Molar Mass

Molar Mass is defined as the mass in grams of one mole of the given compound. A mole is a unit to measure the quantity of any substance. Any substance or compound that contains the N_a amount of entities, i.e., atoms, molecules, ions, is known as a mole, where N_a is called the Avogadros Number and the value of N_a is 6.023 × 10²³. 

The molar mass is also known as the sum of the total mass (in grams) of all the atoms present in a molecule per mole of the substance. It is calculated by finding the sum of all the individual elements of the molecule and taking its unit gram. Molecular mass is measured in grams and sometimes in kilograms.

It is also called Molecular Weight. Let’s learn about molar mass in more detail.

What is Molar Mass?

Molar mass is the mass of one mole of the compound in grams. It is also defined as “mass per mole”. Molar mass is the sum of the mass of atoms in 1 mole of a substance. The unit of molar mass is grams/mol. Mole is the unit used as a standard value in chemistry, and the standard value of 1 mole of any substance (atoms, molecules, etc.) is 6.023 × 10²³ units. It is also represented using Avogadro’s Number, (represented as N_A). The value of Avogadro’s Number (N_A) is 6.023 × 10²³

Learn more about, Mole Concept

Molar Mass Unit

The standard unit of molar mass is grams per mole. The molar mass unit is represented as grams/mol. The SI unit of molar mass is kg mol^-1. The following formula may be used to calculate molar mass is,

Molar Mass of Substance = (Mass of Substance in grams)/(Number of Moles of Substance)

The number of atoms present in 12 grams of C-12 isotope is the number of particles present in 1 mole of the substance. One mole of any substance contains the same amount of units i.e. 6.023 × 10²³ units. Therefore, for convenient 6.023 × 10²³ is named Avogadro’s Number (N_A).

Mole Definition

Mole, also written as mol, is the fundamental unit used to measure the amount of substance. A mole is defined as the amount of substance containing the same number of different entities (such as atoms, ions, molecules, and compounds) as the number of atoms in a sample of pure 12C weighing precisely 12 g. Even a gram of any pure element contains a high amount of atoms. One mole is also defined as the amount of a substance that contains as many entities as there are atoms in exactly 12 g of the ¹²C isotope. 

Molar Mass Formula

We can calculate the mass of atoms, molecules, etc. However, it becomes difficult to calculate the mass of each particle present in the substance. In order to make the measurement of masses more useful and easier, quantities are to be represented on a macroscopic level. The bridge between the substance and the macroscopic level is molar mass. Molar mass is important in the mole concept. The formula of molar mass is grams per mole. The formula is written as:

Molar mass = mass/mole = g/mol

Units of Molar Mass: SI unit is kg/ mol or gm/mol.

Below are some of the important formulas regarding molar mass:

Number of Moles of Atom	(Mass of Element in Gram)/(Relative Atomic Mass)
Number of Moles of Molecules	(Mass of Substance in Gram)/(Relative Molecular Mass)
Percentage Yield	(Actual mass of Product)/(Theoretical Mass of Product)
Percentage of Composition	(Mass of Entity present in Substance)/(Total Mass of Substance)
Mole fraction formula	(Number of Moles of Component in Mixture)/(Total Number of Moles in Component)

How is Molar Mass Calculated?

The French physicist Jean Baptiste introduced “Avogadro’s number”. Avogadro’s number is present in 1 mole of a substance. The substance can be atoms, molecules, etc.

1 mol = 6.023 × 10²³ units

Molar Masses of Compounds

The molar mass of the compound is the total molar mass of all the atoms present in the compound. It is calculated by taking the individual molar mass of each atom of the compound and adding all of them. 

For example, the molar mass of Methane CH₄ is calculated as,

It is clear from the chemical formula of methane that it has 1 carbon atom and 4 hydrogen atoms.

Thus, the molar mass of Methane is calculated as,

Mass of 4 hydrogen atoms = 4 × Mass of 1 Hydrogen atom = 4 × 1 = 4 amu

Mass of 1 carbon atom = 1 × Mass of 1 Carbon atom = 1 × 12 = 12 amu

Molar mass of Methane = 4 + 12 = 16 amu

Now, let’s take a look at some more examples to understand to find the molar mass of molecules,

Molar Mass of Water

The molar mass of water is the total sum of atomic masses of the atoms, and water (H₂O) contains 2 atoms of hydrogen and 1 atom of oxygen. The atomic mass of hydrogen is 1 amu and the atomic mass of oxygen is approximately 16 amu. Therefore, the molar mass of water becomes 18 g/mol.

Molar Mass of CO₂

The molar mass of CO₂ is the total sum of atomic masses of the atoms, and CO₂ contains 2 atoms of oxygen and 1 atom of carbon. The atomic mass of carbon is 12 amu and the atomic mass of oxygen is approximately 16 amu. Therefore, the molar mass of CO₂ becomes 44 g/mol.

