Oxidation Numbers, Quantum Chemistry, and Atomic Theory Study of and Atomic History

Concept of Oxidation Number

An oxidation number is the hypothetical electrical charge assigned to an atom within a compound. This number serves as an indicator of the quantity of electrons that an atom has gained, lost, or shared when bonding with other elements. Understanding these numbers is fundamental to tracking the movement of electrons in chemical reactions.

Fundamental Rules for Assigning Oxidation Numbers

The following rules must be applied systematically to determine the oxidation state of atoms in various chemical structures:

All elements found in their natural state, whether they are monoatomic or polyatomic, are assigned an oxidation number of $0$. Examples include $Na^0$, $Cl_2^0$, $S^0$, and $N^0$.

Hydrogen exhibits different oxidation states depending on the element it is bonded to. When hydrogen forms a compound with oxygen or non-metals, its oxidation number is $+1$. Examples include $H_2O$ and $HCl$. Conversely, if hydrogen forms a compound with a metal (known as a hydride), its oxidation number becomes negative, specifically $-1$. Examples include $NaH$ and $CaH_2$.

Oxygen typically possesses an oxidation number of $-2$ when forming compounds with any element or hydrogen. Examples include $HClO_4$ and $H_4P_2O_7$. An exception to this rule occurs in peroxides, such as $Na_2O_2$, where the oxygen's oxidation state is adjusted to sum correctly with the bonding metal.

Peroxides and Specific Groups

Peroxides are formed primarily by metals from Group 1 and Group 2 of the periodic table. For instance, Hydrogen Peroxide—commonly known as oxygenated water—has the formula $H_2O_2$. In the case of Group 1 metals like Lithium ($Li$), Sodium ($Na$), Potassium ($K$), Rubidium ($Rb$), Cesium ($Cs$), and Francium ($Fr$), they form compounds where the metal is $+1$. For Group 2 metals such as Beryllium ($Be$), Magnesium ($Mg$), Calcium ($Ca$), Strontium ($Sr$), Barium ($Ba$), and Radium ($Ra$), the metal is $+2$. Examples of formation include $4Li + O_2 \rightarrow 2Li_2O$ (Basic Oxide) and $Ca + O_2 \rightarrow CaO_2$ (Calcium Peroxide).

Mathematical Calculation of Oxidation Numbers

To determine the oxidation number of a central element like Sulfur ($S$) in a compound such as Sodium Sulfate ($Na_2SO_4$), a specific algebraic process is followed. First, assign known oxidation numbers to the external elements. Sodium ($Na$) from Group 1 is assigned $+1$, and Oxygen ($O$) is assigned $-2$. Multiply these oxidation numbers by their respective subscripts: for Sodium, $+1 \times 2 = +2$; for Oxygen, $-2 \times 4 = -8$. To ensure the compound's total charge is neutral ($0$), the calculation is as follows: $+2 + x - 8 = 0$. Therefore, $x = +6$. The oxidation number of Sulfur in this context is $+6$.

Formation and Behavior of Ions

Ions are atoms that have become electrically charged through the gain or loss of electrons. There are two primary types:

Cations are ions with a positive electrical charge. This occurs when a neutral atom loses one or more electrons from its original configuration, a phenomenon known as ionization. Cations are represented with a positive oxidation state. Common examples in the human body include Sodium ($Na^+$) and Potassium ($K^+$). Aluminum produces the Aluminum ion ($Al^{3+}$).

Anions are ions with a negative electrical charge, resulting from an atom gaining an excess of electrons.

In polyatomic contexts, complex ions and compounds are formed. For example, Aluminum Hydroxide is represented as $Al(OH)_3$. When acidic ions lose hydrogen, they form specific anions such as the phosphate ion ($H_3PO_4$ losing hydrogen to become $HPO_4^{2-}$) or the bicarbonate ion ($H_2CO_3$ losing a hydrogen to become $HCO_3^-$). Silicates like $H_4Si_4O_9$ can lose ions to form $Si_4O_9^{4-}$ or $H_2Si_4O_9^{2-}$.

Redox Reactions: Oxidation and Reduction

Redox processes are defined by the transfer of electrons between substances. When a substance undergoes oxidation, it loses electrons. This substance is referred to as the Reducing Agent because it facilitates the reduction of another species. On a number scale, oxidation involves moving from left to right.

When a substance undergoes reduction, it gains electrons. This substance acts as the Oxidizing Agent. On a number scale, reduction involves moving from right to left (toward more negative values).

