1.5-1.7 - Isotopes And Relative Masses

Same Element, Different Neutrons

A sample of chlorine can contain atoms with mass number 35 and atoms with mass number 37. Both are chlorine, so both must have 17 protons. The difference is in the number of neutrons.

Because the proton number is the same, isotopes of an element have the same atomic number and the same electron arrangement if the atoms are neutral. Because the neutron number is different, their mass numbers are different. Chemical reactions rearrange electrons, so neutral isotopes have the same chemical reactions because their electronic configurations are the same; their different masses can affect physical properties and reaction rates.

[DIAGRAM: asset_name: Isotope Nuclei Comparison; asset_slug: edexcel_a_level_chemistry_l002_isotope_nuclei_comparison; recommended_method: matplotlib; description: Pale-colour schematic of two isotope nuclei with the same number of protons and a different number of neutrons, plus a legend for proton and neutron.]

Use the notation carefully:

For example, carbon-12 and carbon-13 are both carbon isotopes:

The tempting error is to say that isotopes are "different forms of atoms with different masses". That is too vague. The key statement must identify the same number of protons and different numbers of neutrons.

The Carbon-12 Scale

Atoms are far too small for ordinary gram masses to be convenient. Chemists therefore use a relative scale. The reference is carbon-12: one atom of carbon-12 is assigned a relative mass of exactly 12.

That means one relative mass unit is based on:

$\frac{1}{12}$ of the mass of one carbon-12 atom.

Relative masses are ratios, so they have no units. A mass number is an integer count of nucleons; a measured relative isotopic mass is a mass ratio and is not generally an exact integer. Carbon-12 is exactly 12 by definition; rounded isotope masses are supplied in the calculations here. Saying that an atom has a relative isotopic mass of about 16 means its mass is about 16 times $1/12$ of the mass of a carbon-12 atom.

For example, the relative isotopic mass of $\ce{^{24}Mg}$ refers to one atom of that isotope, not to a natural sample containing several magnesium isotopes.

Relative atomic mass is different because it describes a whole sample of the element, not one isotope.

The word mean matters because many elements exist naturally as mixtures of isotopes, so the periodic table value may be a decimal.

This lesson uses the weighted-mean idea to understand why $A_r$ can be a decimal. The next lesson uses mass-spectrometry data to calculate that weighted mean.

Using Relative Atomic Mass

$A_r$ values are the numbers you normally take from the periodic table when calculating masses from formulae. At A level, treat them as relative masses of atoms on the carbon-12 scale, not as masses in grams and not as mass numbers.

The difference is visible with chlorine:

$A_r(\ce{Cl})$ being 35.5 does not make chlorine a molecule, and it does not mean every chlorine atom has mass 35.5. It means that when a calculation involves chlorine atoms in a typical sample, the average relative mass per chlorine atom is 35.5.

Worked example: choosing the correct mass value

A student wants to calculate the relative mass contribution of chlorine in $\ce{HCl}$. They have these possible numbers:

35, 37, 35.5

For ordinary formula calculations, use $A_r(\ce{Cl}) = 35.5$, because the formula is not specifying a single isotope. Hydrogen contributes $A_r(\ce{H}) = 1.0$, so:

relative mass contribution from H = 1.0

relative mass contribution from Cl = 35.5

If a question specifically said $\ce{H^{35}Cl}$, then the chlorine isotope would be specified and the isotope mass would be used instead. In most formula calculations at this point, use the periodic-table $A_r$.

Relative Molecular Mass

Relative molecular mass, $M_r$, is used for substances made from molecules.

The chemical decision comes before the arithmetic: ask whether the formula represents a molecule. Water, carbon dioxide, ammonia and many organic compounds are molecular, so $M_r$ is the right language.

Worked example: water

Calculate the relative molecular mass of water, $\ce{H2O}$.

Use:

$A_r(\ce{H}) = 1.0$

$A_r(\ce{O}) = 16.0$

There are two hydrogen atoms and one oxygen atom in each water molecule:

$M_r(\ce{H2O}) = [2\times 1.0] + 16.0$

$M_r(\ce{H2O}) = 18.0$

The answer has no unit because it is a relative mass. If the same formula later appears in a mole calculation, 18.0 $\mathrm{g\,mol^{-1}}$ would be the molar mass, but this lesson is about the relative value.

Worked example: carbon dioxide

Calculate $M_r(\ce{CO2})$.

$A_r(\ce{C}) = 12.0$

$A_r(\ce{O}) = 16.0$

$M_r(\ce{CO2}) = 12.0 + [2\times 16.0]$

$M_r(\ce{CO2}) = 44.0$

The subscript applies only to the atom immediately before it. In $\ce{CO2}$, there is one carbon atom and two oxygen atoms.

Relative Formula Mass For Giant Structures

Some compounds do not contain separate molecules. Sodium chloride is a giant ionic lattice, not a collection of $\ce{NaCl}$ molecules. Magnesium oxide is also a giant ionic lattice, and silicon dioxide is a giant covalent structure. For compounds with giant structures, use the term relative formula mass.

The arithmetic is the same as for $M_r$. The difference is the chemical meaning of the formula: it represents the simplest ratio or formula unit in the structure, not a separate molecule.

Worked example: sodium chloride

Calculate the relative formula mass of sodium chloride, $\ce{NaCl}$.

$A_r(\ce{Na}) = 23.0$

$A_r(\ce{Cl}) = 35.5$

relative formula mass of $\ce{NaCl}$ = 23.0 + 35.5

relative formula mass of $\ce{NaCl}$ = 58.5

Do not call this the mass of one sodium chloride molecule. There are no discrete $\ce{NaCl}$ molecules in the ionic lattice.

Worked example: magnesium hydroxide

Calculate the relative formula mass of magnesium hydroxide, $\ce{Mg(OH)2}$.

The brackets mean there are two $\ce{OH}$ groups:

$A_r(\ce{Mg}) = 24.3$

$A_r(\ce{O}) = 16.0$

$A_r(\ce{H}) = 1.0$

relative formula mass = 24.3 + 2(16.0 + 1.0)

relative formula mass = 24.3 + 34.0

relative formula mass = 58.3

The key step is showing that the multiplier outside the bracket applies to both oxygen and hydrogen.

Quick Recap

Isotopes share a proton number but have different neutron numbers. Relative isotopic mass describes one isotope; relative atomic mass is a weighted mean, both on the carbon-12 scale. Add atomic contributions for a molecular mass or formula mass, choosing the term from the substance’s structure.