Periodic Trends
Chapter 07
Periodic Trends
Elements in groups exhibit similar properties as a result of their similar valence shell electron configurations. Trends emerge that allows us to predict, qualitatively, different properties of elements.
Atomic radius
Atomic radii are difficult to measure given that there is no ‘hard-edge’ to an atom that is surrounding by an electron cloud. However, one way to define an atomic radius is by measuring the distance between two identical nuclei in a molecule (such as Cl2) and dividing by two. This provides a good estimate for an atomic radius for an element.
The atomic radius of atoms tend to increase as you move
- down (a group)
- left (across a period)
Transition metals can show exceptions to this trend.
The calculated atomic radii are given below.
The radius increases moving left across a period due to the decrease in effective nuclear charge (Zeff) that outer electrons experience from the nucleus due to the decrease number of protons in the nucleus.
The radius also increases as you move down a group due to the increasing size of the outer shell (n).
Ionic radius
The removal of electrons decrease the size of the atom. The ionic radii of cations of the main group elements tend to increase as you move
- down (a group)
- left (across a period)
The addition of electrons increases the size of the atom. The ionic radii of anions of the main group elements tend to increase as you move
- down (a group)
- left (across a period)
The ionic radii of main group elements adopting their common ionic state is shown below.
Ionic radius trend for anions
Why does the ionic radius increase when going from F → O → N?
Firstly, we interpret this as comparing the ionic radius of F–, O2–, and N3–.
N3– has a larger ionic radius due to a
- decreased number of protons in the nucleus (lower nuclear charge and effective nuclear charge)
Why does the ionic radius increase when going from F → Cl → Br?
We interpret this as comparing the ionic radius of F–, Cl–, and Br–.
Br– has the largest ionic radius due to
- the outer valence electrons that reside in the highest shell (n = 4) leading to a larger atomic orbital size.
- less electron shielding between the nucleus and the outer valence electrons
Why does the ionic radius increase when going from Mg → Na → F?
We interpret this as comparing the ionic radius of Mg2+, Na+, and F–.
These ions are isoelectronic with neon. Mg and Na have more protons than F resulting in an increased effective nuclear charge on the outer valence electrons drawing them closer to the nucleus.
Lattice energy
A lattice energy (ΔlatticeH in kJ mol–1) is the energy change when one mole of a crystalline ionic compound is formed from its constituent ions in the gas state. Lattice energy is a negative quantity meaning the ionic compound is lower in energy (more stable) than its gas phase ionic counter parts. Lattice energy is an indicator of the strength of an ionic bond. The larger (more negative) the lattice energy, the stronger the ionic bond.
The lattice energy for sodium chloride can be written as
\[\mathrm{Na^+(g)} + \mathrm{Cl^-(g)} \longrightarrow \mathrm{NaCl(s)} \quad \Delta_{\mathrm{lattice}}H = -786~\mathrm{kJ~mol^{-1}}\]
Lattice energy can be estimated using Coulomb’s law which states that oppositely charged ions are attracted to each other (attractive interactions). Coulomb’s law is given as
\[E = \dfrac{k~q_1~q_2}{r^2}\]
where E is the potential energy between two charges, k is Coulomb’s constant, q1 and q2 are the charges of the ions of interest, and r is the distance between the ionic centers.
Coulomb’s law illustrates that a stronger ionic bond (more negative E) results from ions of increasing charge difference and shorter distance.
Ionic bond strength vs distance
Ionic bond strength vs ion charge difference
Ionization energy
An ionization energy of an atom or molecule is the energy required to remove an electron from a ground state particle in the gas phase and is equivalent to an internal energy change, ΔU.
\[\mathrm{X(g)} ~~\longrightarrow ~~ \mathrm{X^+(g)} + e^- \qquad \Delta U\]
For example, the first ionization energy (i.e. the energy required to remove an electron from a neutral particle; IE1) of 1 mole of carbon atoms is given as
\[\mathrm{C(g)} ~~\longrightarrow ~~ \mathrm{C^+(g)} + e^- \qquad \mathrm{IE_1} = 1086~\mathrm{kJ~mol^{-1}}\]
As one continues to remove electrons, the energy requirement increases dramatically. For example, the second ionization energy (IE2) of carbon is
\[\mathrm{C^+(g)} ~~\longrightarrow ~~ \mathrm{C^{2+}(g)} + e^- \qquad \mathrm{IE_2} = 2352~\mathrm{kJ~mol^{-1}}\]
Because like-charges attract, it is inherently more difficult to remove negative charge from a positively charged particle.
The third ionization energy increases even more.
\[\mathrm{C^{2+}(g)} ~~\longrightarrow ~~ \mathrm{C^{3+}(g)} + e^- \qquad \mathrm{IE_3} = 4620~\mathrm{kJ~mol^{-1}}\]
The fourth ionization energy increases even more.
\[\mathrm{C^{3+}(g)} ~~\longrightarrow ~~ \mathrm{C^{4+}(g)} + e^- \qquad \mathrm{IE_4} = 6222.7~\mathrm{kJ~mol^{-1}}\]
The fifth ionization energy increases even more.
\[\mathrm{C^{5+}(g)} ~~\longrightarrow ~~ \mathrm{C^{5+}(g)} + e^- \qquad \mathrm{IE_5} = 37~831~\mathrm{kJ~mol^{-1}}\]
Notice how the fifth ionization energy for carbon skyrockets. This is because a core electron is now being removed as opposed to a valence electron (as seen with the first four ionization energies).
In summary,
\[\mathrm{IE_1} < \mathrm{IE_2} < \mathrm{IE_3} < \cdots <~\mathrm{IE}_n\]
See the ionization energies below.
First Ionization Energies
First ionization energies tend to increase as you move
- up (a group)
- right (across a period)
Second Ionization Energies
Second ionization energies tend to increase as you move
- up (a group)
- right (across a period)
Third Ionization Energies
Third ionization energies tend to increase as you move
- up (a group)
- right (across a period)
Electron affinity
An electron affinity (Eea) of an atom or molecule is the amount of energy required to remove an electron from an anion given as
\[\mathrm{X^-(g)} \longrightarrow \mathrm{X(g)} + e^-\]
The first electron affinities for atoms tend to be positive values (Eea > 0) meaning that a neutral atom is higher in energy than its –1 charge counterpart. The removal of an electron from an anion with a –1 charge is an endothermic process. Electron affinities that are reported to be negative (or zero) means that the anion form is not stable.
The reverse of an electron affinity is the electron attachment energy which the energy change when a neutral atom gains an electron. Electron attachment energies tend to be negative.
\[\mathrm{X(g)} + e^- \longrightarrow \mathrm{X^-(g)}\]
Electron affinity tends to increase as you move
- up (a group)
- right (across a period)
To aid in the interpretation of the table and values below, simply interpret the reported electron affinity to be the energy change from the anionic form of the element to its neutral form.
Electron attachment enthalpy (ΔeaH) is the enthalpy change when a gaseous neutral atom gains an electron to form a gaseous anion.
\[\mathrm{X(g)} + e^- \longrightarrow \mathrm{X^-(g)} \quad \Delta_{\mathrm{ea}}H\]
These enthalpies tend to be negative for most elements indicating that energy of an atom is released when an electron is gained.