Air is a mixture of many gases. however, in calculating its molar mass we need consider only the three major components: nitrogen gas, oxygen gas, and argon. given that one mole of air at sea level is made up of 78.08 percent nitrogen, 20.95 percent oxygen, and 0.97 percent argon, what is the molar mass of air?

Multiply the % of each element by the molar masses and divide by 100% to get the mass that each element contributes to air.
(78.08% (N) x 28g/mol) / 100% = 21.86g/mol
(20.95% (O) x 32 g/mol) / 100% = 6.7g/mol
(0.97% (Ar) x 40 g/mol) /100% = 0.388g/mol

added together gives you 28.948 g/mol

Answer: 28.947 g/mol

Answer Link

AkshayG AkshayG · Answer 2 · 2019-12-16T10:12:09+01:00

The molar mass of air is [tex]\boxed{28.96{\text{ g/mol}}}[/tex].

Further Explanation:

The formula to calculate the mass of the component is as follows:

[tex]{\text{Mass of component}} = \left( {\dfrac{{{\text{Given \% }}}}{{{\text{100 \% }}}}} \right)\left( {{\text{Molar mass of component}}} \right)[/tex] ...... (1)

Air has three major components, namely, nitrogen, oxygen, and argon gas.

The percentage of nitrogen in the air is 78.08 %.

The molar mass of nitrogen gas is 28.02 g/mol.

Substitute these values in equation (1) to calculate the mass of nitrogen gas.

[tex]\begin{aligned}{\text{Mass of nitrogen gas}}&= \left( {\frac{{{\text{78}}{\text{.08 \% }}}}{{{\text{100 \% }}}}} \right)\left( {{\text{28}}{\text{.02 g/mol}}} \right) \\ &= 21.88\;{\text{g/mol}}\\\end{aligned}[/tex]

The percentage of oxygen in the air is 20.95 %.

The molar mass of oxygen gas is 31.99 g/mol.

Substitute these values in equation (1) to calculate the mass of oxygen gas.

[tex]\begin{aligned}{\text{Mass of oxygen gas}} &= \left( {\frac{{{\text{20}}{\text{.95 \% }}}}{{{\text{100 \% }}}}} \right)\left({{\text{31}}{\text{.99 g/mol}}} \right)\\&= 6.70\;{\text{g/mol}}\\\end{aligned}[/tex]

The percentage of argon in the air is 0.97 %.

The molar mass of argon gas is 39.95 g/mol.

Substitute these values in equation (1) to calculate the mass of argon gas.

[tex]\begin{aligned}{\text{Mass of oxygen gas}}&= \left( {\frac{{{\text{0}}{\text{.97 \% }}}}{{{\text{100 \% }}}}} \right)\left( {{\text{39}}{\text{.05 g/mol}}} \right)\\&= 0.38\;{\text{g/mol}}\\\end{aligned}[/tex]

The formula to calculate the molar mass of air is as follows:

[tex]{\text{Molar mass of air}}=\left( \begin{aligned}{\text{Mass of nitrogen gas}}+\\{\text{Mass of oxygen gas}}+\\{\text{Mass of argon gas}}\\\end{aligned} \right)[/tex] ...... (2)

The mass of nitrogen gas is 21.88 g/mol.

The mass of oxygen gas is 6.70 g/mol.

The mass of argon gas is 0.38 g/mol.

Substitute these values in equation (2).

[tex]\begin{aligned}{\text{Molar mass of air}} &= 21.88{\text{ g/mol}} + 6.70{\text{ g/ml}} + 0.38{\text{ g/mol}}\\&= 28.96{\text{ g/mol}}\\\end{aligned}[/tex]

Learn more:

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Answer Details:

Grade: Senior School

Chapter: Mole concept

Subject: Chemistry

Keywords: air, nitrogen, oxygen, argon, 28.96 /mol, 21.88 g/mol, 6.70 g/mol, 0.38 g/mol, molar mass, percentage, 100 %, 78.08 %, 20.95 %, 0.97 %.