Q.Naturally occurring chlorine consists of two isotopes: $^{35}\text{Cl}$ (mass $34.97\ \text{u}$, abundance $75.77\%$) and $^{37}\text{Cl}$ (mass $36.97\ \text{u}$, abundance $24.23\%$). Calculate the average atomic mass of chlorine.

Individual atoms are far too light to be weighed directly on a laboratory balance, so chemists express atomic

mass on a relative scale rather than in grams. One atomic mass unit (u) is defined as exactly $\dfrac{1}{12}$ of

the mass of a single atom of the carbon-12 isotope, so $1\ \text{u} \approx 1.66 \times 10^{-24}\ \text{g}$. On

this scale, hydrogen has an atomic mass of about $1.008\ \text{u}$ and oxygen about $16.00\ \text{u}$.

Most elements occur in nature as a fixed mixture of two or more isotopes — atoms with the same number of

protons but different numbers of neutrons, and hence slightly different masses. The atomic mass listed for an

element on the periodic table is therefore not the mass of any single atom, but the abundance-weighted average

across all of that element's naturally occurring isotopes:

Chlorine, for example, occurs as roughly $76\%$ $^{35}\text{Cl}$ and $24\%$ $^{37}\text{Cl}$, giving a weighted

average atomic mass of about $35.45\ \text{u}$ — a value that is not itself the mass of either isotope.

The molecular mass of a substance is the sum of the atomic masses of every atom present in one molecule of

that substance, with each atomic mass multiplied by the number of times that element appears in the molecular

formula. For water, $\text{H}_2\text{O}$, the molecular mass is $2(1.008) + 16.00 = 18.02\ \text{u}$.

Some substances, most ionic compounds such as $\text{NaCl}$ or $\text{CaCO}_3$, do not exist as discrete

molecules at all, but as a continuous lattice of ions. For these, chemists calculate a formula mass instead

— computed identically, by summing the atomic masses of the atoms shown in the simplest formula unit, even

though that unit is not itself a physically isolable particle.

Atomic, molecular and formula masses computed this way are pure relative numbers. Their real significance

emerges when they are re-expressed in grams per mole as the molar mass — the bridge that connects this

relative mass scale to quantities that can actually be weighed out on a balance.