Atomic and molecular masses

What are atomic and molecular masses?

In plain words: atoms are far too light to weigh in grams one at a time, so chemists compare them with a standard atom. On this scale carbon-12 is exactly 12, hydrogen is about 1 and oxygen about 16. Adding up these numbers gives the mass of any molecule on the same scale.

Atomic mass and the carbon-12 scale

Atoms are extremely small, and an atom’s mass is tiny (NCERT Section 1.7.1, page 16). Today mass spectrometry measures atomic masses accurately. In the nineteenth century, chemists could only find the mass of one atom relative to another. Hydrogen, the lightest atom, was given a mass of 1 (with no unit) and other elements were measured against it. Since 1961 the standard has been carbon-12, ^¹²C, one of the isotopes of carbon, which is given a mass of exactly 12 (page 16).

One atomic mass unit is defined as a mass exactly equal to one-twelfth of the mass of one carbon – 12 atom.

NCERT Chemistry Part I (Class 11), Section 1.7.1, page 16

NCERT gives 1 amu = 1.66056 × 10^⁻²⁴ g and the mass of a hydrogen atom as 1.6736 × 10^⁻²⁴ g (page 17). So a hydrogen atom is (1.6736 × 10^⁻²⁴ g)/(1.66056 × 10^⁻²⁴ g) = 1.00785… u, which is 1.0079 u, or 1.008 u to four significant figures. NCERT prints 1.0078 amu and then 1.0080 amu; the first line drops digits instead of rounding them. An oxygen-16 atom is 15.995 u. NCERT’s mass of a carbon-12 atom, 1.992648 × 10^⁻²³ g (page 18), gives 1 u = 1.66054 × 10^⁻²⁴ g, a rounded approximation to the modern value. The difference does not matter at this level.

At present, ‘amu’ has been replaced by ‘u’, which is known as unified mass.

NCERT Chemistry Part I (Class 11), Section 1.7.1, page 17

Its full name is the unified atomic mass unit; it is also called the dalton (Da), the name used for the masses of proteins in biology.

Average atomic mass

Many elements occur naturally as a mixture of isotopes, atoms of the same element with different masses (their discovery changed postulate 2 of Dalton’s theory). The atomic mass used in calculations is the average over the isotopes, each weighted by its relative abundance (NCERT Section 1.7.2, page 17).

Here x_i is the fractional abundance of isotope i (its per cent abundance divided by 100) and m_i its mass. NCERT’s carbon data (page 17):

Average = (0.98892)(12 u) + (0.01108)(13.00335 u) + (2 × 10^⁻¹²)(14.00317 u)

= 11.86704 u + 0.14408 u + 2.8 × 10^⁻¹¹ u

= 12.01112 u ≈ 12.011 u.

Note that 2 × 10^⁻¹⁰ per cent is the fraction 2 × 10^⁻¹²; ^¹⁴C is far too rare to change the answer. Isotopes have the same proton number but different neutron numbers and masses; the mass difference can be used to separate them: see Example 3 in kinetic theory of an ideal gas.

In the periodic table of elements, the atomic masses mentioned for different elements actually represent their average atomic masses.

NCERT Chemistry Part I (Class 11), Section 1.7.2, page 17

Molecular mass

Molecular mass is the sum of atomic masses of the elements present in a molecule.

NCERT Chemistry Part I (Class 11), Section 1.7.3, page 17

Multiply the atomic mass of each element by the number of its atoms in the molecule, and add (page 17). For example:

• methane, CH₄: 12.011 u + 4 × 1.008 u = 16.043 u;
• water, H₂O: 2 × 1.008 u + 16.00 u = 18.02 u.

Formula mass

Some substances, such as sodium chloride, do not consist of separate molecules (NCERT Section 1.7.4, page 17). In solid NaCl, sodium ions Na^⁺ and chloride ions Cl^⁻ are packed in a three-dimensional pattern, each Na^⁺ surrounded by six Cl^⁻ and each Cl^⁻ by six Na^⁺ (NCERT page 17, Fig. 1.10). There is no single NaCl molecule, so the formula NaCl stands for the simplest ratio of ions, and its mass is the formula mass:

formula mass of NaCl = 23.0 u + 35.5 u = 58.5 u (page 18).

