Introduction to Chemistry: Atoms, Forces, and Energy

CEM 141 – Chapter 1 Notes

This is a condensed set of notes, designed to be augmented with in-class discussions, questions, and specific details from your instructor.

Science is both amazing and often counter-intuitive. Key aspects include that matter is composed of atoms which are mostly empty space, and energy and matter can be considered versions of the same thing. Matter can also exhibit properties of both a particle and a wave. Atoms and molecules frequently interact to produce substances with emergent properties; these properties are different from the sum of their individual component reactants. Furthermore, the properties we observe in "stuff" are determined by its molecular-level structure, and remarkably, collections of cells can form a self-conscious entity.

The Scientific Process

There is no single "scientific method"; instead, science involves a continuous cycle of inquiry. Scientists typically ask questions, design experiments, gather and analyze data and evidence, make claims based on this data, and develop theories to explain how and why the universe behaves as it does.

Scientific questions are those that can be answered by conducting experiments, making observations, or taking measurements. All such activities must be reproducible, meaning if a finding cannot be replicated by others, it is not considered scientific. An example scientific question is: "What temperature will my coffee be if I add milk to it?" This question can be tested experimentally by varying factors such as initial coffee temperature, milk temperature, and milk volume, leading to a prediction or hypothesis about what will happen (e.g., "The coffee will cool down").

Every claim made in science must be supported by evidence, which is derived from experiments. For instance, "The temperature of the coffee/milk mixture was 10^\text{o}\text{C} lower than the temperature of the coffee alone" serves as evidence. With sufficient evidence, a scientific model can be constructed. A scientific model helps us to make sense of phenomena by predicting what will happen under untested, quantifiable conditions (e.g., "The temperature of the coffee/milk mixture depends on the amount of milk added") and explaining how something happens. Models can manifest in various forms, including drawings, graphs, diagrams, equations, or physical/mental constructs.

Scientific Explanations and Theories

Constructing a scientific explanation requires three parts: a claim, which is the specific statement or target of your explanation; evidence, which is the data or scientific principle supporting your claim; and reasoning, which provides the logical connection linking your claim to your evidence.

For example, to explain why coffee cools with milk, the claim is that the coffee cools down because adding cold milk transfers thermal energy from the hot coffee to the colder milk until thermal equilibrium is reached. The evidence is that experiments show the final temperature of the mixture is lower than the initial coffee temperature, and the milk absorbs this energy as its temperature increases, aligning with the principle of conservation of energy and heat transfer. The reasoning is that heat spontaneously flows from a region of higher temperature (hot coffee) to a region of lower temperature (cold milk and the surroundings). As milk molecules gain kinetic energy and coffee molecules lose kinetic energy through collisions, the overall average kinetic energy of the coffee decreases, resulting in a lower observed temperature for the mixture.

A scientific theory is the most robust and well-substantiated explanation of a body of existing evidence, data, and observations. It explains why phenomena occur, makes testable predictions, and is falsifiable (meaning it can be proven false by new experiments or data). Theories may be revised or modified as new evidence becomes available, such as Dalton's atomic theory. In contrast, a scientific law describes the phenomenon itself, telling what happens under certain conditions, often expressed as mathematical statements summarizing observations. An analogy is that a law describes that a ball falls, while a theory explains why it falls (gravity).

To further differentiate, consider these classifications: A fact is an atom of hydrogen having one proton. A law is Newton's Law of Universal Gravitation, stating that the force of attraction between masses is proportional to the product of the masses and inversely proportional to the square of the distance between them (F = G\frac{m1 m2}{r^2}). A hypothesis is the statement, "If we add reagent X to a reaction, it will go faster." A theory is, for instance, the Big Bang Theory. A question would be, "What will happen if we add X to the reaction?"

Atoms

Introduction to Atoms

According to Richard Feynman, the single most important scientific statement is: "All things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling on being squeezed into one another." Surprisingly, only about 5\% of the mass and energy in the Universe appears to be made of atoms or parts of atoms. Regarding what contains atoms, cells, air, and gold all consist of atoms, whereas heat is a form of energy and does not. In terms of relative sizes, cells are larger than molecules, which are larger than atoms. An atom is approximately 0.1 \text{ nanometer } (0.1 \times 10^{-9} \text{ m}) in diameter.

