Problem 35 - Chemistry: The Central Science

Question

Provide a brief explanation for each of the following: (a) \(\mathrm{O}^{2-}\) is larger than O. (b) \(\mathrm{S}^{2-}\) is larger than \(\mathrm{O}^{2-}\). (c) \(\mathrm{S}^{2-}\) is larger than \(\mathrm{K}^{+}\). (d) \(\mathrm{K}^{+}\)is larger than \(\mathrm{Ca}^{2+}\).

Step-by-Step Solution

Answer

(a) O²⁻ is larger than O because as O gains 2 electrons to form O²⁻, the greater repulsive forces between electrons expand the electron cloud. (b) S²⁻ is larger than O²⁻ because S has an additional energy level of electrons compared to O. (c) S²⁻ is larger than K⁺ because S²⁻ has an extra energy level of electrons and is an anion while K⁺ is a cation. (d) K⁺ is larger than Ca²⁺ because Ca²⁺ has a higher effective nuclear charge resulting in a smaller ionic size compared to K⁺.

Step 1: (a) Why O²⁻ is larger than O

Adding electrons to an atom forms a negatively charged ion or anion. In this case, when O gains 2 electrons to form O²⁻, there are more electrons than protons. This causes greater repulsive forces between the electrons, pushing them away from each other, causing the electron cloud to expand, and making O²⁻ larger than O.

Step 2: (b) Why S²⁻ is larger than O²⁻

O and S are both in the same group in the periodic table (Group 6), but S is one period lower than O. This means that S has one additional energy level of electrons compared to O. When both elements form a 2- ion, this extra energy level makes S²⁻ larger than O²⁻.

Step 3: (c) Why S²⁻ is larger than K⁺

When an atom loses an electron, it becomes a positively charged ion or cation (in this case, K⁺). This causes an increase in the effective nuclear charge experienced by the remaining electrons, causing them to be drawn closer to the nucleus, making the ion smaller than the neutral atom. Comparing S²⁻ and K⁺, S²⁻ has an extra energy level of electrons and is an anion, so it is larger than K⁺, which is a cation.

Step 4: (d) Why K⁺ is larger than Ca²⁺

K⁺ and Ca²⁺ are both in the same period of the periodic table (Period 4), but K is one group to the left of Ca. When forming cations, K loses one electron while Ca loses two, resulting in Ca²⁺ having a higher effective nuclear charge than K⁺. The remaining electrons in Ca²⁺ are drawn more tightly to the nucleus due to this higher charge, resulting in a smaller ionic size compared to K⁺.

Key Concepts

Anions and Cations

Anions and cations are types of ions, which are atoms or molecules that have gained or lost one or more electrons, resulting in a net charge. Anions are negatively charged ions, formed when an atom gains electrons. For example, the oxygen atom (O) gains two electrons to become the oxide ion (\(\mathrm{O}^{2-}\)), turning it into an anion. This increase in electrons leads to more electron-electron repulsion, which causes the ionic radius to expand.
Anions can be remembered as seeking 'additional electrons', and therefore, they are usually larger than their neutral parent atoms because of the additional repulsion between the extra electrons.
Cations, on the other hand, are positively charged ions formed when an atom loses electrons. For instance, potassium (K) loses an electron to become the potassium ion (\(\mathrm{K}^{+}\)). The loss of an electron means that there are fewer electrons compared to protons, resulting in a stronger pull from the nucleus on the remaining electrons. Consequently, cations tend to be smaller than their neutral counterparts.

• Anions are larger due to addition of electrons.
• Cations are smaller due to electron loss and stronger nuclear pull.

Periodic Table Trends

Periodic table trends help us understand how elements behave and change their properties across different periods and groups. Trends in ionic size, for instance, evolve predictably. As we move down a group in the periodic table, atoms have more energy levels, and their atomic and ionic radii increase. For example, sulfur (\(\mathrm{S}\)) is below oxygen (\(\mathrm{O}\)) in the same group, which means that \(\mathrm{S}^{2-}\) has more electron shells than\(\mathrm{O}^{2-}\), resulting in a larger ionic radius.
Across a period, moving from left to right, atoms generally become smaller. This is because the effective nuclear charge increases, pulling the electrons closer to the nucleus. For identical charges, such as \(\mathrm{K}^{+}\) and \(\mathrm{Ca}^{2+}\) in the same period, the cation with a higher effective nuclear charge will be smaller. Thus,\(\mathrm{Ca}^{2+}\) is smaller than \(\mathrm{K}^{+}\).

### Key points about periodic trends:

• Atomic and ionic sizes increase down a group.
• Sizes decrease across a period from left to right.
• More electron shells contribute to larger ionic radii.

Effective Nuclear Charge

Effective nuclear charge is a crucial concept that influences the size of ions. The effective nuclear charge is the net positive charge experienced by electrons in an atom. It plays a critical role in determining how strongly electrons are held in orbit by the nucleus.
For cations, like \(\mathrm{Ca}^{2+}\), losing electrons reduces electron shielding, increasing the effective nuclear charge. The remaining electrons are pulled in more tightly, making the ion smaller. On the other hand, anions, such as \(\mathrm{O}^{2-}\), experience more electron-electron repulsion due to added electrons. These repulsive forces lead to an expanded electron cloud.

• Anions: Increased repulsion = expanded size.
• Cations: Higher effective nuclear charge = smaller size.

The effective nuclear charge can be roughly calculated by taking the total charge of an atom's nucleus and subtracting the shielding or screening effect of the inner electrons. This helps predict the size and chemical properties of ions and how they compare when ranked together, such as more tightly packed cations versus expanded anions.