Chemistry Lecture Notes: Chemical Formulas, Species, and Isotopes

Introduction to Chemical Formulas and Sulphuric Acid

Sulphuric acid, historically known as Oil of Vitriol, is represented by the chemical formula $H_2SO_4$. In chemistry, a chemical formula is defined as a description of the composition of a compound in terms of the symbols of the constituent elements present in one formula unit or molecule, as well as the specific ratio between them.

A chemical formula provides two primary pieces of information regarding the composition of a compound. First, it identifies the constituent elements that make up the substance. Second, it specifies the ratio between these elements in one formula unit. For example, the chemical formula for water, $H_2O$, reveals that a single molecule of water is composed of hydrogen ($H$) and oxygen ($O$) in a ratio of $2:1$.

The Criss-Cross Method for Writing Chemical Formulas

The Criss-Cross method is a systematic process used to determine the chemical formula of a compound based on the valencies of its constituent elements. The procedure consists of four foundational steps. In Step 1, the symbols of the elements are written down. In Step 2, the valencies of the elements are written beneath or beside the symbols. In Step 3, the valencies are swapped between the elements and, if possible, reduced to the lowest whole-number ratio. Finally, in Step 4, the chemical formula is written with the appropriate subscripts.

Specific examples of this method include the formation of Boron oxide, where the symbols are $B$ and $O$. The valencies are $3$ and $2$ respectively; after swapping, the chemical formula becomes $B_2O_3$. In the case of Ammonia, the symbols are $N$ and $H$ with valencies of $3$ and $1$, resulting in $NH_3$. For water, symbols are $H$ and $O$ with valencies of $1$ and $2$, leading to the formula $H_2O$. Another example provided is phosphorous trichloride, $PCl_3$.

Classification of Chemical Formulas

Chemical formulas are classified into two distinct types: Molecular Formula and Empirical Formula. A Molecular Formula describes the composition of one molecule or formula unit of a compound in terms of its actual ratio of atoms. Conversely, an Empirical Formula, also known as the simplest or experimental formula, describes the composition of one molecule or formula unit in terms of the simplest ratio of its atoms.

A classic example of the conversion from a molecular formula to an empirical formula is glucose. The molecular formula for glucose is $C_6H_{12}O_6$. By reducing the actual ratio ($6:12:6$) to the simplest whole-number ratio ($1:2:1$), the empirical formula is derived as $CH_2O$.

Comparative Analysis of Elements, Compounds, and Mixtures

Chemistry distinguishes between elements, compounds, and mixtures based on several characteristic properties. An element is a pure substance made up of the same types of atoms. It is represented by a symbol and constitutes the simplest form of matter. Elements exhibit unique properties of their constituent atoms, cannot be decomposed into simpler substances by ordinary means, and are generally homogenous with sharp, fixed melting points.

A compound is a pure substance made up of the same molecules or formula units resulting from the chemical combination of different elements. It is represented by a chemical formula and exhibits unique properties that differ from its component elements. The components of a compound cannot be separated by physical means. Compounds are homogenous and, like elements, possess sharp and fixed melting points.

A mixture is an impure substance formed by the physical combination of different substances without a fixed formula. It shows the properties of all its individual components. The components of a mixture can be separated by physical means. Mixtures may be either homogenous or heterogeneous and do not possess sharp or fixed melting points.

Classification of Chemical Species

A chemical species is defined as an atom or a group of atoms that undergoes a chemical reaction. These species are classified into three main categories: Free Radicals, Molecules, and Ions.

Free Radicals are atoms or groups of atoms having an incomplete octet or duplet. Defined as a neutral species with unpaired valence electrons, they are represented by putting a dot over the symbol of the element. Because of these unpaired electrons, free radicals are highly reactive as they seek to complete their octet or duplet. Examples include the Hydrogen atom ($H^{\cdot}$), Chlorine atom ($Cl^{\cdot}$), and Methylene radical ($CH_3^{\cdot}$). They are formed by the homolytic bond cleavage of a molecule, such as $H-Cl \rightarrow H^{\cdot} + Cl^{\cdot}$. Free radicals are unstable units, can exist independently, and are always electrically neutral (where the number of protons equals the number of electrons).

Molecules are atoms or groups of atoms having a complete octet or duplet. A molecule is a neutral species where all valence electrons are paired. Due to this pairing, molecules typically do not undergo immediate chemical reactions and show stability under normal conditions. Examples include the diatomic hydrogen molecule ($H-H$), oxygen molecule ($O=O$), and nitrogen molecule ($N \equiv N$).

Ions are atoms or groups of atoms that carry a positive or negative charge. They are the building units of ionic compounds and are relatively stable compared to free radicals. Unlike free radicals, a single positive or negative ion cannot exist independently. Ions are formed by heterolytic bond cleavage, such as $HCl \rightarrow H^+ + Cl^-$. For any ion, the number of protons is not equal to the number of electrons ($No.\,of\,p^+ \neq No.\,of\,e^-$).

