole fractions of each compound in the outlet stream can now be calculated:
    yO2 = 750 moles O2 / 4660 moles Total
    yO2 = 0.1609
    yN2 = 3760 moles N2 / 4660 moles Total
    yN2 = 0.8069
    yCO2 = 150 moles CO2 / 4660 moles Total
    yCO2 = 0.0322
Again, to make sure the answer is reasonable, add the mole fractions together to see if the sum is 1.0:
    yTOTAL = 0.1609 + 0.8069 + 0.0322
    yTOTAL = 1.0000

Both sets of mole fractions add up to 1.0, so our answers for each stream are reasonable.

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