Rules for Semi-reactions and Dissociation

When forming oxidation and reduction semi-reactions, specific dissociation rules apply to different chemical species:

1. Oxygenated compounds, including basic oxides and acid oxides (anydrides), do not dissociate. For example, $Na_2O$ remains as a single unit in a semi-reaction.
2. Oxacids, such as Phosphorus acid ($H_3PO_4 \rightarrow PO_4^{3-}$), do dissociate by releasing their hydrogen ions.
3. Hydracids, hydroxides (bases), and non-metals also undergo dissociation.
4. Salts, including oxisalts and halogenated salts, dissociate into their constituent ions.
5. Peroxides do not dissociate in the context of a semi-reaction.

Historical Figures in Atomic Theory

Marie Curie was born Maria Skłodowska on November 7, 1867, in Warsaw, Poland. She moved to France to study at the University of Paris, where she met and married Pierre Curie. Following the death of her husband, she continued her investigations and discovered the elements Polonium and Radium. She was the first person to receive two Nobel Prizes, one in Physics and one in Chemistry, for her pioneering research on radioactivity.

Niels Bohr was born on October 7, 1885, in Copenhagen, Denmark. He studied physics at the University of Copenhagen and married Margrethe Norlund. He developed the Bohr atomic model, which explains that electrons are located in specific energy levels around the nucleus. His research was fundamental to the development of quantum physics and earned him the Nobel Prize in Physics.

J. J. Thomson was born on December 18, 1856, in Manchester, England. He studied at the University of Cambridge and married Rose Paget. As the director of the Cavendish Laboratory, he discovered the electron in 1897 through experiments with cathode rays. He proposed the "Plum Pudding" atomic model and received the Nobel Prize in Physics.

Ernest Rutherford was born on August 30, 1871, in Brightwater, New Zealand. He studied at the University of New Zealand and later worked in Canada and the United Kingdom. He married Mary Newton. Through his famous gold foil experiment, he discovered that the atom has a central nucleus. He proposed the nuclear atomic model, conducted vital research on radioactivity, and received the Nobel Prize in Chemistry.

Quantum Numbers and Atomic Structure

Quantum numbers are used to describe the location, energy, and behavior of electrons within an atom.

The Principal Quantum Number ($n$) indicates the energy level associated with an electron shell. These levels are denoted as $K, L, M, N, O, P, Q$ corresponding to numerical values $1, 2, 3, 4, 5, 6, 7$. As the value of $n$ increases, the electron's distance from the nucleus and its energy both increase.

The Secondary or Azimuthal Quantum Number ($l$) indicates the spatial shape of the orbitals. The value is determined by the formula $l = n - 1$. The subshells are assigned as follows:

• Subshell $s$: $l = 0$
• Subshell $p$: $l = 1$
• Subshell $d$: $l = 2$
• Subshell $f$: $l = 3$

The Magnetic Quantum Number ($m$) describes the orientation of the orbitals in space. It is calculated using the formula $m = 2l + 1$. For example, the $p$ subshell ($l=1$) has $3$ possible orientations: $p_x, p_y, p_z$. The values range from $-l$ to $+l$. For subshell $d$, there are $5$ orientations.

The Spin Quantum Number ($s$) indicates the rotation of the electron. An electron can have a spin of $+1/2$ (represented by an upward arrow $\uparrow$) or $-1/2$ (represented by a downward arrow $\downarrow$). A complete rotation is considered $360^\text{o}$. When an electron is positive ($+1/2$), it is often referred to as an unpaired electron.

Chemical Bonds and Matter

Chemical substances are categorized based on their composition and the nature of their bonds:

Covalent bonds generally occur between two non-metals when they share electrons. This typically happens when the electronegativity difference is less than $1.7$. Ionic bonds occur between a metal and a non-metal where electrons are transferred (gained or lost), creating an electronegativity difference greater than or equal to $1.7$.

An atom is the basic unit of matter that composes everything in the universe. For instance, an oxygen atom is part of the air. An element is a substance formed by only one type of atom, such as Gold ($Au$). A compound is a substance formed by the union of two or more different elements, such as Sodium Chloride ($NaCl$). A molecule is the union of two or more atoms, such as water ($H_2O$), which consists of 2 hydrogen atoms and 1 oxygen atom.

Chemical Reactions

A chemical reaction is a process in which initial substances are transformed into different substances. Common everyday examples of chemical reactions include baking bread and combustion.