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# Molar Mass

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 Sub Topics The term molar mass is used all the time in chemical calculations. Whether we are dealing with elements or compounds the molar mass of a species is the mass in grams of one mole (6.023 $\times$ 1023) of that species: one mole of atoms one mole of molecules or one mole of formula units.Molar mass is an extremely useful term that can be applied to any chemical species. Molar mass is the mass per mole of a substance. The units of molar mass are gmol-1. For the atoms of an element the molar mass is simply the relative atomic mass g mol-1.

## What is Molar Mass?

"The molar mass of any substance in grams per mole is numerically equal to atomic, molecular or formula mass of that substance in atomic mass units."

To make measurements of mass useful we must express chemical quantities at the macroscopic level. The bridge between the particulate and the macroscopic levels is molar mass, the mass in grams of one mole of a substance. The units of molar mass follow from its definition: grams per mole (g/mol).

## Molar Mass Definition

Definition of molar mass

The definition of molar mass, the mole and atomic mass are all directly or indirectly related to carbon-12.This leads to two important facts.
1. The mass of one atoms of caron-12 the atomic mass of carbon-12 is exactly 12 atomic mass units.
2. The mass of one mole of carbon-12 atoms is exactly 12 grams its molar mass is exactly 12 grams per mole.

Atomic mass and the molar mass of carbon-12 are numerically equal. They differ only in units. Atomic mass is measured in atomic mass units and molar mass is measured in grams per mole.

## Molar Mass Formula

The mass of one mole of an element or compound is called its molar mass (symbol M). The molar mass of copper is 63.5 g mol-1. The molar mass of sodium hydroxide is 40 g mol-1. There is a quantity that relates to the number of particles in a mass of substance. This quantity is called the amount of substance.

$Amount\ of\ substance\ = \frac{Mass}{Molar\ mass}$

Molar mass equation is obtained by rearranging the above equation.

$Molar\ Mass = \frac{Mass}{Amount\ of\ substance}$

If mass is stated in g and molar mass in g mol-1, then the unit of amount is mol.

## Molar Mass Units

The SI unit of molar mass is kilogram per mole (kg/mol).

Quantity symbol: M

Mass of a substance divided by its amount of substance

$M = \frac{m}{n}$

For a mixture this term is often called "mean molar mass". The molar mass is also expressed in g mol-1, but it is important to remember that in making calculations in which all other quantities are expressed in SI units the molar mass must be expressed in kg mol-1.

## How to Find Molar Mass?

Finding molar mass

The molar mass of a compound is the sum of the relative atomic masses of the atoms in a molecule or formula unit of the compound expressed in g mol-1.

How to calculate molar mass?

To calculate molar mass the mass and amount of substance must be known. Below some of the molar mass examples are given.

### Solved Examples

Question 1: Assuming that atmospheric air is a mixture of nitrogen and oxygen in the mole ratio 79:21 estimate the molar mass of air.
Solution:

The mass of one mole of a substance is called molar mass.
Basis: 1 mole of air

N2 present in air = 0.79 mol and O2 present in air = 0.21mol
Molar mass of nitrogen = 28 $\times$ 10-3kg
Molar mass of oxygen = 32 $\times$ 10-3kg
Molar mass of air = 0.79 $\times$ 28 $\times$ 10-3 + 0.21 $\times$ 32 $\times$ 10-3
Molar mass of air = 28.84 $\times$ 10-3kg

Question 2: What is the molar mass of glucose C6H12O6?
Solution:

Sum of relative atomic mass = 6A(C) + 12A(H) + 6A(O)
Molar mass = (6 $\times$ 12) + (12 $\times$ 1) + (6 $\times$ 16) = 180
Molar mass = 180 g mol-1

## Periodic Table with Molar Mass

Take a look at the periodic table molar mass. Notice how there is a number which represents the atomic mass of each atom. Usually it is located right under the symbol for that element, like this

$_{20.18}Ne^{10}$

The number underneath the symbol is the atomic mass of that element. For neon the atomic mass is 20.108. This number is also known as molar mass.

The molar mass tells how many grams are in a mole of atoms of that elements. So 6.02 $\times$ 1023 atoms of neon will have a mass of 20.108 grams.

The following diagram illustrates how to calculate the mass of atoms by using their molar masses.

## Molar Mass Table

Molar mass of a compound is the mass in grams of Avogadro number of molecules of a compound. Molar masses of some compound are listed in the following table.

 S.No Name of the molecule Molar mass (g/mol) 1 Molar mass of water 18.0153 2 Molar mass of NaOH 39.997 3 Molar mass of ethanol 46.06844 4 Molar mass of NaCl 58.44 5 Molar mass of CO2 44.01 6 Molar mass of air 28.97 7 Molar mass of HCl 36.46094 8 Molar mass of glucose 180.16 9 Molar mass of sucrose 342.2965 10 Molar mass of H2O 18 11 Molar mass of O2 31.9988 12 Molar mass of N2 28.01344 13 Molar mass of carbon 12.01078 14 Molar mass of acetic acid 60.05 15 Molar mass of copper 63.5463 16 Molar mass of helium 4.002 17 Molar mass of NH3 17.031 18 Molar mass of aluminum 26.98153868 19 Molar mass of butane 58.12 20 Molar mass of methanol 32.04 21 Molar mass of iron 55.845 22 Molar mass of magnesium 24.30506 23 Molar mass of KCl 74.5513 24 Molar mass of CaCO3 100.0869 25 Molar mass of Na2CO3 105.9886 26 Molar mass of methane 16.04 27 Molar mass of H2SO4 98.079 28 Molar mass water 18.0153 29 Molar mass of CaCl2 110.98 30 Molar mass of ammonia 17.031 31 Molar mass of silver 107.8682 32 Molar mass of acetone 58.08 33 Molar mass of argon 39.948 34 Molar mass of calcium 40.08 35 Molar mass of benzene 78.11 36 Molar mass of aspirin 180.157 37 Molar mass of sodium 22.989 38 Molar mass of hexane 86.18 39 Molar mass of H2 2.0158 40 Molar mass of urea 60.06 41 Molar mass of zinc 65.41 42 Molar mass of NaHCO3 84.007 43 Molar mass of sulfur 32.065 44 Molar mass of benzoic acid 122.12 45 Molar mass of CuSO4 159.62 46 Molar mass of chlorine 35.453 47 Molar mass of salicylic acid 138.121 48 Molar mass of CO 28.010 49 Molar mass of potassium 39.10 50 Molar mass of KOH 56.1056 51 Molar mass of NH4Cl 53.4917 52 Molar mass of iodine 253.8

## Molar Mass Problems

When the formula weight of an ionic compound is determined by the addition of its component relative atomic masses and expressed in grams, it is called the molar mass. Some of example problems are given below.

### Solved Examples

Question 1: Find the molar mass of a gas when the density is given as 1.25 g/L.
Solution:

Since it is known that 1 mol of a gas occupies 22.4L at STP we can solve this problem by multiplying the mass of 1L by 22.4 L/mol.

$\frac{1.25\ g}{L} \times \frac{22.4\ L}{1\ mol}$ = 28 g/mol

Even if the weight given is not for 1L, the same setup can be used.

Question 2: Find the molar mass of 1 mole of H2SO4.
Solution:

The molar mass id equivalent to the mass of 1 mole of that compound expressed in grams.

2 H = 1.00794 $\times$ 2 = 2.01588
1S = 32.066
4 O =
15.9994 $\times$ 4 = 63.9976

1 mole of H2SO4 =
2.01588 + 32.066 + 63.9976 = 98.07 g/mol