Evidence for the Existence of Atoms

While early atomic theories were philosophical, modern science provides direct evidence for the existence of atoms. We can now "see" atoms using advanced techniques like Atomic Force Microscopy (AFM), which generates images by scanning a sharp probe across a surface and detecting forces between the probe and surface atoms. Scanning Tunneling Microscopy (STM) also uses quantum tunneling to image surfaces at the atomic level.

Development of Atomic Theory

Ancient Greek ideas, notably from Democritus, represent the earliest atomic theory, based on philosophical reasoning rather than experiments. Democritus observed the movement of dust motes in sunlight (macroscopic Brownian motion) and proposed that "atomos" (indivisible particles) were in constant motion with a "void" between them. He believed elements were Earth, Fire, Air, and Water, and proposed that the shape of atoms determined their properties (e.g., cubic for earth), which, while incorrect, foreshadowed the modern idea that molecular structure determines observable properties.

John Dalton's Atomic Theory, proposed in 1808, established several key tenets:

1. Elements are composed of small, indivisible, indestructible particles called atoms (later proven partly false as atoms are divisible into subatomic particles and can be destroyed in nuclear reactions).

2. All atoms of a given element are identical and possess the same mass and properties (later proven false due to isotopes).

3. Atoms of one element differ from atoms of all other elements (still true, defined by the number of protons).

4. Compounds are formed by combinations of atoms of two or more elements in fixed ratios (still true).

5. Chemical reactions involve the rearrangement of atoms, where atoms (matter) are neither created nor destroyed during a reaction. This tenet, representing the Law of Conservation of Mass, still holds true for chemical reactions.

Dalton's theory marked a shift from the Greek idea that atoms determined properties to the assertion that they determined composition.

Elements and Atoms

An atom is defined as the smallest unit of an element. Atoms of different elements are distinguished by their number of protons. There are approximately 91 to 98 naturally occurring elements, systematically organized in the periodic table. The difference between an atom and an element is that an individual atom is a nanoscale entity (e.g., a single gold atom), whereas an elemental substance (e.g., a piece of gold ore) is a macroscopic collection of many atoms of that element, exhibiting very different observable properties.

Atomic Sub-structure: The Discovery of Subatomic Particles

1. The Electron (Discovered by J.J. Thomson, 1906 Nobel Prize)

Evidence for the electron came from cathode ray tube experiments, where a high voltage applied to a low-pressure tube with two electrodes caused a ray of "particles" to be emitted from the cathode. This ray was observed to bend toward a positive electric plate and was deflected by magnetic fields, indicating that the particles carried a negative charge. These particles had a mass approximately 1/2000 that of a hydrogen atom. Crucially, the particles were identical regardless of the metal used for the cathode, leading Thomson to conclude that all atoms contain these negatively charged particles, which he named electrons. Thomson proposed the "Plum Pudding" model, envisioning atoms as a sphere of diffuse positive charge with negatively charged electrons embedded within it, like plums in a pudding or chocolate chips in a cookie.

2. The Nucleus (Discovered by Ernest Rutherford, 1908 Nobel Prize)

Rutherford discovered the nucleus through his famous Gold Foil Experiment. He fired positively charged alpha particles (which are helium nuclei composed of 2 protons and 2 neutrons) at a thin sheet of gold foil. Thomson's "Plum Pudding" model predicted that all alpha particles should pass straight through with only minor deflections. However, Rutherford's observations showed that while most alpha particles passed straight through or were only slightly deflected, a small percentage were deflected at large angles, and a very few even bounced directly back. Rutherford concluded that the atom is mostly empty space and contains a dense, positively charged nucleus at its center, which holds most of its mass. This led to Rutherford's "Planetary Model," proposing that electrons orbit the nucleus like planets around the sun, though this model had a flaw, as orbiting electrons should continuously emit energy and spiral into the nucleus.

3. The Neutron (Discovered 1932)

The neutron was discovered much later than the electron and proton because it carries no electric charge, making it harder to detect. These particles reside within the nucleus and are slightly heavier than a proton.

