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# Molar Mass

We know that atoms are smallest units of any matter. The chemical and physical properties of any state of matter is entirely depends upon their constituent atoms. Therefore it is necessary to calculate the mass of an atom so that we calculate the mass of a molecule also. The atomic and molecular mass can be represented in terms of "Mole concept". A mole can be defined as a collection of atoms whose mass is equal to the atomic mass in grams. The number of atoms in a mole is 6.02 x 1023. This number is known as Avogadro’s number.

One mole is the amount of substance that contains as many particles (atoms or molecules) as there are in 12.0 g of C-12 (Carbon 12). For example, the atomic mass of nitrogen is 14.00 amu. This means that a sample with a mass of 14.00 grams has 6.02 x 1023 atoms of nitrogen in it. In the same way, 1 mole H2O has the same number of molecules as in 18.015 g of H2O. Or one mole hydrogen molecule contains the same number of molecules as in 2.016 g of H2. The mass of one mole of a substance is known as Molar Mass which symbolized by M. The unit of M is g/mol. Let’s discuss the molar mass of some other atoms and molecules.

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## Molar Mass Units

Let us consider an example of the molecule, sodium hydroxide. The atom of sodium combines with an atom of oxygen and hydrogen to form a molecule of sodium hydroxide. Thus, it is expected that the mass of the molecule would be the sum of the masses of sodium, oxygen and hydrogen. This is the molar mass of sodium hydroxide.

The unit of this mass is gram per mole. However, when this mass is shown in grams instead of atomic mass unit, it is known as a mole. The atomic masses of sodium, oxygen and hydrogen are 23, 16 and 1 respectively. The molar mass is, therefore, 23 plus 16 plus 1, which is 40. This molar mass when expressed in grams that is 40 grams is a mole of sodium hydroxide. The units of molar mass are grams per mole. Sometimes another unit known as Dalton is also used for molar mass.

## Molar Mass Equation

The volume of the liquid, usually can be calculated very easily. We use the gas equation
P V = n R T

n = $\frac{PV}{RT}$
After calculating the number of moles of the gas, we can use the relationship:

Moles of the liquid = Mass in grams / Molar mass

So, Molar mass can be calculated as:

Molar mass = Mass in grams / Moles of the liquid

This method of finding the molar mass of a liquid is called as VICTOR- MEYER’S METHOD.

Use the below widget to calculate the molar mass.

## Relevance on Molar Mass

There is a difference between molecular mass and molar mass. Molar mass is never measured directly. It is calculated by summing up the atomic masses. The molecular mass is measured directly. For example, molecule of water and molecule of heavy water. The molecular masses are different as both have different isotopes of hydrogen.

It is a very useful term and is used in different chemical calculations of stoichiometry and other colligative properties.

For example, in the Avogadro’s gas law equation:

PV = nRT

where, n is number of moles.

The molar masses are indispensable in other studies such as freezing point depression etc.

## Molar Mass of Water

Water is made up of hydrogen and oxygen, with a formula of H2O. There are 2 mole of Hydrogen and 1 moles of Oxygen.

Therefore, Molar mass of water would be:
2 x H + O = 2 x 1.008 + 16
= 18.016 g/mol = 18 g/mol

## Molar Mass of Gas

Let us calculate molar mass of air :
The experiment to determine the molar mass of a gas is given as follows. There are certain precautions to be taken before the experiment is done.
1. How can we find the volume of the flask in which the gas is placed?
2. Since the flask will contain air, how can it be measured empty?
Once all these problems are overcome, these are the calculations done to calculate the molar mass of a gas, say ethane.

Calculations:
At room temperature and pressure,
Density of air = 1. 205 x 10-3 g/cm
Mass of flask + air = 58. 262 g
Mass of flask + ethane = 58. 285g
Volume of flask = 242.5 cm3

First, we find the mass of the flask :

Mass of the flask = ( mass of flask + air) – (mass of air)
But,
Mass of air = Density of air x volume of air

So, Mass of flask = 58. 262 – (1.205 x 10-3 g/cm3)
= 57.97grams

Now we use this result to give us the mass of ethane,

Mass of ethane = (Mass of flask + ethane) – Mass of flask
= 58.285g – 57.97 g = 0.315 grams

Therefore, the mass of 1 mol of ethane is given by
0.315 g x 24000cm3 / 242.5 cm3 = 31.18 gram
M(ethane) = 31.18 g/mol

The molar mass of ethane is almost exactly 30 grams/mol. So, there is an error of nearly 4% in the result.

## How to Calculate Molar Mass?

Molar mass of a compound is usually calculated by adding the individual molar mass of all the elements present in it.

### Solved Examples

Question 1: Let us say, for example, we need to calculate the molar mass of Sodium hydroxide.
Solution:
The formula of Sodium hydroxide is NaOH. It contains sodium, hydrogen and oxygen.

Let us add the molar masses of all these elements:

Na: 22.98 g/mol

O: 16 g/mol

H: 1.008 g/mol.

22.98 + 16 + 1.008 = 39.98 g/mol

The molar mass of Sodium hydroxide is usually rounded off to

40gram /moles.

Question 2: Calculate the molar mass of Copper sulphate
Solution:
Copper sulphate contains: Cu + S + 4 x O

Cu = 63.55 g/mol

S = 32 g/mol

O = 16g/mol

Cu + S + 4 x O = 63.55 + 32 + 4 x 16 = 159.55 = 160 g/mol.

So, molar mass of Copper sulphate is 160 grams/mol.

## Average Mass of Atoms from Molar Mass

Average mass of all the atoms of any element can be done using the molar mass value of that particular element.

### Solved Example

Question: Find the mass of a single atom of Silicon.
Solution:
Molar mass of Silicon = 28.09 grams/mole.

Avagadro’s constant = 6.023 x 1023 per mole.

Mass of one silicon atom = 28.09 g Si / 1 mole of Si x 1mole of Si /6.023 x 1023 atoms of Si

Mass of one atom of Si = 4.665 x 10-23 grams/atom.

## Mole Conversion using Molar Mass

Below are some Mole Conversion problems.

### Solved Examples

Question 1: Determine the mass in grams of 3.50 moles of Copper.
Solution:
We know that moles are associated with mass in grams, by the relationship

Moles of a compound/element = $\frac{Mass\ in\ grams}{Molar\ mass\ of\ the\ compound/element}$.

Thus, Moles of copper = 3.50 moles.

Molar mass of Cu = 63.55 grams/mol.

So, this can be written as: 63.55 g Cu / 1 mole of Cu

Multiplying the number of moles with this factor

= 3.50 moles of Cu x 63.55 g Cu/1 mole of Cu

= 222 grams of Copper

Question 2: Determine the number of moles represented by 237 grams of Strontium.
Solution:
Molar mass of Strontium = 38 grams/mol.

So, Molar mass of Strontium = 38 grams of Sr/ 1 mole of Sr.

Multiplying the number of grams by this factor:

237 g of Sr x 1 mole of Sr/38 grams of Sr

Moles of Strontium = 6.24 moles.

Question 3: Find the mass in grams of 8.6 moles of Bromine atoms.
Solution:
Molar mass of Bromine = 80 grams/mol.

So, Molar mass of Bromine = 80 grams of Br / 1 mole of Br.

Multiplying the number of moles by this factor,

= 8.6 moles of Br x 80 grams of Br/1 mole of Br

= 688 grams of Br.

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