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# How to Calculate the Molar Mass of a Gas?

Molar Mass can be defined as the mass of a sample divided by the number of moles present in the substance. We know that all the particles present in this world are made of smaller molecules known as molecules or atoms. Due to the extremely small size of these particles, it is very difficult to measure the weight of these particles. So for this reason the molar mass of a molecule is considered when it is required.

## What is Molar Mass?

Molar Mass can also be defined as the mass of a substance in grams in one mole of the given compound. A mole is defined as the number of molecules of a substance present in the given substance. The number of molecules or atoms present on any mole is constant and is 6.02214076 × 1023. The unit of molar mass is gram per mole.

The molar mass of gases can be calculated with the help of the Ideal gas Equation.

## Ideal Gas Equation

An ideal gas is a theoretical gas and is not present practically. It is said to have collisions among the particles and these collisions are perfectly elastic. The ideal gas equation is used to prove the existence of Ideal gases and find out more about their properties. It is derived by using Boyle’s law and Charles’s law.

By Boyle’s law, at constant temperature for a fixed number of moles, the volume of the gas is inversely proportional to the pressure of the gas.

v ∝ 1/p

By Charles’s law, at constant pressure for a fixed number of moles, the volume of the gas is directly proportional to the temperature of the gas.

v ∝ T

By Avogadro’s law, at constant pressure and temperature, the volume of the gas is directly proportional to the number of moles.

v ∝ n

If we combine all the above equations we get:

v ∝ nT/P

PV = nRT

Thus, the Ideal gas Equation is

PV = nRT

where,

P is the pressure on the Gas.
V is the Volume of the Gas
n is the number of moles present in the Gas.
R is the Universal Gas Constant
T is the temperature of the Gas

## How to Calculate the Molar Mass of a Gas?

We know that the molar mass is the ratio of the mass of gas and the number of moles of gas.

M = m/n

n = m/M

substituting the value of n in the Ideal gas Equation.

PV = m(RT)/M

Thus, the molar mass of gas is calculated by the formula given below,

M = mRT / PV

where,

M is the molar mass of gas.
m is the mass of Gas.
P is the pressure on the Gas.
V is the Volume of the Gas
R is the Universal Gas Constant
T is the temperature of the Gas

## Solved Examples on Molar Mass

Example 1: Calculate the molar mass of a gas if the mass of gas is 1.211 grams and the volume of 677 ml at a temperature of 23o C at a pressure of 0.987 atm.

Solution:

mass = 1.211 grams
volume = 677 ml = 0.677 L
Temperature = 23o = 296 K
Pressure = 0.987 atm
R = 0.08206

the number of moles is

n = PV / RT

n= ( 0.987 × 0.677 ) / (0.08206 × 296)
n= 0.0275 moles.

The molar mass is the ratio of the mass of gas and the number of moles of gas.

M = m/n

M= 1.211/0.0275
M= 44 gram / moles

Example 2: Calculate the density of Nitrogen gas at STP.

Solution:

Molecular mass is 2 × 14 grams per mole = 28

1 mole of gas has 22.4 liters

density = 28/22.4

d = 1.25 grams per liters.

Example 3: Calculate the molar mass of gas present in a 3-liter tank at 300 K temperature at 650 Hg pressure when the mass is 14.5 grams.

Solution:

P = 650/760

P = 0.855

V = 3 lit

m = 14.5 grams

T = 300 K

From the equation

M = mRT / PV

M =(14.5 × 0.05206 × 300)/ (0.0855 × 3)

M =139.1 g/liter

Example 4: Calculate the molar mass of the given gas if it has a density of 1.48g/l at a temperature of 40°C and pressure of 125 KPa.

Solution:

Temperature = 40° C or 313 K

Density (d) = 1.48

Pressure = 125 Kpa

dRT = PM

M = dRT/P

M = (1.48 × 0.08206× 313) / 1.224

M = 30.8 g/l

Example 5: What is the molar mass of the gas if 7.723g of gas occupies a volume of 2.4 liters at a temperature of 27°C if the pressure is 1.8 atm?

Solution:

PV = nRT

PV = mRT / M

MPV = mRT

M = mRT / PV

M = (7.723)×(0.08206)×(27+273) / (1.8)×(2.4)

M = (7.723)×(0.08206)×(300) / (1.8)×(2.4)

M = 44.01 g/mol

## FAQs on Molar Mass of Gas

Question 1: What is a mole?

A mole is defined as the number of molecules of a substance present in the given substance. The number of molecules or atoms present on any mole is constant and is 6.02214076 × 1023. The unit of molar mass is gram per mole.

Question 2: What is Molar Mass?

Molar mass can be defined as the mass of a sample divided by the number of moles present in the substance, Molar Mass can be defined as the mass of a substance in grams in one mole of the given compound.

Question 3: State the Avogadro law.

By Avogadro’s law, at constant pressure and temperature, the volume of the gas is directly proportional to the number of moles.

v ∝ n

Question 4: State the Boyles law.

By Boyle’s law, at constant temperature for a fixed number of moles, the volume of the gas is inversely proportional to the pressure of the gas.

v ∝ 1/p

Question 5: State the Charles law.

By Charles’s law, at constant pressure for a fixed number of moles, the volume of the gas is directly proportional to the temperature of the gas.

v ∝ T

Question 6: State the Ideal Gas Equation.

We know that the Ideal gas Equation is

PV = nRT

where,

P is the pressure on the Gas.
V is the Volume of the Gas
n is the number of moles present in the Gas.
R is the Universal Gas Constant
T is the temperature of the Gas

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