 ## Molar Mass

The molar mass of a substance (chemical element or compound) is the mass of one mole of the substance. It is a physical quantity that is measured and expressed in g/mol.

### How to Calculate Molar Mass

The molar mass of a substance is calculated by summing up the product of the relative atomic mass and number of atoms of all the elements that make up the substance as expressed in its chemical formula. For an element, the molar mass is the atomic mass of the element.

For example: calculate the molar mass of the following substances:

1. Water, H2O

The relative atomic masses of the elements in water, H2O are: H = 1, O = 16.

Therefore, the molar mass is: relative atomic mass of hydrogen x number of atoms of hydrogen + relative atomic mass of oxygen x number of atoms of hydrogen.

This is expressed as 1x2 + 16x1 = 2 + 16 = 18

The molar mass of water, H2O is therefore 18g/mol

2. Hydrochloric acid, HCl

The relative atomic masses of the elements in hydrochloric acid, HCl are H = 1, Cl = 35.5.

The molar mass is calculated as follows: relative atomic mass of H + relative atomic mass of chlorine, which is 1 + 35.5 = 36.5g/mol

3. Tetraoxosulphate(VI) acid, H2SO4

The relative atomic masses of the elements in H2SO4 are: H = 1, S = 32, O = 16.

Calculating the molar mass, we have: 1x2 + 32 + 16x4

= 2 + 32 + 64 = 98

The molar mass of H2SO4 is 98g/mol

4. Glucose, C6H12O6

The relative atomic masses of elements in C6H12O6  are: C = 12, H = 1, O = 16.

