Problem 57 - A Complete Resource Book in Chemistry for JEE Main

Question

Arrange \(\mathrm{P}^{3-}, \mathrm{S}^{2-}, \mathrm{H}^{-}, \mathrm{I}^{-}\)in the order of increasing ionic radii (a) \(\mathrm{P}^{3-}, \mathrm{S}^{2-}, \mathrm{I}-, \mathrm{H}^{-}\) (b) \(\mathrm{S}^{2-}, \mathrm{P}^{3-}, \mathrm{H}^{-}, \mathrm{I}^{-}\) (c) \(\mathrm{S}^{2-}, \mathrm{H}^{-}, \mathrm{P}^{3-} \mathrm{I}^{-}\) (d) \(\mathrm{H}^{-}, \mathrm{S}^{2-}, \mathrm{P}^{3-}, \mathrm{I}^{-}\)

Step-by-Step Solution

Answer

(d) H^-, S^{2-}, P^{3-}, I^{-}

Step 1: Understand Ionic Radii

Ionic radii refer to the size of an ion. Generally, negative ions (anions) are larger than their parent atoms because they gain electrons, increasing electron-electron repulsion, which leads to a larger size.

Step 2: Compare Charges and Element Sizes

Consider how each element compares in terms of periodic trends. As you go down a group, ionic size increases because additional electron shells are added. Compare phosphorus, sulfur, hydrogen, and iodine as possible anions in terms of their position in the periodic table.

Step 3: List Elements by Expected Order

Start with hydrogen at the top of the periodic table, which is small as a monatomic anion ( H^-). Then consider sulfur (S^{2-}), phosphorus (P^{3-}), and finally iodine (I^{-}). Based on position and understanding from the periodic table, the ionic size typically increases in the order: H^-, S^{2-}, P^{3-}, I^{-}.

Step 4: Select the Correct Answer

Based on our order, the increasing order of the anions based on ionic radii is H^-, S^{2-}, P^{3-}, I^{-}. This corresponds to option (d) in the provided list.

Key Concepts

Anions and Their Characteristics

Anions are negatively charged ions formed when an atom gains one or more electrons. This extra electron density increases the electron-electron repulsion within the atom's electron cloud, which causes the ion to expand. Therefore, anions tend to be larger than their original neutral atoms.

• For example, when phosphorus ( P ) gains three electrons to become P^{3-} , it becomes notably larger than a neutral phosphorus atom.
• Sulfur ( S ) when gaining two electrons becomes S^{2-} and also enlarges.
• Even iodine ( I ) becomes larger as I^{-} when it gains one extra electron.

Thus, understanding that the formation of anions typically results in increased atomic size is key to predicting the order of ionic radii.

Periodic Trends in Ionic Sizes

Periodic trends significantly affect the comparison of ionic sizes, especially when considering anions. As one moves down a group in the periodic table (from top to bottom), the ionic radii tend to increase. This occurs because with each step down a group, a new electron shell is added, increasing the overall size of the atom or ion.

• For instance, iodine ( I^{-} ) lies below both phosphorus ( P ) and sulfur ( S ) in the periodic table, which usually translates to I^{-} having a larger ionic radius than P^{3-} and S^{2-} due to the additional electron shell.
• Contrary to this trend, hydrogen ( H^{-} ) sits at the top of the periodic table and lacks any additional filled electron shells, making it quite small comparatively.

By understanding these periodic trends, we can predict that within any period, increasing atomic number will lead to a decrease in size, but moving down a group will typically result in an increase in size.

Ionic Size Comparison

When comparing ionic sizes, especially among anions, it is crucial to consider both the number of additional electrons and the electron shells. An effective way to determine the relative size is to consider the periodic context and the degree of electron-electron repulsion.

• Hydrogen ( H^{-} ), with its single additional electron, has the smallest ionic radius among our listed anions due to its position at the top of the periodic table.
• Sulfur ( S^{2-} ) increases in size relative to H^{-} , as it not only gains two electrons but is also lower down the table, thus larger.
• Phosphorus ( P^{3-} ) comes next, expanding further because of the additional shell and three additional electrons.
• Iodine ( I^{-} ), sitting below the others with its significant atomic radius to start with, ends up the largest due to more electron shells and electron addition.

In summary, the comparative sequence of ionic radii increasing in size is: H^{-}, S^{2-}, P^{3-}, I^{-}. Understanding these comparisons is essential for organizing ions by size.