Edexcel A-Level Chemistry

Sub-atomic particles

An atom has a tiny, dense nucleus made of protons and neutrons, surrounded by electrons in shells. Almost all the mass is in the nucleus, because a proton and a neutron are each about 1836 times heavier than an electron.

The atomic (proton) number, $Z$, is the number of protons in the nucleus, and it decides which element the atom is. The mass number, $A$, is the total number of protons and neutrons. An atom is written with $A$ as a superscript and $Z$ as a subscript before the symbol, so $\ce{^{27}_{13}Al}$ has 13 protons and $27 - 13 = 14$ neutrons. In a neutral atom the number of electrons equals the number of protons, and an ion has gained or lost electrons.

For a molecule or a polyatomic ion, add up the numbers over all the atoms and then take account of the overall charge. The ammonium ion has $7 + 4 = 11$ protons, and because it carries a charge of +1 it has $11 - 1 = 10$ electrons.

Isotopes

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons, so they have the same atomic number and different mass numbers. Carbon-12 and carbon-14 are both carbon: each has 6 protons, but they have 6 and 8 neutrons.

Isotopes of an element have the same chemical properties, because chemistry depends on the electron arrangement, which is fixed by the number of protons. Their physical properties differ where mass matters. A heavier isotope has a slightly higher density and diffuses a little more slowly, and a molecule containing it has a slightly different boiling temperature.

Relative isotopic mass and relative atomic mass

Atoms are far too light to be weighed in grams in everyday work, so their masses are compared with a standard. The standard is the carbon-12 isotope, which is given a mass of exactly 12 units.

The relative isotopic mass is the mass of an atom of an isotope compared with one twelfth of the mass of an atom of carbon-12.

The relative atomic mass, $A_\mathrm{r}$, of an element is the weighted mean mass of an atom of the element, taking account of the abundance of its isotopes, compared with one twelfth of the mass of an atom of carbon-12.

Relative atomic mass is therefore usually not a whole number. Chlorine has two main isotopes, and a mixture of about three parts of chlorine-35 to one of chlorine-37 gives a relative atomic mass of about 35.5, which is a mean and matches no single atom.

The relative molecular mass, $M_\mathrm{r}$, of a simple molecule is found by adding the relative atomic masses of every atom in the formula. The term relative formula mass is used for a compound with a giant structure, such as sodium chloride, where there are no separate molecules. Both are calculated in the same way, and neither has units.

For calcium nitrate, $\ce{Ca(NO3)2}$, with $A_\mathrm{r}$ values of Ca 40.1, N 14.0 and O 16.0:

Mass spectrometry of elements

A mass spectrometer separates ions by their mass-to-charge ratio, $m/z$. A sample is vaporised and then ionised, usually by a beam of high-energy electrons that knocks one electron off each particle to leave a $1+$ ion. The ions are accelerated, separated according to their mass (lighter ions are deflected or travel faster than heavier ones with the same charge) and detected. The output is a mass spectrum, a bar chart of relative abundance against $m/z$. Because nearly all the ions carry a single positive charge, the $m/z$ value of a peak is the mass of the ion.

Finding a relative atomic mass from a spectrum

Each peak in the spectrum of an element is one isotope, and its height shows how much of it there is. The relative atomic mass is the weighted mean:

A sample of boron gives peaks at $m/z = 10$ (abundance 19.9) and $m/z = 11$ (abundance 80.1).

The calculation also runs backwards. An element has two isotopes of relative isotopic mass 63 and 65, and its relative atomic mass is 63.5. If the percentage of the lighter isotope is $x$, then

so the abundances are 75 % and 25 %.

Molecules of an element

When the element exists as diatomic molecules, the spectrum shows the molecular ion and, in the case of chlorine, more peaks than there are isotopes, because two atoms are combined at random. Chlorine is about 75 % $\ce{^{35}Cl}$ and 25 % $\ce{^{37}Cl}$, so for one atom the probabilities are 0.75 and 0.25. For a $\ce{Cl2}$ molecule:

The three molecular-ion peaks at 70, 72 and 74 are in the ratio $0.5625 : 0.375 : 0.0625$, which is $9 : 6 : 1$. Fragmentation of the molecule also produces peaks for single atoms at $m/z = 35$ and 37, in the ratio 3 : 1.

Bromine is about half $\ce{^{79}Br}$ and half $\ce{^{81}Br}$, so $\ce{Br2}$ gives peaks at 158, 160 and 162 in the ratio $1 : 2 : 1$ ($0.5^2 : 2 \times 0.5^2 : 0.5^2$). The same probability method works for any diatomic molecule once the isotopic abundances are known.

Molecular ions of compounds

For a compound, the peak at the highest $m/z$ (ignoring very small peaks from heavier isotopes such as carbon-13) is normally the molecular ion, $\mathrm{M}^+$, formed by removing one electron from the whole molecule. Its $m/z$ value equals the relative molecular mass, so a molecular ion at $m/z = 46$ shows a molecule of $M_\mathrm{r} = 46$, such as ethanol or methanoic acid.