Composition of air – ravnik.eu

Problem

When a compustion process is considered it is important to know the mass fraction of oxygen in the air. Estimate mass fraction of oxygen in air, which is composed of three gases having the following mole fractions: $78.1\:\%$ nitrogen, $20.9\:\%$ oxygen in $0.9\:\%$ argon.

Data

$\psi_{N_2}=0.781$
$\psi_{O_2}=0.209$
$\psi_{Ar}=0.009$
$\xi_{O_2}=\:?$

Solution

The equation relating mole and mass fractions is

$\xi_i=\frac{\psi_iM_i}{\sum_j\psi_jM_j}$

where $\xi_i$ is the mass fraction of $i$ -th component and $\psi_i$ is the mole fraction and $M_i$ is the molar mass.

From the periodic table of elements we find that molar mass of oxygen is $M_{O_2}=32\:kg/kmol$ , of nitrogen $M_{N_2}=28\:kg/kmol$ and of argon $M_{Ar}=40\:kg/kmol$ .

Using the above equation we can write

$\xi_{O_2}=\frac{\psi_{O_2} M_{O_2}}{\sum_i\psi_iM_i}=\frac{\psi_{O_2}M_{O_2}}{\psi_{O_2}M_{O_2}+\psi_{N_2}M_{N_2}+\psi_{Ar}M_{Ar}}=0.231.$

Thus we discover that the mass fraction of oxygen is $23.1\:\%$ . It is interesting to note, that the mass fraction is higher than the mole fraction. The reason for this is the fact that the molar mass of oxygen is higher than the molar mass of air ( $M_{air}\approx 29~kg/kmol$ ). Since it is only slightely higher, the difference between molar and mass fractions is not large.

Mass fraction of nitrogen and argon can be calculated in the same manner. One can also make use of the fact that $\sum_i\xi_i=1$ .

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