Question

Consider \(\mathrm{S}, \mathrm{Cl}\), and \(\mathrm{K}\) and their most common ions. (a) List the atoms in order of increasing size. (b) List the ions in order of increasing size. (c) Explain any differences in the orders of the atomic and ionic sizes.

Short answer

The order of increasing atomic size for S, Cl, and K is: S < Cl < K. The order of increasing ionic size for their most common ions (S^(2-), Cl^(-), and K^(+)) is: K^(+) < Cl^(-) < S^(2-). The difference in orders is due to the gain or loss of electrons and the variation in effective nuclear charge. As ions form, the number of electrons changes compared to the neutral atom, and this affects the overall size of the ion.

Step-by-step solution

Identify the most common ions

The most common ions for each element are as follows: - For sulfur (S): Sulfide ion (S^(2-)) - For chlorine (Cl): Chloride ion (Cl^(-)) - For potassium (K): Potassium ion (K^(+)) Now that we have the most common ions, we can proceed to arrange them based on their sizes.

Arrange the atoms in order of increasing size

To arrange the atoms in order of increasing size, we need to consider their atomic radii. As we move across a period (left to right) in the periodic table, the atomic radius generally decreases. Sulfur, chlorine, and potassium are in the 3rd period with atomic numbers 16, 17, and 19, respectively. Therefore, their order of increasing size is: S < Cl < K

Arrange the ions in order of increasing size

When it comes to ions, their size depends on the number of electrons and the effective nuclear charge. Let's arrange the most common ions of the given elements in order of increasing size: - Sulfide ion (S^(2-)): Gains 2 electrons, so it becomes larger compared to the original atom. - Chloride ion (Cl^(-)): Gains 1 electron, so it becomes larger compared to the original atom. - Potassium ion (K^(+)): Loses 1 electron, so it becomes smaller compared to the original atom. Taking these factors into account, the ions can be ordered in terms of increasing size as follows: K^(+) < Cl^(-) < S^(2-)

Explain any differences in the orders of atomic and ionic sizes

Comparing the orders of the atomic and ionic sizes, we can observe the following differences: 1. In the atomic size order (S < Cl < K), the size increases as we move across the period due to decreasing atomic radii. However, in the ionic size order (K^(+) < Cl^(-) < S^(2-)), the size is influenced by the gain or loss of electrons and effective nuclear charge. 2. For atoms, the number of electrons is equal to the atomic number. But for ions, the number of electrons changes due to the gain or loss of electrons. 3. Comparing the positions of S and Cl in both orders, the atomic size of Cl is greater than S while Cl^(-) has a smaller size than S^(2-). This is because Cl^(-) has gained only 1 electron, while S^(2-) has gained 2 electrons making it larger.

Key concepts

Atomic Radius

The atomic radius refers to the size of an atom. It is typically measured from the center of the nucleus to the boundary of the electron cloud surrounding the nucleus. Understanding atomic radius is key in predicting and explaining various properties of elements such as reactivity, ionization energy, and metallic or nonmetallic character.

As we move across a period in the periodic table, the atomic radius decreases. This is because of the addition of electrons to the same energy level while the effective nuclear charge increases, pulling electrons closer to the nucleus. Conversely, as we move down a group, the atomic radius increases due to the addition of extra energy levels, which places the outermost electrons further from the nucleus.

For example, within the 3rd period, the atomic radius of sulfur (S) is smaller than that of chlorine (Cl), which in turn is smaller than that of potassium (K). This decreasing trend is a result of increasing nuclear charge without a significant increase in electron shielding.

Ionic Radius

The ionic radius is essentially the measure of an atom's size once it has lost or gained electrons to form an ion. The trend in ionic radius is more complex than that of atomic radius because it depends not only on the nuclear charge but also on the number of electrons present in the ion.

Anions (negatively charged ions) are larger than their parent atoms since the addition of electrons leads to greater electron-electron repulsion in the valence shell, which increases the size of the electron cloud. For cations (positively charged ions), the removal of electrons results in a smaller ionic radius compared to the neutral atom as the effective nuclear charge acting on the remaining electrons is stronger.

Using Sulfur (S), Chlorine (Cl), and Potassium (K) as examples: When these atoms become ions, S^(2-), Cl^(-), and K^(+), their size changes. The sulfide ion (S^(2-)) becomes the largest due to the addition of two extra electrons, while potassium ion (K^(+)), which has lost one electron, becomes the smallest.

Effective Nuclear Charge

The concept of effective nuclear charge (Z_eff) is vital to understanding atomic and ionic sizes. It represents the net positive charge experienced by an electron in the valence shell. It accounts for both the actual nuclear charge (number of protons) and the shielding effect caused by electrons in the inner shells. The more effective nuclear charge electrons feel, the more tightly they are drawn to the nucleus, resulting in a smaller atomic or ionic radius.

In the periodic table, the effective nuclear charge increases from left to right and is more or less constant moving down a group. This charge is a central aspect when discussing the size of ions as it helps to explain why cations are smaller than their parent atoms while anions are larger. For instance, when potassium loses an electron to form K^(+), the remaining electrons are more strongly attracted to the nucleus due to the increased Z_eff, making the ionic radius smaller than the atomic radius.

Electron Configurations

Electron configurations describe the distribution of electrons among the various orbitals in an atom. These configurations influence chemical behavior and properties such as atomic and ionic sizes. The arrangement of electrons across different energy levels and sublevels follows a set of rules, which include the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

Each electron configuration is unique to its element and can predict an atom's ability to gain or lose electrons during bond formation. For example, S with electron configuration [Ne]3s^23p^4 is more likely to gain two electrons to achieve a stable octet, becoming S^(2-). Consequently, the electron repulsion within a larger number of electrons causes an increase in ionic radius compared to the atomic radius. Thus, knowledge of electron configurations is crucial for understanding trends in atomic and ionic radii across the periodic table.