Question

Which ion in each pair has greater charge density? Explain. (a) \(\mathrm{Na}^{+}\) or \(\mathrm{Cs}^{+}\) (b) \(\mathrm{Sr}^{2+}\) or \(\mathrm{Rb}^{+}\) (c) \(\mathrm{Na}^{+}\) or \(\mathrm{Cl}^{-}\) (d) \(\mathrm{O}^{2-}\) or \(\mathrm{F}^{-}\) (e) \(\mathrm{OH}^{-}\) or \(\mathrm{SH}^{-}\) (f) \(\mathrm{Mg}^{2+}\) or \(\mathrm{Ba}^{2+}\) (g) \(\mathrm{Mg}^{2+}\) or \(\mathrm{Na}^{+}\) (h) \(\mathrm{NO}_{3}^{-}\) or \(\mathrm{CO}_{3}^{2-}\)

Short answer

\text { } \(\text{Na}^{+} > \text{Cs}^{+}\), \(\text{Sr}^{2+} > \text{Rb}^{+}\), \(\text{Na}^{+} > \text{Cl}^{-}\), \(\text{O}^{2-} > \text{F}^{-}\), \(\text{OH}^{-} > \text{SH}^{-}\), \(\text{Mg}^{2+} > \text{Ba}^{2+}\), \(\text{Mg}^{2+} > \text{Na}^{+}\), \(\text{CO}_{3}^{2-} > \text{NO}_{3}^{-}\)

Step-by-step solution

Understanding Charge Density

Charge density is the ratio of the charge of an ion to its volume. Smaller ions with higher charges have greater charge density.

Compare Na+ and Cs+

Na+ and Cs+ both have a +1 charge. Na+ is a smaller ion compared to Cs+, making its charge density greater. Therefore, \(\text{Na}^{+}\) has greater charge density.

Compare Sr2+ and Rb+

Sr2+ has a +2 charge, while Rb+ has a +1 charge. Since Sr2+ has a greater charge and is smaller in size compared to Rb+, \(\text{Sr}^{2+}\) has greater charge density.

Compare Na+ and Cl-

Na+ has a +1 charge, and Cl- has a -1 charge. Since they have different charges and Cl- is larger in size, \(\text{Na}^{+}\) has greater charge density.

Compare O2- and F-

O2- and F- both have similar sizes, but O2- has a -2 charge while F- has a -1 charge. This makes \(\text{O}^{2-}\) have a greater charge density.

Compare OH- and SH-

OH- and SH- have the same charge, -1, but OH- contains oxygen which is smaller than sulfur in SH-. Therefore, \(\text{OH}^{-}\) has greater charge density.

Compare Mg2+ and Ba2+

Mg2+ and Ba2+ both have a +2 charge. Mg2+ is smaller in size compared to Ba2+. Thus, \(\text{Mg}^{2+}\) has greater charge density.

Compare Mg2+ and Na+

Mg2+ has a +2 charge, while Na+ has a +1 charge. Mg2+ is also smaller in size, which means \(\text{Mg}^{2+}\) has greater charge density.

Compare NO3- and CO32-

NO3- has a -1 charge, while CO32- has a -2 charge. Although CO32- might be larger in volume, the greater charge on CO32- generally gives it a higher charge density. Therefore, \(\text{CO}_{3}^{2-}\) has greater charge density.

Key concepts

Cation

A cation is an ion with a positive charge. Cations form when an atom loses one or more electrons, which results in a positive charge because the number of protons in the nucleus exceeds the number of electrons.
For example, \(\text{Na}^{+}\) (sodium ion) becomes a cation after losing one electron from its neutral state. Cations tend to be smaller than their neutral atoms because the loss of electrons usually means the loss of an electron shell, reducing the ion's size.
In chemical bonding, cations often pair up with anions (negatively charged ions) to form ionic compounds, such as sodium chloride (\(\text{NaCl}\)).

Anion

An anion is an ion with a negative charge. Anions form when an atom gains one or more electrons, resulting in a negative charge due to the higher number of electrons compared to protons.
For instance, \(\text{Cl}^{-}\) (chloride ion) becomes an anion after gaining an extra electron from its neutral state. Anions are typically larger than their neutral atoms as the addition of extra electrons increases electron-electron repulsion in the electron cloud, leading to a larger radius.
Anions are crucial in creating ionic bonds with cations. For example, in sodium chloride, \(\text{Cl}^{-}\) pairs with \(\text{Na}^{+}\) to form the bond needed for the compound's stability.

Ionic Size

The size of an ion is known as the ionic radius, which significantly influences the ion's properties.
For cations, losing electrons leads to a decrease in the ionic radius as the remaining electrons are drawn closer to the nucleus due to decreased electron-electron repulsion. Conversely, gaining electrons makes an anion larger by increasing these repulsive forces within the electron cloud.
An important factor in determining an ion's behavior, ionic size influences charge density, chemical bonding, and how ions interact with each other in compounds. Smaller ions with high charges often have greater charge density and form stronger ionic bonds.

Ionic Charge

Ionic charge refers to the electrical charge an ion holds, determined by the difference between the number of protons and electrons in the atom.Before the ion forms, atoms are electrically neutral, with equal numbers of protons and electrons.
When an atom gains or loses electrons, it generates an imbalance, resulting in either a positive or negative charge.
Charge density, an important property of ions, depends on both the ionic charge and ionic size. It is highly relevant in chemical bonding and affects the strength of interactions between ions within a compound.

Chemical Bonding

Chemical bonding describes the force that holds atoms or ions together in a molecule or compound. The most common types of chemical bonds are ionic bonds and covalent bonds.In ionic bonding, ions with opposite charges (cations and anions) attract each other, forming a stable compound like sodium chloride (\(\text{NaCl}\)).
These bonds typically form between metals and non-metals, where one atom transfers electrons to another, leading to formation of the respective ions.
Intermolecular attractions govern the physical properties such as melting and boiling points of ionic compounds, which are also influenced by charge density, with higher charge densities typically resulting in stronger bonds.