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# derive the relationship between density and molar mass of a gaseous substance

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## Derive a relation between density and molar mass of the gas with the help of ideal gas equation.

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## Derive a relation between density and molar mass of the gas with the help of ideal gas equation.

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Updated on : 2022-09-05

The relationships between molar mass and density for a monoatomic gas can be easy.

Solution Verified by Toppr

The Ideal Gas Law, PV = nRT can be arranged so that n moles equals the mass/molar mass of the gas to become,

PV = M mRT ​

where m is the mass and M is the molar mass.

M = PV mRT ​

, if you hold the temperature of the gas constant the equation reduces to the Boyle's law or

PV m ​

The mass will be constant assuming the container is closed and so the gas cannot be escaped so, PV will be constant.

D = V m ​ and M = PV mRT ​ M = P DRT ​

The higher the density of the gas the higher the molar mass and vice versa.

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## Derive a relation between density and molar mass of the gas with the help of the ideal gas equation.

Derive a relation between density and molar mass of the gas with the help of the ideal gas equation.. Ans: Hint: In order to answer this question, we need to have a basic idea about the ideal gas law. Even knowing the definition of density and molar ...

## Derive a relation between density and molar mass of the gas with the help of the ideal gas equation.

Last updated date: 16th Jan 2023

• Total views: 194.6k • Views today: 3.92k Answer Verified 194.6k+ views 9 likes

Hint: In order to answer this question, we need to have a basic idea about the ideal gas law. Even knowing the definition of density and molar mass of a gas, will be helpful in solving the question.

In terms of density we can derive the Ideal gas law as:

PV = nRT PV = nRT Where,

P = pressure of the gas

V = Volume of the gas

T = Temperature of the gas

n = number of moles of the gas

R = gas constant Number of moles = Given mass Molar mass

= Given massMolar mass

PV = w M × RT PV = wM × RT Where,

M = molar mass of the gas

w = mass of the gas ∴ P = wRT VM ∴ P = wRTVM ⇒P = ρ × RT M ⇒P =  ρ × RTM ∴ ρ = density = mass volume

∴ ρ = density = massvolume

⇒ ρ = PM RT ⇒ ρ = PMRT

Note: We should know that the ideal gas law, also called the general gas equation is the equation of state of a hypothetical ideal gas. It is a good approximation of the behaviour of many gases under many conditions although it has several limitations. Some of the limitations are mentioned below:

The ideal gas model tends to fail at lower temperatures or higher pressures when intermolecular forces and molecular size become important. It also fails for most heavy gases such as many refrigerants and for gases with strong intermolecular forces, notably water vapour.

We should also know that the ideal gas equation holds well as long as a density is kept low.

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## 6.9 Density and the Molar Mass of Gases (Video)

Last updated Sep 2, 2021

6.8 Second Type of Ideal Gas Law Problems (Video)

7: Thermochemistry

This project was preformed to supply Libretext Authors with videos on General Chemistry topics which can be used to enhance their projects.  Also, these videos are meant to act as a learning resource for all General Chemistry students.

Video Topics

The ideal gas law equation can be manipulated to show the relationship between the density of a gas and the molecular weight of the gas. The equation is d = MP/RT, d is the density of the gas in g/L, M is the molar mass of the gas in g/mol, P is pressure of the gas in ATM and R is the gas law constant. The equation shows that as the density of gas increases as the molar mass increases. This videos contains a sample calculation using this equation.