Periodic Table & Periodicity

(A) The electronic configurations are:

For carbon (C): $1s^2\\ 2s^2\\ 2p^2$

For $\mathrm{C}^{+}$: $1s^2\\ 2s^2\\ 2p^1$

For boron (B): $1s^2\\ 2s^2\\ 2p^1$

For $\mathrm{B}^{+}$: $1s^2\\ 2s^2$

The second ionisation energy ($\\mathrm{IE}_2$) means the energy required to remove one electron from a singly charged positive ion. Since in $\mathrm{B}^{+}$, the next electron is removed from a completely filled 2s orbital, which is more stable, more energy is needed. Hence, $\\mathrm{IE}_2$ of B is greater than $\\mathrm{IE}_2$ of C. This statement is correct.

(B) The ions $\mathrm{Al}^{3+}$, $\mathrm{Mg}^{2+}$, and $\mathrm{Na}^{+}$ all have the same number of electrons (10), so they are called isoelectronic species.

For isoelectronic ions, the ionic size depends on the number of protons; more protons mean greater attraction, leading to a smaller size.

Number of protons:

${Al}^{3+}$ → 13

${Mg}^{2+}$ → 12

${Na}^{+}$ → 11

Therefore, the size order is: ${Al}^{3+} < {Mg}^{2+} < {Na}^{+}$. This statement is correct.

(C) Density values are:

Potassium (K): $0.86\\ {g/cm^3}$

Sodium (Na): $0.97\\ {g/cm^3}$

Since the density of Na is greater than that of K, this statement is incorrect as per the given periodic trend.

(D) Bond energies:

H–H bond energy = $435.88\\ {kJ/mol}$

F–F bond energy = $155\\ {kJ/mol}$

The F–F bond is weaker than the H–H bond because the small size of fluorine atoms leads to strong repulsion between lone pairs of electrons. Hence, this statement is incorrect.

The solubility of ionic compounds in water is influenced by two principal factors: lattice energy and hydration energy. Lattice energy is the amount of energy that is released when the ions of an ionic compound come together to form a crystalline lattice. On the other hand, hydration energy is the amount of energy released when water molecules surround and interact with the ions of a solute.

The solubility of an ionic compound in water generally increases when its hydration energy is greater than its lattice energy. This is because the energy provided by the water molecules (hydration energy) compensates for and surpasses the energy required to break apart the ions in the crystal lattice (lattice energy).

For sodium sulphate ($\text{Na}_2\text{SO}_4$), it is highly soluble in water. This is because its hydration energy exceeds its lattice energy. The ions in sodium sulphate (Na+ and $\text{SO}_4^{2-}$) are effectively stabilized by the relatively high hydration energy resulting from water molecules surrounding these ions, which compensates for the energy needed to separate the ions from the lattice. Thus, Option A is a correct statement describing this scenario.

In the case of barium sulphate ($\text{BaSO}_4$), it is sparingly soluble in water because its lattice energy is greater than its hydration energy. The ions (Ba$^{2+}$ and $\text{SO}_4^{2-}$) form a very stable lattice which requires a lot of energy to be disrupted. The hydration energy provided by the surrounding water molecules is not sufficient to overcome this high lattice energy. Therefore, Option B correctly describes why barium sulphate is sparingly soluble.

Option C is incorrect as the lattice energy does indeed play a crucial role in determining the solubility of an ionic compound. It is one of the key factors that need to be overcome by hydration energy for dissolution to occur.

Option D is also incorrect because stating that the hydration energy of sodium sulphate is less than its lattice energy would imply that sodium sulphate is not soluble in water, which contradicts the known high solubility of the compound.

Therefore, Option A is correct for sodium sulphate, and Option B is correct for barium sulphate.

The periodic table is a vital tool in chemistry and physics, classifying elements according to their properties and atomic structures. We can validate each option to see if each statement is true regarding the long form of the periodic table:

Option A: "It reflects the sequence of filling the electrons in the order of sub-energy levels s, p, d, and f"

True. The long form of the periodic table is designed based on the electron configuration of elements, where elements are arranged in blocks corresponding to the type of atomic orbital (s, p, d, or f) being filled with electrons. The filling order reflects the Aufbau principle, which predicts the order in which orbitals are filled: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. This arrangement allows chemists and physicists to understand and predict the electronic structure of the atoms.

Option B: "It helps to predict the stable valency states of the elements"

True. The periodic table provides information on the valence electrons of elements, which are the electrons that participate in chemical bonding. The elements in the same group (column) have similar valence electron configurations, leading to similar chemical behaviors, including valency. For example, all elements in Group 1 have one electron in their outermost shell and typically exhibit a +1 oxidation state in compounds.

Option C: "It reflects trends in physical and chemical properties of the elements"

True. The periodic table systematically arranges elements in rows (periods) and columns (groups) based on increasing atomic number and similar electronic configurations, respectively. This setup reflects and predicts trends in both physical (such as atomic radius, ionization energy, and electronegativity) and chemical properties (such as reactivity and common oxidation states) across periods and down groups.

Option D: "It helps to predict the relative ionicity of the bond between any two elements"

Generally, less accurate compared with other statements. While the periodic table can suggest trends in electronegativity (which affects ionic character when different elements form compounds), predicting the relative ionicity of bonds between any two elements requires more specific information about their electronegativity differences, which may not be directly inferred from the periodic table alone. Rather, it requires specific calculations or additional data aside from just the position in the periodic table.

In conclusion, Options A, B, and C are true statements regarding the long form of the periodic table, whereas Option D, while somewhat supported by trends indicated in the periodic table, is not fully accurate without further information or context. Thus, D is less directly supported by the layout of the periodic table alone.