Problem 59 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Arrange the following in : (i) Arrange the following ions in order of their increasing radii: \(\mathrm{Li}^{+}\), \(\mathrm{Mg}^{2+}, \mathrm{K}^{+}, \mathrm{Al}^{3+}\) (ii) Increasing order of basic character : \(\mathrm{MgO}, \mathrm{SrO}, \mathrm{K}_{2} \mathrm{O}, \mathrm{NiO}, \mathrm{Cs}_{2} \mathrm{O}\) (iii) Increasing order of ionic size : \(\mathrm{N}^{3-}, \mathrm{Na}^{+}, \mathrm{F}^{-}, \mathrm{O}^{2-}, \mathrm{Mg}^{2+}\) (iv) Increasing size : \(\mathrm{Cl}^{-}, \mathrm{S}^{2-}, \mathrm{Ca}^{2+}, \mathrm{Ar}\) (v) Increasing first ionization potential: Mg, Al, Si, Na (vi) Increasing acidic property: \(\mathrm{ZnO}, \mathrm{Na}_{2} \mathrm{O}_{2}, \mathrm{P}_{2} \mathrm{O}_{5}, \mathrm{MgO}\) (vii) Decreasing ionic size : \(\mathrm{Mg}^{2+}, \mathrm{O}^{2-}, \mathrm{Na}^{+}, \mathrm{F}^{-}\)

Step-by-Step Solution

Answer

(i) \(\mathrm{Al}^{3+} < \mathrm{Mg}^{2+} < \mathrm{Li}^{+} < \mathrm{K}^{+}\), (ii) \(\mathrm{NiO} < \mathrm{MgO} < \mathrm{SrO} < \mathrm{K}_{2}\mathrm{O} < \mathrm{Cs}_{2}\mathrm{O}\), (iii) \(\mathrm{Mg}^{2+} < \mathrm{Na}^{+} < \mathrm{F}^{-} < \mathrm{O}^{2-} < \mathrm{N}^{3-}\), (iv) \(\mathrm{Ar} < \mathrm{Ca}^{2+} < \mathrm{Cl}^{-} < \mathrm{S}^{2-}\), (v) \(\mathrm{Na} < \mathrm{Mg} < \mathrm{Al} < \mathrm{Si}\), (vi) \(\mathrm{Na}_{2}\mathrm{O}_{2} < \mathrm{MgO} < \mathrm{ZnO} < \mathrm{P}_{2}\mathrm{O}_{5}\), (vii) \(\mathrm{O}^{2-} > \mathrm{F}^{-} > \mathrm{Na}^{+} > \mathrm{Mg}^{2+}\).

Step 1: Arrange Ions in Increasing Radii Order (i)

We compare the ionic radii based on their charges and positions in the periodic table. Cations are smaller than their parent atoms, and higher charges result in smaller size. The order is: \(\mathrm{Al}^{3+} < \mathrm{Mg}^{2+} < \mathrm{Li}^{+} < \mathrm{K}^{+}\).

Step 2: Increasing Order of Basic Character (ii)

The basic character of oxides increases down the group in the periodic table as they become more ionic. The order of increasing basic character is: \(\mathrm{NiO} < \mathrm{MgO} < \mathrm{SrO} < \mathrm{K}_{2}\mathrm{O} < \mathrm{Cs}_{2}\mathrm{O}\).

Step 3: Increasing Order of Ionic Size (iii)

Typically, more negative ions are larger. The order considering their ionic charges and size is: \(\mathrm{Mg}^{2+} < \mathrm{Na}^{+} < \mathrm{F}^{-} < \mathrm{O}^{2-} < \mathrm{N}^{3-}\).

Step 4: Increasing Order of Size (iv)

Noble gases have smaller sizes compared to their ionic counterpart, and anions are larger. The increasing order is: \(\mathrm{Ar} < \mathrm{Ca}^{2+} < \mathrm{Cl}^{-} < \mathrm{S}^{2-}\).

Step 5: Increasing First Ionization Potential (v)

First ionization potential increases across a period. Therefore, the order is: \(\mathrm{Na} < \mathrm{Mg} < \mathrm{Al} < \mathrm{Si}\).

Step 6: Increasing Acidic Property (vi)

Acidic property decreases as we move towards more metallic oxides. The order is: \(\mathrm{Na}_{2}\mathrm{O}_{2} < \mathrm{MgO} < \mathrm{ZnO} < \mathrm{P}_{2}\mathrm{O}_{5}\).

