Fundamentals of Chemistry

This is a mini-book on chemistry, including atomic structure, general chemistry and the theory of reactions, using chemical equations, stoichiometry, Lewis theory, and a brief introduction to quantum chemistry. Topics to be added with time include valence bonding theory, VSEPR theory, and energy changes within reactions.

I owe a debt of gratitude to Professor Steven Tysoe of Rensselaer Polytechnic Institute for his instruction and permission to share this with everyone, and I have tried to ensure there are as few sentences copied verbatim from his lecture materials as possible. There is no need for attribution for redistributing this mini-book in part of in whole, or permission to use them for commercial purposes. In fact, I release it to the public domain (dual licensed with Creative Commons CC0, whichever is more permissive in the given jurisdiction) so that it belongs to everyone. Copy from it, study from it, and give it to others freely and without limits - I would welcome that!

In these notes, there is general information as well as optional asides for more advanced/interested readers that are not important for studying general chemistry. Read the asides only if interested, otherwise, just read the main content.

A high-level introduction to chemistry

Chemistry is the empirical (evidence and experimentally-based) study of the matter and the interactions of matter that analyzes the microscopic properties of matter to describe its macroscopic behavior.

While physics is usually on the scale of generally big life-sized things (projectiles, rockets, trains), very big things (black holes, galaxies, the entire universe even) or very very small things (elementary particles like electrons and quarks), chemistry analyzes things on the scale of atoms and molecules, and up to compounds and materials, that generally form a bigger whole.

Stability (that is, descent to a lower energy state that is more stable) and conservation (quantities that do not change) are essential to chemistry. In addition, the behavior of electrons is essential to understanding chemical interactions. This is because electrons are the mediators of the electromagnetic interaction and therefore responsible for all chemistry (other than nuclear chemistry). Armed with this knowledge, we can explain the rich and diverse landscape of chemistry.

The quantum origins of chemistry

Fundamental chemistry comes from the quantum world that governs matter on the atomic and subatomic scales. Atoms constitute the fundamental building blocks of ordinary matter. Therefore, atoms and the structures they form are the main objects of study in chemistry.

Atoms are not the only important factor in the chemical properties of matter. For instance, graphite and diamond are both composed of carbon atoms, but their differing arrangement of electrons results in greatly different macroscopic properties.

As a high-level overview, matter is anything that occupies space (more technically, a cross-sectional area in which it interacts) and has mass. The structure and composition of matter determines its properties. In addition, the energy present in matter determines its state and structure. Energy is divided into two general types, kinetic energy and potential energy (energy that is stored in some thing and capable of being released). In chemistry, kinetic energy measured macroscopically typically takes the form of thermal energy (heat) and potential energy measured macroscopically typically takes the form of chemical energy.

Note for the advanced reader: Chemical energy, which we can broadly speak of as energy stored in chemical bonds, is actually the sum of the individual electromagnetic potential energies associated with each of the electrons in matter. The results of quantum electrodynamics (a type of quantum field theory) is necessary for a complete description of chemical energy in terms of the energy of the individual electrons that form the total chemical energy we consider in chemistry. Nuclear chemistry in addition extends this to the theories of quantum chromodynamics. This will be explained in an optional section further down but is not necessary for general chemistry or even conventional treatments of the quantum chemistry which simply use the Schrödinger equation and non-relativistic quantum mechanics.

The chemistry lexicon

An intensive property is a characteristic that is intrinsic to a substance, but an extensive property can vary based on how much of the substance there is.

Significant figures are the proper way to record scientific measurement, which involves writing a value in terms of a value and an uncertainty in the form of limited precision, such as $3.57 \pm 0.005\ \pu{kg}$. Significant figures ignore leading zeroes and round after a certain number of digits, truncating the rest and (often) writing an uncertainty to represent the fact that values were omitted.

Accuracy and precision are not identical in chemistry and have specific meanings. Accuracy is how well a measurement can be made to ensure that it is as close as possible to the real value. Precision is a measure of the spread of a measurement.

Units are a prerequisite for doing chemistry. The SI system of measurement is the predominant unit system used in science, but regardless of what unit is used, you should never report a measurement without units (unless if the quantity is dimensionless).

Modern atomic theory

Modern atomic theory regards substances according to three key observations of nature:

Note: the law of the conservation of mass takes a different form in relativistic quantum chemistry, in which case mass and energy may be converted into each other, and mass posseses intrinsic energy.

The chemist John Dalton was one of the originators of atomic theory. He recognized that elements do not magically turn into each other; rather they participate in chemical reactions that change the compounds they form. Chemist J. J. Thomson proved the existence of electrons as particles that are inside of atoms. Rutherford's gold foil experiment found that electrons are negatively charged, and that the nucleus is positively charged. Eventually, it was found that neutral neutrons as well as positively-charged protons made up of the nucleus.

Elements are identified by the atomic number $Z$ which is the number of protons within the atom, as well as the atomic mass $A$ which is the sum of the number of protons and number of neutrons as given in atomic mass units $\pu{amu}$. We therefore notate an element with $\ce{^A_Z S}$ where $S$ is the element name. For instance, $\ce{^4_2 He}$ denotes the helium atom, with an atomic mass of 4 (2 protons and 2 neutrons) and an atomic number of 2 (because of its two protons).

Due to the equal and opposite charges of electrons as compared to protons, there are equal numbers of electrons and protons in a neutral atom, so that atoms are generally electrically neutral and thus stable. However, the same element can have different numbers of neutrons; variations of the same element are called isotopes and are important for nuclear chemistry and nuclear physics. One common example is uranium, which has several well-known isotopes, uranium-238 denoted $\ce{^{238}_{92} U}$, and uranium-235 denoted $\ce{^{235}_{92} U}$.

Periodic table

The periodic table categorizes the properties of all known elements. All elements are represented by a specific chemical symbol, such as $\ce{Cu}$ for copper, $\ce{Fe}$ for iron, and $\ce{C}$ for carbon. The original periodic table was able to predict the properties of 2 then-unknown elements, affirming its success as a theory of the elements. The phenomena that allows the periodic table to exist is called periodicity, where repeating groups of elements share the same chemical properties. This is caused by the arrangement of valence (outermost) electrons, which are the same in elements of the same group. For example, the alkali metals (sodium, potassium, cesium, etc. referred together as group I) all have one valence electron. The underlying reasons behind periodicity, however, must be explained in the quantum behavior of electrons, which will be covered further down.

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