Modern Atomic Model (Simplified)

The modern atomic model simplifies the atom as being electrically neutral, meaning a neutral atom possesses an equal number of protons and electrons. The nucleus is very small, approximately 2 \times 10^{-15} \text{ m} in diameter, and contains protons (+1 elementary charge, mass 1 \text{ amu}) and neutrons (0 charge, mass 1 \text{ amu}). The electron cloud takes up most of the atom's volume, approximately 20-200 \times 10^{-12} \text{ m} in diameter, and contains electrons (-1 elementary charge, mass \text{approx } 1/1800 \text{ amu}). Thus, electrons contribute negligible mass but are crucial in determining the atom's size and chemical interactions.

Atomic Interactions and Energy

Forces

An interaction is synonymous with a force. There are four fundamental forces in the universe: Gravity, responsible for attraction between objects possessing mass and always attractive; the Electromagnetic Force, which causes attraction and repulsion between objects with electric charge (electrostatic force) and magnetic moments (magnetic force), being the dominant force at the atomic and molecular level; the Strong Nuclear Force, a short-range interaction holding quarks together to form protons and neutrons, and also binding protons and neutrons within the nucleus, overcoming electrical repulsion; and the Weak Nuclear Force, a short-range interaction between elementary particles, weaker than the electromagnetic or strong forces, and involved in radioactive decay.

Gravity (Revisited)

Newton's Law of Universal Gravitation describes what happens: the gravitational force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers. The formula is F = G\frac{m1 m2}{r^2}, where G is the gravitational constant. As the mass of interacting objects increases, the gravitational force increases. Conversely, as the distance between the objects increases, the gravitational force decreases by a factor of 1/r^2, an inverse-square law. Objects with mass create gravitational fields and are affected by them; gravitational forces require two objects and are always attractive.

Electromagnetic (Electrostatic) Force

The electromagnetic force is mediated by electric and magnetic fields, acting at a distance. Our primary focus will be on the electrostatic force between charged particles, which is significantly stronger than gravity. This force can be both attractive (between opposite charges) and repulsive (between like charges). Coulomb's Law describes what happens for electrostatic forces: the electrostatic force (F) between two charged particles is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. Its formula is F = k\frac{q1 q2}{r^2}, where k is Coulomb's constant. Like charges repel, unlike charges attract, and this is also an inverse-square law, similar in form to Newton's law of gravitation. In chemistry, gravitational forces are too weak to be significant at the atomic/molecular level; thus, the electromagnetic (electrostatic) force is paramount for understanding how atoms and molecules interact.

Forces and Equilibrium

If an object is not moving, it means either no forces are acting on it, or the forces acting on it are equal and opposite, meaning they are balanced. For instance, a ball held in your hand experiences both a downward gravitational force and an upward electromagnetic force from your hand, resulting in a net force of zero.

Energy

In physics, there is no simple definition of what energy is, but we know how to calculate its value and understand its crucial property: it is conserved. The Law of Conservation of Energy (First Law of Thermodynamics) states that the total energy of an isolated system remains constant. Energy can be transferred from one object to another or transformed from one type to another (e.g., potential to kinetic), but it is never lost or created. A system is the specific part of the universe being studied for energy changes, while surroundings encompass everything else. The SI unit for energy is the Joule (1 \text{ J} = 1 \text{ kg} \text{ m}^2 \text{ s}^{-2}), with another common unit being the calorie (1 \text{ calorie} = 4.184 \text{ J}). Key principles include that any change in matter is accompanied by a change in energy, and changes in energy are caused by changes in forces.

Types of Energy

Kinetic Energy (KE) is the energy associated with motion, calculated by the formula KE = \frac{1}{2}mv^2, where m is mass and v is velocity. For example, as a ball falls, its speed and thus velocity increase, causing its kinetic energy to increase.

Potential Energy (PE) is energy associated with the position of a system of objects in a field (gravitational, electric, magnetic). It is not stored within a single object but rather in the field connecting two or more objects, therefore requiring two or more objects and a field. When the position of two objects in a field changes, the potential energy of the system changes. For instance, as a ball falls toward the Earth, the potential energy of the ball + Earth system decreases because the attractive gravitational force does work as the distance between the objects decreases. Assuming an isolated system, the total energy (KE + PE) of the ball + Earth system stays the same, as the decrease in potential energy is compensated by an increase in kinetic energy.

