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Calculate Molar Mass of A Gas Using Ideal Gas Law

Ideal gas law is an equation of state for a gas. This means that the state of the gas is its condition at a given time. It is important to recognize that the ideal gas law is an empirical equation that based on experimental measurements. The gas that obey this ideal gas law is said to behave ideally. However most gas obey the ideal gas law equation closely enough at pressure below 1 atm that only minimal errors result from assuming ideal behavior. A particular state of the gas is described by its pressure, volume, temperature, and number of moles. The knowledge of any three of these properties is enough to define the state of the gas, since the fourth property can be determined from the equation.

Here is the example how we calculate the molar mass of the gas using ideal gas law:

“What is the molecular mass of a gas if a volume of 500 cm³ has a mass of 1.00 g at -25⁰C and 98.4 KPa?”

use the ideal gas law formula

in which:
P = Pressure in atm
V = Volume in Liter
n = mol
R = universal gas constant 0.08206 L.atm/K.mol
T = Temperature in K

First change the unit of all of the formula above

1 atm = 101325 Pa , so
P = 98.4 KPa = 98400 Pa
P = 98400 Pa/101325 Pa x 1 atm = 0.971 atm
V = 500 cm3 = 500 mL = 0.5 L
T = (-25) + 273 = 248 K

and substitute to the ideal gas law we have

0.971 atm x 0.5 L = n x 0.08206 L.atm/K.mol x 248 K
n = 0.024 mol

we know that mol = mass / Mr , thus

Mr = mass/mol
Mr = 1 / 0.024
Mr = 41.667
Mr = 42

thus the molecular mass of the gas is 42 gr/mol

Add comment June 8th, 2008

The Ideal Gas Law Formula

The three laws of the behavior of the gas are discribe with the Boyle’s, Charles’s, and Avogadro’s law as mention below:

Boyle’s law (at constant T and n )

Charles’s law (at constant P and V)

Avogadro’s law ( at constant T and P)

The relationships in which the volume of the gas that depends on pressure, temperature, and the number of moles of gas can be write as:

the equation above can be writen as :

the equation above more familiar called “The Ideal Gas law”

P = pressure in atm
V = volume in Liter
n = number of moles in mol
R = universal gas constant = 0.08205 L.atm/K.mol

The ideal gas law can be used to solved a variety of problems. You can find one of the characteristic of the gas if the other three is known.

Add comment June 8th, 2008