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 y_{H2} = 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, y_{A} is the mole fraction of A in the mixture, which is defined as:
Equation 4: y_{A} = n_{A} /
n_{total}
For the two streams the total moles must be calculated first. For the inlet stream:
n_{TOTAL} = 750 moles O_{2} + 3760 moles N_{2} + 150 moles CO_{2} + 200 moles H_{2}O
n_{TOTAL} = 4860 moles total
The mole fractions of each compound in the inlet stream can now be calculated:
y_{O2} = 750 moles O_{2} / 4860 moles Total
y_{O2} = 0.1543
y_{N2} = 3760 moles N_{2} / 4860 moles Total
y_{N2} = 0.7737
y_{CO2} = 150 moles CO_{2} / 4860 moles Total
y_{CO2} = 0.0309
y_{H2O} = 200 moles H_{2}O / 4860 moles Total
y_{H2O} = 0.0412
To make sure the answer is reasonable, add the mole fractions together to see if the sum is 1.0:
y_{TOTAL} = 0.1543 + 0.7737 + 0.0309 + 0.0412
y_{TOTAL} = 1.0001
For the outlet stream, the total number of moles can be calculated:
n_{TOTAL} = 750 mol O_{2} + 3760 mole N_{2} + 150 moles CO_{2}
n_{TOTAL} = 4660 moles total
The mole fractions of each compound in the outlet stream can now be calculated:
y_{O2} = 750 moles O_{2} / 4660 moles Total
y_{O2} = 0.1609
y_{N2} = 3760 moles N_{2} / 4660 moles Total
y_{N2} = 0.8069
y_{CO2} = 150 moles CO_{2} / 4660 moles Total
y_{CO2} = 0.0322
Again, to make sure the answer is reasonable, add the mole fractions together to see if the sum is 1.0:
y_{TOTAL} = 0.1609 + 0.8069 + 0.0322
y_{TOTAL} = 1.0000
Both sets of mole fractions add up to 1.0, so our answers for each stream are reasonable.
