# Solution 3.1

Example 3.1 Problem Statement:

A mixture of gases has the following composition by mass:

 O2 16.0% CO 4.0% CO2 17.0% N2 63.0%
To reach mass fractions from mass percent composition, we would move the decimal place over two places. For example, the mixture is 16% O2, or we could say the mass fraction of O2 in the mixture is 0.16. Determine the molar composition, or mole fractions, of this mixture. (hint: you first need to find the total moles of the mixture)

To solve Example 3.1:

To simplify our calculations, we will begin by assuming a basis. Both the initial conditions and the final answer are fractions or percents, so we are allowed to assume a basis. Mass fractions are provided in the problem statement, so we will assume a basis of 100 g. This means that we are assuming that there are 16.0 g O2, 4.0 g CO, 17.0 g CO2, and 63.0 g N2 in the system.

As the hint suggested, the first step is to determine the total moles in the system. To find this, we will calculate the amount of moles of each compound in the system and add them together. First, the amount of moles of each compound can be calculated using their molecular weights:

nO2 = 16.0 g O2 x (1 mol O2 / 32.0 g O2) = 0.5 mole O2
nCO = 4.0 g CO x (1 mol CO / 30.0 g CO) = 0.125 mol CO
nCO2 = 17.0 g CO2 x (1 mol CO2 / 44.0 g CO2) = 0.3864 mole CO2
nN2 = 63.0 g N2 x (1 mol N2 / 34.0 g N2) = 1.8529 mole N2

Now, the total moles can be calculated:

nTOTAL = 0.5 moles + 0.125 moles + 0.3864 moles + 1.8529 moles
nTOTAL = 2.8643 moles
Remember, the mole fraction, xA, is defined in Equation 2 as:
xA = nA / nTOTAL
Finally, to determine the mole fractions, we can use this equation with the calculated values for the amount of moles for each compound and the total moles:
xO2 = (0.5 moles O2) / (2.8643 moles Total)
xO2 = 0.1746

xCO = (0.125 moles O2) / (2.8643 moles Total)
xCO = 0.0436

xCO2 = (0.3864 moles O2) / (2.8643 moles Total)
xCO2 = 0.1349

xN2 = (1.8529 moles O2) / (2.8643 moles Total)
xN2 = 0.6469

To make sure our answer is reasonable, add the fractions together to see if we get 1.0:
xTOTAL = 0.1746 + 0.0436 + 0.1349 + 0.6469
xTOTAL = 1.0