Question

Given that a sample of air is made up of nitrogen, oxygen, and argon in the mole fraction 0.78 N2, 0.21 O2, and 0.010 Ar, what is the density of air at standard temperature and pressure?

Answer 1

The density is 1.29g/L

Step-by-step explanation:

Step 1: Data given

Mol fraction of N2 = 0.78

Mol fraction of O2 = 0.21

Mol fraction of Ar = 0.010

Molar mass N2 = 28 g/mol

Molar mass O2 = 32 g/mol

Molar mass of Ar = 39.95 g/mol

Volume = 22.4 Lat STP

Molar volume = 22.4mol/L at STP

Step 2: Calculate moles

Total moles of sample = 1.00 moles

N2 = 0.78 mol

O2 = 0.21 mol

Ar = 0.01 mol

Step 3: Calculate mass

Mass = moles * molar mass

Mass N2 = 0.78 mol * 28 g/mol = 21.84 grams

Mass O2 = 0.21 mol * 32 g/mol = 6.72 grams

Mass Ar = 0.01 mol * 39.95 g/mol = 0.3995 grams

Total mass in 1 mol of gas = 28.9595 grams

Step 4: Calculate density

Density = mass / volume

Density 28.9595 grams / 22.4 L

Density = 1.29 g/L

The density is 1.29g/L

Answer 2

1.293 kg/m³

Step-by-step explanation:

Density: this can be defined as the ratio of the mass of a body and its volume.

The S.I unit of density is kg/m³

D = m/v............................ Equation 1

D = density of air, m = mass of air, v = volume of air.

Note: Since the air is made up of nitrogen, oxygen and argon. the mass and volume of air will be the sum of the mass and sum of the volume of nitrogen, oxygen, and argon respectively.

(i) Mass of one mole of N₂ = 28 g

Therefore, mass of 0.78 mole of N₂ = 28×0.78 = 21.84 g.

(ii) Mass of one mole of O₂ = 32 g

Therefore, mass of 0.21 mole of O₂ = 32×0.21 = 6.72 g

(iii) Mass of one mole of Ar = 40 g

Therefore mass of 0.01 mole of Ar = 0.01×40 = 0.4 g

m = 21.84 + 6.72 + 0.4 = 28.96 g

Also Note: One mole of every gas at standard temperature and pressure = 22.4 dm³

Therefore,

(i) volume of 0.78 mole of N₂ = 22.4×0.78 = 17.47 dm³

(ii) volume of 0.21 mole of O₂ = 0.21×22.4 = 4.704 dm³

(iii) volume of 0.01 mole of Ar = 0.01×22.4 = 0.224 dm³

Therefore,

v = 17.47+4.704+0.224

v = 22.398 dm³

Substituting the value of v and m into equation 1

D = 28.96/22.398

D = 1.293 g/dm³

D = 1.293 kg/m³