The arithmetic is the same as for a molecular mass; only the name differs. The idea that ordinary matter is made of such tiny particles is set out in physics in the molecular nature of matter.

Solved examples

Common mistakes to avoid

Quick revision summary

• Atomic masses are relative to carbon-12, which is exactly 12 u; 1 u = 1/12 of the mass of a ^¹²C atom = 1.66056 × 10^⁻²⁴ g (NCERT value). ‘amu’ is now written ‘u’.
• Average atomic mass = Σ (fractional abundance × isotopic mass); the periodic table lists these averages.
• Molecular mass = sum of the atomic masses of all the atoms in a molecule (CH₄ 16.043 u, H₂O 18.02 u, glucose 180.162 u).
• Ionic solids such as NaCl have formula masses (58.5 u), worked out the same way.

Questions students ask

What is the difference between atomic mass and mass number?

Mass number, A, is the number of protons plus neutrons in a nucleus, a whole number with no unit, while atomic mass is the actual mass of an atom in u, which is generally not a whole number; carbon-12 is the defining exception (exactly 12 u by definition). An iron-56 atom has mass number 56 but an atomic mass of 55.935 u, and natural iron, a mixture of isotopes, has an average atomic mass of 55.85 u. The mass number identifies an isotope; the average atomic mass is used for ordinary samples; isotopically enriched samples require their own composition.

Is atomic mass the same as atomic weight?

In everyday chemistry atomic mass and atomic weight mean the same periodic-table number: ‘atomic weight’ is the traditional name for the relative atomic mass, A_r, such as 16.00 for oxygen, and many books use the two terms interchangeably. Strictly, atomic weight (relative atomic mass; a standard atomic weight is a recommended value or interval for normal terrestrial materials) is a pure number, the average mass of an element’s atoms in natural samples divided by one-twelfth of the mass of a carbon-12 atom, while an atomic mass is a mass in u. The word ‘weight’ survives from history: the quantity is a ratio of masses, not a force.

What is the difference between amu and u?

Today amu and u name the same unit, one-twelfth of the mass of a carbon-12 atom (about 1.6605 × 10^⁻²⁴ g), and NCERT now writes u, the unified atomic mass unit. Before 1961 ‘amu’ had two slightly different meanings: physicists used one-sixteenth of the mass of an oxygen-16 atom, and chemists one-sixteenth of the average mass of the atoms in natural oxygen. The carbon-12 unit unified the two scales, which is why it is called ‘unified’, and it changed the chemists’ atomic masses by only about 0.004%.

Why are atomic masses not whole numbers?

Atomic masses are not whole numbers because most elements are mixtures of isotopes, and because even a single isotope’s mass is not exactly its mass number. Bromine, for example, is about 50.7% bromine-79 (78.918 u) and 49.3% bromine-81 (80.916 u), so its average atomic mass is 79.90 u. A single isotope’s mass (except carbon-12’s, exactly 12 u by definition) is not a whole number because a proton (1.00728 u) and a neutron (1.00866 u) each have a mass a little more than 1 u, and some mass is lost as binding energy when the nucleus forms: an oxygen-16 atom is 15.995 u, about 0.137 u less than its 8 protons, 8 neutrons and 8 electrons taken separately.

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. Calculate the molecular masses of (i) H₂O, (ii) CO₂, (iii) CH₄, using H = 1.008, C = 12.01 and O = 16.00 u (NCERT Exercise 1.1, page 25).

   Show answerHide answer

   (i) 2 × 1.008 + 16.00 = 18.02 u. (ii) 12.01 + 2 × 16.00 = 44.01 u. (iii) 12.01 + 4 × 1.008 = 16.04 u (with C = 12.011 u, as in the text, it is 16.043 u). (NCERT asks for molar masses; these are the same numbers in g mol^⁻¹.)

2. Q2. Find the formula mass of calcium carbonate, CaCO₃ (Ca = 40.08, C = 12.01, O = 16.00 u).

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   40.08 + 12.01 + 3 × 16.00 = 100.09 u.

3. Q3. Copper is 69.15% ^⁶³Cu (62.93 u) and 30.85% ^⁶⁵Cu (64.93 u). Find its average atomic mass.

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   0.6915 × 62.93 + 0.3085 × 64.93 = 43.516 + 20.031 ≈ 63.55 u.