Singapore-Cambridge A-Level Chemistry (H2)

Protons, neutrons and electrons

An atom has a very small, dense, positively charged nucleus containing protons and neutrons, surrounded by electrons in the much larger space outside it. Almost all of the mass is in the nucleus and almost all of the volume is empty space occupied by the electron cloud. Alpha particle scattering showed this: nearly all particles passed straight through a thin gold foil, a few were deflected through large angles, and a very few rebounded, which means the positive charge and the mass are concentrated in a tiny region.

In an electric field between two charged plates the three particles behave differently. Protons are deflected towards the negative plate, electrons towards the positive plate and neutrons are not deflected, because they carry no charge. The electron is deflected through a much larger angle than the proton, because its charge is the same size but its mass is about 1840 times smaller, so the same force gives it a far larger acceleration. A beam of ions with a higher charge, or a lower mass, is deflected more.

Proton number, nucleon number and isotopes

The proton number $Z$ is the number of protons in the nucleus, and it fixes the element. The nucleon number $A$ is the total number of protons and neutrons. An atom is written $\ce{^{A}_{Z}X}$, so $\ce{^{35}_{17}Cl}$ has 17 protons, $35 - 17 = 18$ neutrons and, being neutral, 17 electrons.

For an ion, the electron count is adjusted by the charge. The ion $\ce{^{27}_{13}Al^{3+}}$ has 13 protons, 14 neutrons and $13 - 3 = 10$ electrons, while $\ce{^{32}_{16}S^{2-}}$ has 16 protons, 16 neutrons and $16 + 2 = 18$ electrons.

Isotopes are atoms of the same element with the same proton number but different numbers of neutrons, so different nucleon numbers. Chlorine-35 and chlorine-37 have 18 and 20 neutrons. Isotopes have the same electronic configuration and therefore the same chemical properties, since chemistry is decided by the electrons. They differ in mass, so properties that depend on mass, such as density and the rate of diffusion, differ slightly.

Shells, sub-shells and orbitals

Electrons occupy energy levels called shells, numbered by the principal quantum number $n = 1, 2, 3, \dots$, and the shells are further from the nucleus and higher in energy as $n$ rises. Each shell contains sub-shells, and each sub-shell is made of orbitals, regions of space where there is a high probability of finding an electron. An orbital holds at most two electrons, which must have opposite spins.

The 4s and 4p sub-shells belong to the fourth shell. An s sub-shell has one orbital, a p sub-shell has three and a d sub-shell has five.

The shapes of the orbitals follow from the wave behaviour of electrons, although the mathematics is not needed. An s orbital is spherical, and a 2s orbital is larger than a 1s orbital. A p orbital has two lobes either side of the nucleus, like a dumbbell, and the three p orbitals of a sub-shell point along the $x$, $y$ and $z$ axes at right angles to one another; they have the same energy, so they are said to be degenerate. Four of the five d orbitals have four lobes, in a cloverleaf, with the lobes either between the axes ($d_{xy}$, $d_{xz}$, $d_{yz}$) or along the $x$ and $y$ axes ($d_{x^2-y^2}$); the fifth, $d_{z^2}$, has two lobes along the $z$ axis and a ring around the middle.

The relative energies, from lowest, run 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. The 4s orbital lies below 3d when the orbitals are empty, which is why 4s is filled first. Orbitals within one sub-shell have equal energy, and within a shell a d orbital is higher in energy than an s or a p orbital.

Electronic configurations

Three rules fix how electrons are placed. Orbitals are filled from the lowest energy upwards; an orbital holds two electrons of opposite spin (the Pauli exclusion principle); and orbitals of equal energy are each given one electron, with parallel spins, before any is doubled up (Hund's rule), because two electrons in the same orbital repel each other.

Oxygen, with 8 electrons, is $1s^2\,2s^2\,2p^4$, and in the 2p sub-shell one orbital holds a pair while the other two hold one electron each. Phosphorus is $1s^2\,2s^2\,2p^6\,3s^2\,3p^3$, with three unpaired electrons in separate 3p orbitals. The shorthand uses the previous noble gas for the core, so phosphorus is $[\text{Ne}]\,3s^2\,3p^3$.