Interatomic Interactions: London Dispersion Forces

Why Atoms Stick Together

Atoms are composed of charged particles (protons, electrons), making electrostatic forces crucial for understanding how they interact. Even non-reactive atoms like noble gases (e.g., Helium, with a melting point of 0.95 \text{ K} and boiling point of 4.5 \text{ K}) must have some mechanism to stick together to form solids and liquids at very low temperatures. Reviewing forces, unlike charges attract, while like charges repel. When attraction dominates, potential energy decreases; when repulsion dominates, potential energy increases.

London Dispersion Forces (LDFs)

London Dispersion Forces (LDFs) operate through a specific mechanism: an atom consists of a positively charged nucleus and a "fluffy" negatively charged electron cloud. This electron cloud can momentarily fluctuate, leading to an uneven distribution of charge and creating a temporary, instantaneous dipole. This instantaneous dipole can then induce a dipole in a nearby atom, resulting in a weak, transient attractive electrostatic force between them. These attractions are known as LDFs. LDFs are present between all neutral atoms and molecules in their solid and liquid states (or when they are sufficiently close), and in any system with two or more interacting particles. The strength of LDFs increases with the size of the atom/molecule (specifically, with the number of electrons), as larger electron clouds are more polarizable (more easily distorted) and can form stronger temporary dipoles. LDFs also increase with surface area for molecules, as more points of contact allow for more interactions.

Potential Energy Curves for Atomic Interactions

A potential energy (PE) curve illustrates how the potential energy of a system changes as two atoms approach each other. As two atoms (e.g., Neon) approach, the attractive electrostatic forces (LDFs) between their instantaneous dipoles initially dominate, causing the potential energy to decrease. If the atoms get too close, their electron clouds begin to overlap, and the repulsive electrostatic forces between the negative electron clouds dominate, causing the potential energy to increase sharply.

The PE curve displays several features: the potential minimum (well), which is the lowest point on the curve, represents the most stable internuclear distance (equilibrium distance) where attractive and repulsive forces are optimally balanced (net force = 0). The x-axis position of this minimum indicates the internuclear distance between the atom centers at their most stable point, with larger atoms typically having longer internuclear distances (minimum shifted right). The depth of the potential well signifies the strength of the interaction between the atoms, i.e., how much energy is required to overcome the interaction and separate them.

Regarding dynamics near the potential minimum, atoms in the well oscillate (vibrate) around the equilibrium distance due to their kinetic energy. To form a stable interaction where atoms do not fly apart, excess kinetic energy must be removed from the system, for example, by transfer to a third collision partner. Without such energy removal, the atoms would simply approach, repel, and then separate again.

Thermal Energy and Temperature

Thermal Energy is defined as the sum of the kinetic energies (1/2 mv^2) of all the atoms or molecules within a system. Temperature (T), on the other hand, is directly related to the average kinetic energy (1/2 mv^2) of these atoms or molecules. When thermal energy is added (raising the temperature), energy is transferred to the atoms, typically through collisions with container walls or other directly heated atoms. This increases the atoms' kinetic energy, causing them to move faster. If sufficient kinetic energy is transferred, the atoms can overcome the attractive forces, such as LDFs, and fly apart, leading to a phase change (e.g., melting or boiling).

LDF Strength and Phase Transitions

Comparing Helium (He) and Xenon (Xe) LDFs, Xenon has many more electrons than Helium. Consequently, the electron cloud in Xe is larger and more polarizable, leading to stronger LDFs between Xe atoms compared to He atoms. This impacts intrinsic properties: stronger LDFs demand more energy to overcome, resulting in substances with stronger LDFs having higher melting and boiling points. We can predict that Xenon will have a higher boiling point than Neon because Xe is larger and possesses stronger LDFs. Actual data confirms this, with Helium boiling at 4.5 \text{ K} and Xenon at 165 \text{ K}. For larger atoms like Xe, the PE well would be deeper (indicating stronger interaction) and shifted right (indicating a longer internuclear distance) on a potential energy curve compared to He. The internuclear distance at the potential minimum is related to the Van der Waals radius (radius = 1/2 internuclear distance).

