Molar Mass of Gas
We can derive a form of the Ideal Gas Equation, PV=nRT, that incorporates the molar mass of the gas (M,
Learning Objective

Apply knowledge of molar mass to the Ideal Gas Law
Key Points
 The molecular weight (molar mass) of any gas is the mass of one particle of that gas multiplied by Avogadro's number (6.02 x 10^{23}).
 Knowing the molar mass of an element or compound can help us stoichiometrically balance a reaction equation.
 The average molar mass of a mixture of gases is equal to the sum of the mole fractions of each gas (x_{i}) multiplied by the molar mass (M_{i}) of that particular gas:
$\bar { M} =\sum _{ i }^{ }{ { x }_{ i }{ M }_{ i } }$ .
Terms

stoichiometry
the study and calculation of quantitative (measurable) relationships of the reactants and products in chemical reactions (chemical equations)

molar mass
the mass of one mole of an element or compound

ideal gas
a hypothetical gas whose molecules exhibit no interaction and undergo elastic collision with each other and with the walls of the container
Full Text
Molar Mass of Gases and Gas Mixtures
Molar mass (M) is equal to the mass of one mole of a particular element or compound; as such, molar masses are expressed in units of grams per mole (g mol^{–1}) and are often referred to as molecular weights. The molar mass of a particular gas is therefore equal to the mass of a single particle of that gas multiplied by Avogadro's number (6.02 x 10^{23} ). To find the molar mass of a mixture of gases, you need to take into account the molar mass of each gas in the mixture, as well as their relative proportion.
The average molar mass of a mixture of gases is equal to the sum of the mole fractions of each gas, multiplied by their respective molar masses:
The molar volumes of all gases are the same when measured at the same temperature and pressure (22.4 L at STP), but the molar masses of different gases will almost always vary.
Calculating Molar Mass using the Ideal Gas Equation
The molar mass of an ideal gas can be determined using yet another derivation of the Ideal Gas Law:
We can write n, number of moles, as follows:
where m is the mass of the gas, and M is the molar mass. We can plug this into the Ideal Gas Equation:
Rearranging, we get:
Finally, putting the equation in terms of molar mass, we have:
This derivation of the Ideal Gas Equation is useful in determining the molar mass of an unknown gas.
Example
 An unknown gas with a mass of 205 g occupies a volume of 20.0 L at standard temperature and pressure. What is the molar mass of the gas?

$M=\frac{mRT}{PV}$
Key Term Reference
 Avogadro's number
 Appears in these related concepts: Equations of State, Early Models of the Atom, and Converting between Moles and Atoms
 Pressure
 Appears in these related concepts: SI Units of Pressure, Physics and Engineering: Fluid Pressure and Force, and Surface Tension and Capillary Action
 compound
 Appears in these related concepts: Molecules, Compound Inequalities, and Hyphens
 element
 Appears in these related concepts: Development of the Periodic Table, Elements and Compounds, and The Periodic Table
 fraction
 Appears in these related concepts: SI Unit Prefixes, Separable Equations, and Fractions
 gas
 Appears in these related concepts: Three States of Matter, Irreversible Addition Reactions, and Microstates and Entropy
 mixture
 Appears in these related concepts: The Law of Definite Composition, Substances and Mixtures, and Complex Ion Equilibria and Solubility
 mole
 Appears in these related concepts: Avogadro's Number and the Mole, Molar Mass of Compounds, and Concept of Osmolality and Milliequivalent
 mole fraction
 Appears in these related concepts: Writing Formulas for Polymeric Macromolecules, Mole Fraction and Mole Percent, and Dalton's Law of Partial Pressure
 temperature
 Appears in these related concepts: Extractive Metallurgy, Heat and Work, and Temperature
 volume
 Appears in these related concepts: Volumes, Volume and Density, and Shape and Volume
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