Potassium ($Z = 19$) is $[\text{Ar}]\,4s^1$ and calcium is $[\text{Ar}]\,4s^2$. From scandium onwards the 3d sub-shell fills, and iron is $[\text{Ar}]\,3d^6\,4s^2$. Two elements break the simple order, because a half-filled or a full 3d sub-shell is unusually stable: chromium is $[\text{Ar}]\,3d^5\,4s^1$ and copper is $[\text{Ar}]\,3d^{10}\,4s^1$.

When a transition element forms a positive ion, the 4s electrons are lost before the 3d electrons. So $\ce{Fe^{2+}}$ is $[\text{Ar}]\,3d^6$ and $\ce{Fe^{3+}}$ is $[\text{Ar}]\,3d^5$, and $\ce{Cu^{2+}}$ is $[\text{Ar}]\,3d^9$. Negative ions add electrons to the next available orbital: $\ce{Cl-}$ is $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$, the same as argon.

First ionisation energy

The first ionisation energy of an element is the energy required to remove one electron from each atom in one mole of gaseous atoms, forming one mole of gaseous $1+$ ions.

The second ionisation energy refers to the removal of a second electron from each gaseous $1+$ ion, and so on. Ionisation energies are always endothermic, since energy must be supplied to pull an electron away from the attraction of the nucleus.

Three things decide the size of an ionisation energy. The first is the nuclear charge: more protons attract the outer electrons more strongly. The second is the distance of the outer electron from the nucleus, which also involves the shielding by inner shells; an outer electron in a shell further out, with more full shells in between, is held weakly. The third is the sub-shell from which the electron is removed, because, for example, a 3p electron is higher in energy and on average further out than a 3s electron.

Trend down a group

The first ionisation energy falls down a group. Each element down has an extra shell, so the outer electron is further from the nucleus and shielded by more inner electrons. This outweighs the increase in nuclear charge, so the attraction on the outer electron is weaker and less energy is needed to remove it.

Trend across a period

The first ionisation energy generally rises across a period, because the nuclear charge increases while the electrons are added to the same shell and the shielding by inner shells stays about the same. The effective attraction on the outer electrons grows, and the atomic radius shrinks.

Two dips interrupt the rise in period 2 and period 3. Boron is lower than beryllium, and aluminium is lower than magnesium, because the outer electron of boron or aluminium is in a p sub-shell, which is slightly higher in energy and further from the nucleus than the filled s sub-shell of the element before, and is shielded by the s electrons. Oxygen is lower than nitrogen, and sulfur is lower than phosphorus, because in these atoms the p sub-shell has its fourth electron, which must go into an orbital that already holds an electron. The repulsion between the two paired electrons in that orbital makes the electron easier to remove, even though the nuclear charge is higher.

Successive ionisation energies

Removing electrons one after another from the same atom requires more energy each time. After each removal there are fewer electrons sharing the same nuclear charge, so the remaining electrons are held more tightly and the ion shrinks. The pattern of the successive values shows the shell structure, because there is a large jump whenever the next electron has to come from an inner shell, which is closer to the nucleus and less shielded.

A graph of the logarithm of the ionisation energy against the number of electrons removed therefore rises in steps, and the step sizes identify the groups of electrons in each shell.

Reading successive data

Suppose an element $\text{X}$ has these successive ionisation energies in $\mathrm{kJ\ mol^{-1}}$: 590, 1150, 4940, 6480. The first two are fairly close, then the third is over four times larger than the second. This means that two electrons are in the outer shell and the third electron comes from an inner shell, so $\text{X}$ is in Group 2 of the Periodic Table.

For an element whose values are 1000, 1900, 2900, 4960, 6270, 21200, there is a large jump after the fifth electron, so five electrons are in the outer shell and the element is in Group 15. A large jump after the first electron would mean Group 1.

The last two ionisation energies of any element with more than two electrons are the highest of all, because those electrons are removed from the 1s orbital, closest to the nucleus.