Step 7: Decreasing Ionic Size (vii)

Ionic size decreases with higher positive charge and increases with more negative charge. The order is: \(\mathrm{O}^{2-} > \mathrm{F}^{-} > \mathrm{Na}^{+} > \mathrm{Mg}^{2+}\).

Key Concepts

Ionic Radii

Understanding ionic radii is essential when studying periodic trends. Ions are atoms that have gained or lost electrons to achieve a stable electron configuration. Cations, such as \(\mathrm{Li}^{+}\) and \(\mathrm{Mg}^{2+}\), have lost electrons and are typically smaller than their parent atoms. This is because losing electrons reduces electron-electron repulsion, allowing the remaining electrons to be pulled closer by the nucleus.
In contrast, anions, such as \(\mathrm{F}^{-}\) or \(\mathrm{O}^{2-}\), gain electrons, increasing their size due to enhanced electron-electron repulsion and reduced effective nuclear charge. Generally, higher positive charge in cations results in a smaller radius, and higher negative charge in anions leads to a larger radius.
Therefore, in comparing ionic sizes, the order is affected by the ionic charges and the original atomic size, leading us to order ions such as \(\mathrm{Al}^{3+} < \mathrm{Mg}^{2+} < \mathrm{Li}^{+} < \mathrm{K}^{+}\) based on their decreasing size.

Basic Character

The basic character of an oxide refers to its ability to react with an acid to form salt and water. It is influenced by the metal's position in the periodic table. Generally, basicity increases as you move down a group because the metallic character of elements increases.
For example, in group 1, oxides like \(\mathrm{Cs}_{2} \mathrm{O}\) are more basic than \(\mathrm{Li}_{2} \mathrm{O}\), as cesium is lower in the group, making its oxide more ionic and basic. Similarly, \(\mathrm{SrO}\) is more basic than \(\mathrm{MgO}\). In a nutshell, more ionic oxides, that form ionic bonds readily, tend to be more basic, leading to the arrangement: \(\mathrm{NiO} < \mathrm{MgO} < \mathrm{SrO} < \mathrm{K}_{2} \mathrm{O} < \mathrm{Cs}_{2} \mathrm{O}\).

Ionic Size

Ionic size refers to the effective size of an ion in a crystal lattice. Anions are often larger than cations due to gaining additional electrons, which increases their electron cloud size.
For instance, \(\mathrm{N}^{3-}\) is the largest amongst common negative ions because it has the greatest number of excess electrons. Comparatively, cations like \(\mathrm{Mg}^{2+}\) are smaller since they lose electrons, reducing their ionic radius. The order of increasing ionic size. \(\mathrm{Mg}^{2+} < \mathrm{Na}^{+} < \mathrm{F}^{-} < \mathrm{O}^{2-} < \mathrm{N}^{3-}\), reflects this rule as more negatively charged and fully or partially filled inner shell configurations result in larger ionic sizes.

Ionization Potential

Ionization potential, or ionization energy, is the energy required to remove an electron from an atom in its gaseous state. It tends to increase across a period because as atomic numbers rise, the effective nuclear charge that holds electrons increases, making it harder to remove an electron.
When comparing the elements like \(\mathrm{Na}, \mathrm{Mg}, \mathrm{Al},\) and \(\mathrm{Si}\), we notice that \(\mathrm{Si}\), being further to the right, has a higher ionization potential due to greater nuclear attraction on its valence electrons. Conversely, \(\mathrm{Na}\), at the start of the period, permits easier electron removal. The order of increasing ionization potential is: \(\mathrm{Na} < \mathrm{Mg} < \mathrm{Al} < \mathrm{Si}\).

Acidic Property

The acidic property of a compound is its tendency to donate protons (H⁺ ions) in a chemical reaction, or to accept electron pairs. In the context of oxides, acidity tends to increase with the nonmetallic nature of the element.
For example, \(\mathrm{P}_{2} \mathrm{O}_{5}\) is noted for its strong acidic properties, whereas \(\mathrm{Na}_{2} \mathrm{O}_{2}\) and \(\mathrm{MgO}\) are basic. As we progress from metallic oxides to nonmetallic oxides, the acidity of the oxides increases, since nonmetallic oxides react with water to form acids. With this reasoning, we can arrange the compounds by increasing acidity as follows: \[\mathrm{Na}_{2}\mathrm{O}_{2} < \mathrm{MgO} < \mathrm{ZnO} < \mathrm{P}_{2}\mathrm{O}_{5}\].