Calculating the molar mass, we have: 12x6 + 1x12 + 16x6

= 72 + 12 + 96 = 180

Therefore, the molar mass of glucose is 180g/mol

5. Calcium trioxocarbonate(IV), CaCO3

The relative atomic masses of elements in CaCO3 are Ca = 40, C = 12, O = 16

Calculating the molar mass, we have: 40 + 12 + 16x3

= 40 + 12 + 48 = 100

Therefore, the molar mass of CaCO3 is 100g/mol

6. Sucrose, C12H22O11

The relative atomic masses of elements in C12H22O11 are: C = 12, H = 1, O = 16

Calculating the molar mass, we have 12x12 + 1x22 + 16x11

= 144 + 22 + 176 = 342

Therefore, the molar mass of sucrose is 342g/mol

7. Methane, CH4

The relative atomic masses of the elements in CH4 are: C = 12, H = 1

Calculating the molar mass gives 12 + 1x4

= 12 + 4 = 16

The molar mass of methane is 16g/mol

8. Acetic acid, CH3COOH

The relative atomic masses of elements in CH3COOH: C = 12, H = 1, O = 16

Calculating the molar mass of CH3COOH, we have 12x2 + 1x4 + 16x2

= 24 + 4 + 32 = 60

Therefore, the molar mass of acetic acid is 60g/mol

9. Sodium hydroxide, NaOH

The relative atomic masses of the elements in NaOH are: Na = 23, O = 16, H = 1

Calculating the molar mass of NaOH: 23 + 16 + 1 = 40

Therefore, the molar mass of sodium hydroxide is 40g/mol

10. Ammonia, NH3 The relative atomic masses of the elements in NH3 are: N = 14, H = 1

Calculating its molar mass: 14 + 1x3

= 14 + 3 = 17

Therefore, the molar mass of NH3 is 17g/mol

11. Butane, C4H10 The relative atomic masses of elements in C4H10 are: C = 12, H = 1

Calculating its molar mass: 12x4 + 1x10

= 48 + 10 = 58

Therefore, the molar mass of butane is 58g/mol

12. Copper(II) sulphate, CuSO4 The relative atomic masses of the elements in CuSO4 are: Cu = 64, S = 32, O = 16

Calculating the molar mass, we have: 64 + 32 + 16x4

= 64 + 32 + 64 = 160

Therefore, the molar mass of CuSO4 is 160g/mol

13. Potassium chloride, KCl

The relative atomic masses of elements in KCl are: K = 39, Cl = 35.5

Calculating its molar mass, 39 + 35.5 = 74.5

The molar mass of KCl is therefore 74.5g/mol

14. Calcium chloride, CaCl2 Relative atomic masses of elements in CaCl2 are: Ca = 40, Cl = 35.5

Calculating its molar mass, we have, 40 + 35.5x2

= 40 + 71 = 111

Therefore, the molar mass of CaCl2 is 111g/mol

15. Methanol, CH3OH

Relative atomic masses of elements in CH3OH are: C = 12, H = 1, O = 16

Calculating the molar mass, we have, 12 + 1x4 + 16

= 12 + 4 + 16 = 32

The molar mass of methanol is 32g/mol

16. Ethanol, C2H5OH

The relative atomic masses of elements in C2H5OH are: C = 12, H = 1, O = 16

Calculating its molar mass = 12x2 + 1x6 + 16

= 24 + 6 + 16 = 46

The molar mass of ethanol is therefore 46g/mol

17. Carbon(IV) oxide, also called carbon dioxide, CO2

The relative atomic masses of the elements in CO2: C = 12, O = 16

Calculating its molar mass, we have 12 + 16x2

= 12 + 32 = 44

Therefore, the molar mass of carbon(IV) oxide is 44g/mol

18. Sodium chloride, NaCl

The relative atomic masses of elements in NaCl: Na = 23, Cl = 35.5

Calculating its molar mass, we have 23 + 35.5 = 58.5

The molar mass of NaCl is 58.5g/mol

19. Acetone, C3H6O The elements in C3H6O and their relative atomic masses are: C = 12, H = 1, O = 16

Calculating its molar mass: 12x3 + 1x6 + 16

= 36 + 6 + 16 = 58

Therefore, the molar mass of acetone is 58g/mol

20. Salicylic acid, C7H6O3

The elements in C7H6O3 and their relative atomic masses are: C = 12, H = 1, O = 16

Calculating its molar mass: 12x7 + 1x6 + 16x3

= 84 + 6 + 48 = 138

Therefore, the molar mass of salicylic acid is 138g/mol

21. Benzene, C6H6 The elements in C6H6 and their relative atomic masses are: C = 12, H = 1

Calculating the molar mass: 12x6 + 1x6

= 72 + 6 = 78

The molar mass of benzene is therefore 78g/mol

22. Aspirin, C9H8O4

The relative atomic masses of elements in C9H8O4 are: C = 12, H = 1, O = 16

Calculating its molar mass: 12x9 + 1x8 + 16x4

= 108 + 8 + 64 = 180

Therefore, the molar mass of aspirin is 180g/mol

### How to Determine the Molar Mass of Air

Air is a mixture of gases; therefore, its molar mass can be determined by summing up the molar masses of all the constituent gases.

The gases that make up air are: oxygen, nitrogen, carbon dioxide (or carbon(IV) oxide), hydrogen, argon, neon, helium, krypton, xenon. The actual molar mass of each gas present in the mixture can be found out by multiplying the mass of one molecule of the gas by its volume ratio to dry air (or the percentage of the gas in dry air).

The volume ratio of the gases to dry air (or the percentage of the gases in dry air) are given as: oxygen (0.2095 or 20.95%); nitrogen (0.7809 or 78.09%); carbon dioxide (0.0003 or 0.03%); hydrogen (0.0000005 or 0.00005%); argon (0.00933 or 0.933%); neon (0.000018 or 0.0018%); helium (0.000005 or 0.0005%); krypton (0.000001 or 0.0001%); xenon (0.09 x 10-6 or 0.09 x 10-4 %).

Calculating the molar mass of each gas in air: Oxygen, O2, molecular mass = 16 x 2 = 32. Molar mass of oxygen in air = 32 x 0.2095 = 6.704g/mol

Nitrogen, N2, molecular mass = 14 x 2 = 28. Molar mass of nitrogen in air = 28 x 0.7809 = 21.88g/mol

Carbon dioxide, CO2, molecular mass = 12 + 16x2 = 12 + 32 = 44. Molar mass of carbon dioxide in air = 44 x 0.0003 = 0.0132g/mol

Hydrogen, H2, molecular mass = 1 x 2 = 2. Molar mass of hydrogen in air = 2 x 0.0000005 = 0.000001g/mol

Argon, Ar, atomic mass = 40. Molar mass of argon in air = 40 x 0.00933 = 0.3732g/mol

Neon, Ne, atomic mass = 20. Molar mass of neon in air = 20 x 0.000018 = 0.00036g/mol

Helium, He, atomic mass = 4. Molar mass of helium in air = 4 x 0.000005 = 0.00002g/mol

Krypton, Kr, atomic mass = 84. Molar mass of krypton in air = 84 x 0.000001 = 0.000084g/mol

Xenon, Xe, atomic mass = 131. Molar mass of xenon in air = 131 x 0.09 x 10-6 = 0.1179 x 10-4

Molar mass of dry air = 6.704 + 21.88 + 0.0132 + 0.3732 = 28.97g/mol

Notice that we didn’t include the molar masses of hydrogen, neon, helium, krypton, and xenon because they are too small to significantly affect the overall molar mass of air.

### The Molar Mass of Diatomic or Polyatomic Molecule

The molar mass of a diatomic or polyatomic molecule is same as the atomic mass of its element multiplied by the number of atoms contained.

Examples: Determine the molar mass of the following:

1. Nitrogen, N2

The relative atomic mass of nitrogen is 14. The molar mass of nitrogen molecule, N2 is 14 x 2 = 28g/mol

2. Oxygen, O2

The relative atomic mass of Oxygen is 16, therefore, the molar mass of oxygen, O2 is 16 x 2 = 32g/mol

3. Chlorine, Cl2

The relative atomic mass of chlorine is 35.5. The molar mass of chlorine molecule Cl2 is 35.5 x 2 = 71g/mol

4. Hydrogen, H2

The relative atomic mass of hydrogen is 1, therefore, its molar mass is 1 x 2 = 2g/mol

5. Sulphur, S8 The relative atomic mass of sulphur is 32, therefore, the molar mass of S8 is 32 x 8 = 256g/mol.

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