Molar mass of H₂SO₄

The chemical formula of Sodium Carbonate is H₂SO₄. It contains two hydrogen atoms, one sulfur atom and four oxygen atoms. We know that the molecular weight of Hydrogen (H) is 1.0078 g/mol, Sulfur (S) is 32.065 g/mol, and Oxygen (O) is 16 g/mol. Therefore, the molar mass of sodium carbonate is,

• H = 2 × 1.0078 = 2.0156 g/mol.
• S = 1 × 32.065 = 32.065 g/mol.
• O = 4 × 16 = 64 g/mol.

By adding all we get = 2.0156 + 32.065 + 64 = 98.081 g/mol. Therefore, the molar mass of H₂SO₄ is 98.081 g/mol.

Molar mass of NaOH

The chemical formula of Sodium Hydroxide is NaOH. It has one hydrogen atom, one oxygen atom, and one Sodium atom. We know that the molecular weight of Hydrogen (H) is 1 g/mol, Oxygen (O) is 16 g/mol and Sodium (Na) is 23 g/mol.

Therefore, the molar mass of sodium hydroxide is,

• Na = 1 × 23 = 23 g/mol
• O = 1 × 16 = 16 g/mol
• H = 1 × 1 = 1 g/mol

By adding all we get = 23 + 16 + 1 = 40 g/mol. Therefore, the molar mass of NaOH is 40 g/mol.

Molar mass of NaCl

The chemical formula of Sodium Chloride is NaCl. It has one Sodium atom and one Chlorine atom. We know that the molecular weight of Sodium (Na) is 23 g/mol and Chlorine (Cl) is 35.5 g/mol.

Therefore, the molar mass of sodium chloride is,

• Na = 1 × 23 = 23 g/mol
• Cl = 1 × 35.5 = 35.5 g/mol

By adding all we get = 23 + 35.5 = 58.5 g/mol. Therefore, the molar mass of NaCl is 58.5 g/mol.

Molar mass of Urea

The chemical formula of Urea is NH₂CONH₂. It has two Nitrogen atoms, four Hydrogen atoms, one Carbon atom, and one Nitrogen atom. We know that the molecular weight of Nitrogen (N) is 14 g/mol, Hydrogen (H) is 1 g/mol, Carbon (C) is 12 g/mol, and Oxygen (O) is 16 g/mol.

Therefore, the molar mass of Urea is,

• N = 2 × 14 = 28 g/mol
• H = 4 × 1 = 4 g/mol
• C = 1 × 12 = 12 g/mol
• O = 1 × 16 = 16 g/mol

By adding all we get = 28 + 4 + 12 + 16 = 60 g/mol. Therefore, the molar mass of Urea is 60 g/mol.

What is the Percentage of Composition?

The percentage of composition of any compound is calculated by following the steps given below,

Step 1: Find the molar mass of the substance (atom) for which we have to find the percentage composition.

Step 2: Find the molar mass of the given substance.

Step 3: Calculate the percentage of the composition by using the formula,

Percentage = (Mass of Substance / Mass of Compound) × 100

Example: Find the mass percentage of hydrogen in a water molecule.

Solution:

Chemical Formula of Water = H₂O

Thus, water has 2 hydrogen atoms and 1 oxygen atom

Mass of 2 hydrogen atoms in 1 mole of water = 2 × Mass of Hydrogen atom = 2 × 1 = 2 g

Mass of 1 mole of water molecule = 2 × Mass of Hydrogen atom + 1 × Mass of Oxygen atom

                                                       = 2 × 1 + 1 × 16 = 18 g

Mass Percentage of Hydrogen in Water = 2 / 18 × 100 = 11.11 %

Molar Mass of Various Compounds

The molar mass of some compounds is discussed in the following table,

Compounds	Chemical Formula	Molar Mass
Urea	CH4N2O	60.06 g/mol
Sulphur	S	32.065 g/mol
Oxygen	O	15.99 g/mol
Oxalic Acid	C2H2O4	90.03 g/mol
Aluminium	Al	26.981 g/mol
Carbon	C	12.011 g/mol
Hydrogen	H	1.007 g/mol
Sodium	Na	22.989 g/mol
Calcium	Ca	40.078 g/mol
Copper	Cu	63.546 g/mol
Iron	Fe	55.845 g/mol
Helium	He	4.002 g/mol
Iodine	I	126.904 g/mol
Oxygen Gas (O2)	O2	15.999 g/mol
Chlorine	Cl	35.453 g/mol
Hydrogen Gas (H2)	H2	2.016 g/mol
Phosphorus	P	30.973 g/mol
Benzene	C6H6	78.11 g/mol
Methane	CH4	16.04 g/mol
Sodium Carbonate	Na2CO3	105.988 g/mol
Acetic Acid	CH3COOH	60.052 g/mol
Calcium Carbonate	CaCO3	100.086 g/mol
Ethanol	C2H5OH	46.07 g/mol
Sucrose	C12H22O11	342.3 g/mol

Read More,

• Atomic Mass
• Molecular Mass
• Molecular Weight

Solved Examples on Molar Mass

Example 1: Find the molar mass of Sodium Carbonate(Na₂CO₃).