Covalent Bonds versus Intermolecular Forces

Covalent Bonds

When certain atoms, such as Hydrogen (H), approach each other, they are attracted much more strongly than noble gas atoms (He) and form a covalent bond. This process results in the formation of a new chemical species, such as the H2 molecule, which exhibits vastly different chemical and physical properties than the individual atoms. Many elements naturally exist as diatomic molecules (e.g., H2, O2, N2, F2, Cl2, Br2, I2) rather than as discrete atoms, unlike noble gases.

Distinguishing Bonds and Intermolecular Forces (IMFs)

A comparison of potential energy curves reveals that the well for a covalent bond (e.g., H-H) is significantly deeper and often has a shorter internuclear distance compared to the well for IMFs (e.g., He-He LDFs). The key differences are: Intermolecular Forces (IMFs), which include LDFs and other van der Waals interactions, are relatively weak interactions that occur between neutral molecules or atoms, and are responsible for physical properties like melting and boiling points (phase changes). Bonds (e.g., Covalent Bonds), on the other hand, are more permanent and much stronger interactions that occur within molecules, holding atoms together. Breaking bonds requires chemical reactions, not just physical phase changes. Therefore, IMFs and bonds are NOT the same thing.

Energy Changes in Bond Breaking and Formation

Breaking attractive interactions, which includes both bonds and IMFs, necessitates an input of energy into the system, meaning energy is absorbed. This is an endothermic process. Energy is typically transferred into the system through collisions with other molecules, which increase kinetic energy and can overcome these attractive forces. For example, breaking LDFs between He atoms requires relatively low energy (e.g., 14 \text{ K} to boil liquid He), whereas breaking covalent bonds between H atoms requires very high energy (e.g., 6000 \text{ K} to dissociate H_2 molecules into H atoms).

Conversely, forming attractive interactions (bonds and IMFs) releases energy from the system; energy is transferred out. This is an exothermic process. Energy is typically removed from the system through collisions, allowing the particles to settle into a more stable, lower potential energy state.

Hydrogen at Different Temperatures

Understanding hydrogen at various temperatures highlights the distinction between the H2 (hydrogen molecule) and H (hydrogen atom). H2 molecules interact with each other via LDFs (IMFs), while the two H atoms within an H_2 molecule are held together by a strong covalent bond.

At 5 \text{ K} (Solid Hydrogen), H2 molecules are closely packed in an ordered, rigid structure. Strong covalent bonds exist within each H2 molecule, and significant London Dispersion Forces exist between H_2 molecules, holding them in the solid lattice.

At 15 \text{ K} (Liquid Hydrogen), H2 molecules remain closely packed but are arranged in a disordered, fluid manner. Strong covalent bonds stay intact within each H2 molecule, and London Dispersion Forces are still present between H_2 molecules, but with enough kinetic energy to allow them to move past one another (LDFs are being broken and reformed).

At 30 \text{ K} (Gaseous Hydrogen), H2 molecules are far apart and move randomly, with minimal interactions. Strong covalent bonds remain intact within each H2 molecule. However, the LDFs between H_2 molecules have been overcome by kinetic energy, meaning molecules are no longer sticking together significantly (this constitutes a phase change: boiling).

At >6000 \text{ K} (Atomic Hydrogen), individual Hydrogen atoms (H) exist. The strong covalent bonds within H_2 molecules have been broken due to the extremely high kinetic energy supplied (this is a chemical reaction: dissociation). In this state, there are no LDFs between H atoms, as they are too energetic to form stable interactions.

Summary of Energy and Interactions

In summary, phase changes such as melting and boiling involve overcoming relatively weak intermolecular forces (IMFs), requiring less energy. In contrast, chemical reactions, like the dissociation of H2 into H atoms, involve breaking much stronger covalent bonds, which demand significantly more energy. This explains why the boiling point of H2 is 20 \text{ K}, but it takes over 6000 \text{ K} to break the H_2 covalent bond.