Question

Compare the density of nitrogen gas to the density of argon gas when both gases are at 298 K and 101.3 kPa.​

Answer 1

Answer:

Ar = 1.63g/L; N₂ = 1.14g/L. The density of Argon is higher than density of nitrogen because molar mass of argon > Molar mass nitrogen

Explanation:

It is possible to obtain the density of a gas using the formula:

ρ = PM / RT

Where ρ is density in g/L

P is pressure of the gas (101.3kPa)

M is molar mass of the gas (Ar: 39.9g/mol; N₂: 28g/mol)

R is gas constant (8.314kPaL/Kmol)

And T is temperature (298K)

Thus, density of Ar and N₂ is:

Ar = 101.3kPa*39.9g/mol / 8.314kPaL/Kmol*298K

Ar = 1.63g/L

N₂ = 101.3kPa*28g/mol / 8.314kPaL/Kmol*298K

N₂ = 1.14g/L

As general rule, under the same conditions, the gas with the higher molar mass will be the gas with higher density.

Answer 2

The argon gas will have greater density when compared to nitrogen gas in the given condition.

The given parameters;

• temperature of the gases, T = 298 K
• pressure of the gases, P = 101.3 kPa

The ideal gas law can be used to determine the density of the gases;

$PV = nRT\\\\PV = \frac{m}{M} RT\\\\PM = \frac{m}{V} RT\\\\PM = \rho RT\\\\\rho = \frac{PM}{RT}$

where;

• M is the molar mass of the gases
• R is ideal gas constant

The molar mass of nitrogen gas is given as;

M = 14 g/mol

The molar mass of argon gas is given as;

M = 40 g/mol

From the formula given above, we can conclude that the gas with greater molar mass will have greater density, in this case the argon gas will have greater density when compared to nitrogen gas in the same condition.

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