Atomic Mass vs. Molar Mass: The Basic Concepts of Chemistry

Atomic mass, also known as atomic weight is the mass of an individual atom expressed in atomic mass units (a.m.u). One a.m.u is the mass of an element relative to the 1/12 mass of a carbon atom. On the other hand, the molar mass is the mass of the one mole of particles ( atoms or molecules) expressed in grams per mole (g/mol).

Atomic mass is so small that it cannot be measured individually. That is why scientists have to use relative terms to define the mass of atoms. For example, the mass of one hydrogen atom (protium) could not be measured directly.

The atomic mass unit (a.m.u)

If we assume for an instant that C-12 is 12 a.m.u with 6 protons and 6 neutrons, and as a hydrogen atom (with one proton) is 12 times lighter than the C-12 atom, the relation between them is 1/12. The value of 1 a.m.u is 1.66 x 10^-24 g which is exactly the mass of 1 mole of carbon atoms.

Molar mass unit (g/mol)

Molar mass is a macroscopic (large scale) unit of masses of atoms or molecules. Molar mass is the weight of the Avogadro number of particles of a substance which is why its unit becomes, the number of grams of a substance in one mole of a substance (g/mol).

N_A = 6.022 x 10²³

The detailed differences between atomic mass and molar mass are as below.

Besides these differences, a similarity exists between atomic mass and molar mass, i.e. they always have the same values.

All masses are derived relative to ¹²C

An atom is very small, in the order of picometers. Its mass cannot be measured directly by any known technique. It has to be related to some known mass which can be kept as a standard. Now, as there are isotopes in compounds as well, the standard has to be the one with the highest relative isotopic abundance, otherwise, the answers will not be as certain. This standard is met by element carbon, which has an isotopic abundance of almost 98.89% for carbon-12 (¹²C).

Atomic Mass

The mass of an atom can be found no matter how small it is unless the number of protons and neutrons in its nucleus is known. This is accomplished via spectrometric techniques. The mass number (number of protons and neutrons) of a sample atom when related to the standard ¹²C, (1/12^th of the mass) gives the mass of an atom, which we call atomic mass or weight.

The mass of individual atoms is very small and cannot be expressed in terms of grams or kilograms. For this reason, chemists use the relative atomic mass scale instead of atomic masses. The relative mass of an atom is called atomic mass or atomic weight.

Unit of Atomic Mass (AMU)

One atomic mass unit is equal to 1/12 of the mass of the carbon-12 atom.

The atomic masses are not the same as the atomic numbers in the periodic table. This is because most elements occur in nature as a mixture of isotopes. Therefore, the average atomic masses of atoms are is taken as the average of the masses of radioactive isotopes. This is why atomic masses usually appear in decimals. For example, the atomic mass of C is 12.011. It can be calculated, as explained below.

Calculating the average atomic Mass

The first step in average atomic mass determination is the correct determination of the number of isotopes and their relative abundances of these isotopes. Such information is obtained by spectrometric techniques (mass spectrometer).

For example, Hydrogen has three isotopes (₁H¹ ≈ 99.972%, ₁H² ≈ 0.0156%, ₁H³ ≈ 10^-18%), Chlorine has two isotopes (Cl³⁵= 75%, Cl³⁷= 25%), etc.

The atomic mass of a given element can be determined by obtaining the sum of the product of the masses of isotopes and their percentage abundances.

Examples

1. Carbon atoms contain a mixture of 98.89% of ¹²C isotope with a mass of 12.00000 a.m.u, and 1.11% ¹³C isotope with a mass of 13.00335 a.m.u. The average atomic mass of carbon will be as;

Average atomic mass = Σ (mass of individual isotope) (Its percentage abundance)

(12.00000 amu) (98.89 / 100) + (13.000335 amu) (1.11 / 100)

C = 12.011 a.m.u

2. Lithium atom contains a mixture of 7.5% of ⁶Li and 92.5% of ⁷Li with 6.01 a.m.u and 7.02 a.m.u masses. The average atomic mass of lithium will be as;

Average atomic mass = Σ (mass of individual isotope) (Its percentage abundance)

(6.01 amu) (7.5 / 100) + (7.02 amu) (92.5 / 100)

Li = 6.94 a.m.u

Molar Mass

Molar mass is the mass in grams of one mole of a substance. Its numerical value is equal to the formula mass that is expressed in a.m.u. For example, glucose has a formula mass of 180.0 a.m.u. So, the molar mass (mass in gram of one mole) of glucose is 180.0 g/mol.

There must be confusion here about molar mass being the same as molecular mass. So, to be very clear, they are not the same.

The formula mass of a compound is the sum of the atomic masses of atoms in a formula unit of that compound, while the molecular mass of the compound is the sum of the atomic masses of atoms in one molecule of the compound.

Below are some examples of calculating molar masses of compounds.

Additional Resources

• Calculating empirical formula
• Basic types of reactions
• Relative vs. standard deviation
• Accuracy and precision

Calculating Molar Masses

1. The molar mass of NaCl

1 atom of Na = 22.9897 g/mol

1 atom of Cl = 35.453 g/mol

Molar mass = Σ (molar masses of individual atoms)

Molar mass of NaCl = 22.9897g/mol + 35.453 g/mol

NaCl = 58.4427 g/mol

2. The molar mass of O₂

1 atom of O₂ = 15.999 g/mol

Molar mass = Σ (molar masses of individual atoms)

Molar mass of O₂ = 15.999 g/mol + 15.999 g/mol

O₂ = 31.998 g/mol

3. The molar mass of CO₂

1 atom of C = 12.011 g/mol

1 atom of O = 15.999 g/mol

Molar mass = Σ (molar masses of individual atoms)

Molar mass of CO₂ = 12.011 g/mol + 15.999 g/mol + 15.999 g/mol

CO₂ = 44.009 g/mol

Key Takeaway(s)

• The molar mass and Atomic mass are different quantities with different units, yet they have the same values.
• Similarly, molecular weights and molar masses are different quantities with the same values.

Concepts Berg

What Is the difference between molar mass and molecular weight?

Molar mass is the mass of mole in a substance while molecular weight tells the mass of a molecule in a particular substance.

How do you convert molar mass to atomic mass?

Atomic and molar masses are interconvertible because they both are the weights of the same element. Moreover, a.m.u is numerically equal to the grams in one mole of a substance.

What Is the difference between a molecule and a mole?

The molecule is the combination of atoms while a mole is equal to Avogadro’s number of particles, which is 6.022 x 10²³ particles.

Are molar mass and molecular mass the same thing?

No, they are different. Molar mass is expressed in g/mole while molecular mass is the mass of a molecule of a compound in a.m.u.

What is the relationship between molecular weight and vapor pressure?

Compounds with high molecular weights have lower vapor pressure. This is because of their increased number of electrons, resulting in more intermolecular forces.

How does molar mass affect the rate of diffusion?

The rate of diffusion is inversely proportional to the square root of its molar mass. By Graham’s law of diffusion;

r ∝ 1/√d

Is molecular weight the same as molecular mass?

Mass and weight are interchangeable quantities in terms of atomic level.

What is the molar mass of ice?

The molar mass of water is exactly 18.01528 g/mol.

References

• Chemistry in Quantitative Language: Fundamentals of General Chemistry, by Christopher O. Oriakhi (MIT, Nike, hp, RSC, etc)
• Atomic Mass and Molecular Mass (vendatu.com)
• Atomic masses (angelo.edu)