Detailed Study of Ions: Cations and Anions

Ions are further classified by the nature of their charge and the number of atoms they contain. Cations are atoms or groups of atoms with a positive charge. They are typically formed when a metal atom loses one or more electrons (a process called oxidation) to achieve a stable octet or duplet. For example, a Sodium atom ($Na$) loses an electron to become a Sodium cation ($Na^+$). Common examples include $H^+$, $Li^+$, $Na^+$, $K^+$, $Mg^{2+}$, $Ca^{2+}$, $Cu^{2+}$, $Fe^{3+}$, and molecular cations like $H_3O^+$ and $NH_4^+$.

Anions are atoms or groups of atoms with a negative charge. They are formed when non-metal atoms gain electrons (a process called reduction) to complete their octet or duplet. For example, a Chlorine atom ($Cl$) gains an electron to become a Chloride anion ($Cl^-$). Examples include $Cl^-$, $Br^-$, $O^{2-}$, $S^{2-}$, $N^{3-}$, and molecular anions like $NO_2^-$, $NO_3^-$, $CO_3^{2-}$, and $SO_4^{2-}$.

Ions are also classified by the number of atoms they contain. Simple ions are composed of a single atom carrying a charge (e.g., $Na^+$, $Cl^-$). Molecular ions, or polyatomic ions, consist of a group of atoms carrying a net charge. These are created when a molecule loses or gains electrons. Anionic molecular ions carry a negative charge (e.g., $SO_4^{2-}$), while cationic molecular ions carry a positive charge (e.g., $NH_4^+$).

Classification of Molecules

Molecules can be classified based on the number of atoms or the nature of the atoms they contain. Based on the number of atoms, they are categorized as Monoatomic (one atom), Diatomic (two atoms), Triatomic (three atoms), or Polyatomic (many atoms). Based on the nature of the atoms, they are categorized as Homoatomic (composed of the same type of atoms) or Heteroatomic (composed of different types of atoms).

Isotopes and Atomic Structure

Isotopes are defined as atoms of the same element that have the same number of protons (and thus the same atomic number) but a different number of neutrons (and thus different mass numbers). The term "Iso" means same, and "Tope" means place or position, referring to their same position on the periodic table.

Hydrogen has three isotopes: Protium ($^1H$), Deuterium ($^2H$), and Tritium ($^3H$). All three have an atomic number ($Z$) of $1$, but their mass numbers ($A$) are $1$, $2$, and $3$ respectively, with neutron counts of $0$, $1$, and $2$. Carbon has three isotopes: $^{12}C$, $^{13}C$, and $^{14}C$, with neutron counts of $6$, $7$, and $8$. Oxygen isotopes include $^{16}O$, $^{17}O$, and $^{18}O$. Uranium isotopes include $^{234}U$, $^{235}U$, and $^{238}U$ with neutron counts of $142$, $143$, and $146$. Chlorine has two main isotopes: $^{35}Cl$ (18 neutrons) and $^{37}Cl$ (20 neutrons).

To justify the definition of isotopes using Chlorine as an example: both $^{35}Cl$ and $^{37}Cl$ have $17$ protons and $17$ electrons, meaning they have the same atomic number ($Z = 17$). However, their mass numbers differ because $^{35}Cl$ has $18$ neutrons while $^{37}Cl$ has $20$ neutrons.

Quantitative Atomic Definitions and Isotope Applications

The Atomic Number ($Z$) is the total number of protons in the nucleus of an atom, also known as the Proton Number. The Mass Number ($A$) is the total number of protons and neutrons in the nucleus, also known as the Nucleon Number. The number of neutrons ($N$) can be calculated using the formula $N = A - Z$. For an atom with $A = 40$ and $Z = 20$, the number of protons is $20$ and the number of neutrons is $20$ ($40 - 20 = 20$).

Atomic Mass is the mass of one atom of an element compared to the 1/12th part by mass of the carbon-12 isotope, measured in atomic mass units ($a.m.u.$). Gram Atomic Mass (or 1 gram atom/1 mole) is the atomic mass of an element expressed in grams. It represents the mass of Avogadro's number of atoms ($6.02 \times 10^{23}$ atoms). For example, the gram atomic mass of Hydrogen is $1\,g$, Carbon is $12\,g$, and Oxygen is $16\,g$.

Radioactive isotopes have numerous applications across various fields. In radiotherapy, Phosphorus-32 and Strontium-90 are used for the treatment of skin cancer, while Cobalt-60 is used for body cancer due to its high penetrating power. Iodine isotopes are utilized for the detection of thyroid glands in the neck. Technetium is used to monitor bone growth in fracture healing. In medical instrumentation, Gamma rays from Cobalt-60 are used for the sterilization of medical instruments and dressings. In industry, Americium is used in safety measures such as smoke detectors, backscatter gauges, and for measuring the ash content of coal.