Classification of Elements and Periodic Table

Na$^+$ is larger than Mg$^{2+}$.

Both are isoelectronic (10 electrons, configuration $1s^2 2s^2 2p^6$), so they have the same electron shells. Mg$^{2+}$ has 12 protons and Na$^+$ has only 11, so the nuclear charge on the same 10 electrons is higher in Mg$^{2+}$. It pulls the electron cloud in more strongly, making Mg$^{2+}$ smaller.

Advantages of the modern periodic table

The modern periodic table is based on the modern periodic law: the properties of elements are a periodic function of their atomic numbers. It is arranged in $18$ groups and $7$ periods, and has the following advantages.

1. Based on atomic number. Atomic number is a fundamental property, so the arrangement is exact and removes the anomalies of Mendeleev's table (e.g. Ar and K, Te and I are now in the right order even though atomic masses are reversed).
2. Correlates with electronic configuration. The position of an element shows its configuration: the period number is the number of the outermost shell, and the group shows the number of valence electrons. Elements are divided into $s$, $p$, $d$ and $f$ blocks.
3. Clear groups. Elements of a group have similar outer electronic configurations, hence similar properties, which makes them easy to study as families.
4. Isotopes. Isotopes of an element share one atomic number, so they occupy one position, which removes the problem of finding places for them.
5. Separation of metals, non-metals and metalloids. They lie in separate regions, and trends in properties (atomic size, ionisation energy, electronegativity, metallic character) are easy to see across periods and down groups.
6. Places transition and inner-transition elements properly, and separates the sub-groups A and B of Mendeleev's table so the confusion between them is removed.
7. Easy to remember, and helps predict properties of unknown elements and their compounds.

Mendeleev's periodic law: The physical and chemical properties of the elements are a periodic function of their atomic masses.

Mendeleev's periodic table: The elements were arranged in order of increasing atomic mass in 7 horizontal rows called periods and 8 vertical columns called groups (I to VIII, with the subgroups A and B). Elements in the same group showed similar properties. Mendeleev left gaps for undiscovered elements and predicted their properties, e.g. eka-aluminium (gallium) and eka-silicon (germanium), and these predictions were later confirmed.

Merits:

• It classified the known elements systematically and made study easier.
• It predicted new elements and corrected doubtful atomic masses.

Anomalies (defects):

1. Hydrogen had no fixed position, since it resembles both alkali metals and halogens.
2. Isotopes have different atomic masses but the same properties, yet had no separate place in the table.
3. Some elements of higher atomic mass were placed before those of lower atomic mass to keep similar elements together, e.g. Ar (39.9) before K (39.1), Co (58.9) before Ni (58.7), Te (127.6) before I (126.9).
4. Dissimilar elements were placed in the same group, e.g. alkali metals (Li, Na, K) with coinage metals (Cu, Ag, Au) in group I.
5. There was no proper place for the lanthanides and actinides, and the position of the eighth group was unclear.

These anomalies were removed when Moseley showed that properties depend on atomic number rather than atomic mass, giving the modern periodic law.

Na⁺ is the smallest.

All four ions are isoelectronic (10 electrons, $1s^2 2s^2 2p^6$), so their size depends on nuclear charge: the greater the number of protons, the stronger the pull on the same number of electrons and the smaller the ion.

Nuclear charge: $\mathrm{N^{3-}}(+7) < \mathrm{O^{2-}}(+8) < \mathrm{F^-}(+9) < \mathrm{Na^+}(+11)$, so size is $\mathrm{N^{3-}} > \mathrm{O^{2-}} > \mathrm{F^-} > \mathrm{Na^+}$.

Mendeleev arranged the elements in order of increasing atomic mass, and this led to several defects.

1. Position of hydrogen. Hydrogen resembles both alkali metals (group I) and halogens (group VII), but has no fixed place.
2. Anomalous pairs. Some elements of higher atomic mass come before those of lower atomic mass to maintain the properties, e.g. Ar (39.9) before K (39.1), Co (58.9) before Ni (58.7), Te (127.6) before I (126.9). This breaks the basic rule.
3. Isotopes. Isotopes of an element have different atomic masses but identical chemical properties. By mass they should occupy different places, but no place was provided for them.
4. Dissimilar elements placed together. Alkali metals (Li, Na, K) and coinage metals (Cu, Ag, Au) were placed in the same group I although their properties differ greatly.
5. Similar elements placed apart. Chemically similar elements, e.g. Cu and Hg or Pt and Au, were placed in different groups.
6. Lanthanides and actinides (14 + 14 elements) had no proper place in the table.
7. Noble gases were not known at the time and had to be added later as a new group; the position of group VIII (Fe, Co, Ni) was also doubtful.
8. Atomic mass does not vary regularly from one element to the next, so the missing elements could not always be predicted reliably.

These defects were removed by the modern periodic law, which uses atomic number (Moseley) as the basis.

Chlorine has the greater electron affinity (about $349\ \text{kJ mol}^{-1}$ for Cl against $328\ \text{kJ mol}^{-1}$ for F).

Fluorine is very small, and its $2p$ subshell is compact. The electron density there is high, so an incoming electron is strongly repelled by the electrons already present. In chlorine the electron enters the larger $3p$ subshell, where the repulsion is much less, so more energy is released.

The $X^{3-}$ ion is formed when the atom gains three electrons, so it has three more electrons than protons, while the nuclear charge (number of protons) stays the same. The same nuclear pull is now shared among more electrons, and the increased electron-electron repulsion makes the electron cloud spread out. Hence the effective nuclear attraction per electron decreases and the ion is larger than the atom.

First ionization energy is the minimum amount of energy required to remove the most loosely bound (outermost) electron from an isolated gaseous atom in its ground state to form a gaseous unipositive ion.

$\text{M}(g) + \text{IE}_1 \rightarrow \text{M}^+(g) + e^-$

Atomic size (or nuclear charge / shielding effect).

Ionisation enthalpy decreases as atomic size increases (the outer electron lies farther from the nucleus, so it is held less tightly), and increases with greater nuclear charge.

(b) Helium

Helium has the highest ionization enthalpy in the periodic table (2372 kJ/mol) because its single electron lies in the tightly held, fully filled 1s orbital closest to the nucleus. Removing this electron requires the most energy, so helium is the most difficult element to ionize.

Reason: Nitrogen has a half-filled stable p-subshell ($2p^3$), while carbon has only a partially filled p-subshell ($2p^2$).

• Carbon: $1s^2\,2s^2\,2p^2$ — one p-orbital is empty.
• Nitrogen: $1s^2\,2s^2\,2p^3$ — all three p-orbitals are singly occupied (half-filled).

A half-filled subshell has extra stability due to greater exchange energy and symmetrical charge distribution. Therefore, removing an electron from nitrogen requires much more energy than from carbon, causing a steep rise in ionisation enthalpy from carbon to nitrogen.