Solution: 

The chemical formula of Sodium Carbonate is Na₂CO₃. It contains two sodium atoms, one carbon atom and three oxygen atoms. We know that the molecular weight of Sodium (Na) is 22.98g/mol, Carbon (C) is 12.011 g/mol and Oxygen (O) is 16 g/mol. Therefore, the molar mass of sodium carbonate is

• Na = 2 × 22.98 = 45.96 g/mol
• C = 1 × 12.011 = 12.011 g/mol
• O = 3 × 16 = 48 g/mol

Molecular Weight of Na₂CO₃ = 45.96 + 12.011 + 48 
                                              = 105.971 amu

Therefore, the molar mass of Na₂CO₃ is 105.971 g/mol.

Example 2: Find the molar mass of hydrochloric Acid (HCl).

Solution:

The chemical formula of Hydrochloric acid is HCl. It contains one Hydrogen atom, one chlorine atom. We know that the molecular weight of Hydrogen (H) is 1.0078g/mol, Chlorine (Cl) is 35.453 g/mol. Therefore, the molar mass of hydrochloric acid is

• H = 1 × 1.0078 = 1.0078 g/mol
• Cl = 1 × 35.453 = 35.453g/mol

Molecular Weight of HCl = 1.0078 + 35.543 
                                        = 36.460 g/mol

Therefore, the molar mass of HCl is 36.460 g/mol.

Example 3: Find the molar mass of Glucose (C₆H₁₁O₆).

Solution:

The chemical formula of Glucose is C₆H₁₁O₆. It contains six carbon atoms, eleven hydrogen atoms and six oxygen atoms. We know that the molecular weight of Carbon (C) is 12.011 g/mol, Hydrogen (H) is 1.0078 g/mol and Oxygen (O) is 16 g/mol. Therefore, the molar mass of glucose is,

• C = 6 × 12.011 = 72.066 g/mol.
• H = 12 × 1.0078 = 12.094 g/mol.
• O = 6 × 16 = 96 g/mol.

Molecular Weight of C₆H₁₁O₆ = 72.066 + 12.094 + 96
                                               = 180.16 g/mol. 

Therefore, the molar mass of Glucose is 180.16 g/mol.

Example 4: Find the molar mass of Potassium Permanganate (KMnO₄).

Solution:

The chemical formula of Potassium Permanganate is KMnO₄. It contains 1 Potassium Atom, 1 Manganese Atom and 4 Oxygen Atoms. We know that the molecular weight of Potassium (K) is 39.098 g/mol, Manganese (Mn) is 54.937 g/mol and Oxygen (O) is 16 g/mol. Therefore, the molar mass of Potassium Permanganate is,

• K = 1 × 39.098 = 38.098 g/mol.
• Mn = 1 × 54.938 = 54.938 g/mol.
• O = 4 × 16 = 64 g/mol.

Molecular Weight of KMnO₄ = 39.098 + 54.938 + 64 

                                             = 158.036 g/mol. 

Therefore, the molar mass of KMnO₄ is 158.036 g/mol.

Example 5: Find the molar mass of Magnesium Chloride(MgCl₂).

Solution:

The chemical formula of Magnesium Chloride is MgCl₂. It contains one Magnesium atom, one chlorine atom. We know that the molecular weight of Magnesium (Mg) is 24.305 g/mol, Chlorine (Cl) is 35.453 g/mol. Therefore, the molar mass of Magnesium Chloride is

• Mg = 1 × 24.305 = 24.305 g/mol
• Cl = 2 × 35.453= 70.906 g/mol

Molecular Weight of MgCl₂  = 24.305 + 70.906 
                                            = 95.211 g/mol

Therefore, the molar mass of Magnesium Chloride is 95.211 g/mol.

FAQs on Molar Mass

Q1: What is molar mass?

Answer:

The molar mass of the compound is defined as the mass of one mole of a compound measured in grams. It is calculated in g/mol. 

Q2: Are molar mass and molecular mass the same?

Answer:

No, molar mass and molecular mass are not the same. Molar mass is the mass of one mole of the substance, which is measured in grams and molecular mass is the mass of one molecule and is measured in AMU.

Q3: Why Avogadro’s number is called a mole?

Answer:

The mole (mol) is a unit that is equal to Avogadro’s number. The word ‘mole’ has come from the word molecule. 1 mole of any substance is equal to 6.023 × 10²³ units, which is the Avogadro’s number. For example, 1 mole of water molecule contains 6.023 × 10²³ molecules.

Q4: What does Avogadro’s law state?

Answer:

Avogadro’s law or the theory of Avogadro is an experimental law which is related to the volume of gas w.r.t the amount of gas. Avogadro’s law states “equal quantities of all gases have same number of molecules at the same temperature and pressure”.

Q5: What is one mole equal to?

Answer:

One mole is the collection of 6.0221367 × 10²³ units of a substance. Here, the substance is atoms, molecules, or ions.