Atomic Structure & Properties

The mole is a fundamental unit in chemistry, representing 6.022 × 10²³ particles. Think of it as a "counting unit" for atoms and molecules, similar to how a dozen means 12 items.

Mass spectrometers analyze elements by showing the relative abundance of isotopes. If you know the percentage of each isotope, you can calculate the average atomic mass and identify the element. In lab work, remember to "zero" your spectrophotometer before measuring absorbances—forgetting this step will result in artificially high readings!

Electron configuration follows a specific pattern related to the periodic table. Valence electrons (those in the outermost energy level) determine chemical properties. Remember that the 4s orbital fills before 3d, even though 3d is considered "inner."

💡 Coulomb's Law explains why elements behave as they do: F = k$q₁q₂/d²$. The greater the charge and the smaller the distance between particles, the stronger the attractive force!

Photoelectron spectroscopy helps visualize electron energy levels. When looking at PES data, remember to label peaks from left to right in increasing energy order (1s, 2s, 2p, etc.), where peak heights correspond to the number of electrons in each sublevel.

Periodic Trends

Periodic trends are predictable patterns that help you understand element properties at a glance. First ionization energy and electronegativity increase toward the top right of the periodic table (think fluorine!), while atomic radius increases toward the bottom left (like cesium).

These trends occur because of two main factors:

• Effective nuclear charge: Elements on the right have more protons pulling electrons inward
• Distance from nucleus: Lower elements have more electron shells, placing valence electrons further from the nucleus

Ion size follows a simple rule: the more positive the charge, the smaller the ion; the more negative, the larger the ion. This makes sense with Coulomb's Law—more protons than electrons means stronger inward pull!

Molecular & Ionic Compound Structure

Ionic bonds form between metals and nonmetals. These compounds:

• Have high melting points
• Are brittle solids
• Conduct electricity when dissolved in solution

Covalent bonds form between nonmetals and come in two types:

• Polar covalent: One atom "hogs" electrons (different electronegativities)
• Nonpolar covalent: Electrons shared equally (similar electronegativities)

🔑 Bond order affects bond strength! Triple bonds (strongest, shortest) > Double bonds > Single bonds (weakest, longest)

Bond strength depends on Coulomb's Law—higher charges create stronger bonds, while larger ion sizes create weaker attractions.

Chemical Bonding Models

Crystal lattices explain why ionic compounds are brittle—when you apply force to the structure, same-charged ions are forced closer together, causing repulsion and breaking.

Metallic bonding involves positive metal ions surrounded by a "sea of electrons." These mobile electrons explain why metals conduct electricity so well. Metal alloys come in two types:

• Substitutional alloys: Similar-sized atoms substitute for each other (brass, bronze)
• Interstitial alloys: Smaller atoms fit between larger ones (steel), increasing hardness

Lewis dot structures help visualize electron arrangements in molecules. Most atoms are stable with eight valence electrons (octet rule), though hydrogen needs only two, and some atoms like sulfur can have an expanded octet.

When multiple valid Lewis structures exist for the same molecule, we call them resonance structures. To determine the most stable structure, calculate the formal charge of each atom using:

Formal charge = (# valence electrons) - (# electrons in Lewis structure)

The most stable molecules usually have formal charges of zero for each atom.

💡 VSEPR Theory predicts molecular shapes based on electron repulsion. The key is counting both bonds AND lone pairs around the central atom!

Hybridization explains bonding in terms of overlapping orbitals:

• 2 regions = sp hybridization (linear, 180°)
• 3 regions = sp² hybridization (trigonal planar, 120°)
• 4 regions = sp³ hybridization (tetrahedral, 109.5°)

Remember that lone pairs take up more space than bonded pairs, causing bond angles to be slightly smaller than expected.

Intermolecular Forces

Molecules interact with each other through three main types of intermolecular forces (IMFs):

1. London dispersion forces (LDF): The weakest force, found in ALL molecules. The more electrons a molecule has, the stronger its LDF. Large molecules with many electrons can have surprisingly strong LDF.

2. Dipole-dipole forces: Moderate strength, occurring between polar molecules where partial charges attract each other.

3. Hydrogen bonding: The strongest IMF, occurring only in molecules with O-H, N-H, or F-H bonds. These special dipole interactions are responsible for water's unique properties.

The stronger the IMF, the higher the boiling point of a substance. This helps explain why different compounds behave differently at the same temperature.

Different solid types have different properties based on their structures:

• Ionic solids: High melting points, brittle, conduct electricity when dissolved
• Covalent network solids: Extremely strong (like diamond), highest melting points
• Molecular solids: Low melting points, weak IMFs (like sugar)

💡 In diamond, each carbon bonds to four others in a 3D network, making it incredibly strong. Graphite, on the other hand, forms sheets held together by weak dispersion forces, which is why it feels slippery and can write on paper!

VSEPR theory helps predict molecular geometry based on electron repulsion. The electrons around a central atom arrange themselves to minimize repulsion, creating specific shapes with predictable bond angles.

States of Matter

Metallic solids have a "sea of electrons" that makes them excellent conductors of electricity and heat. Unlike crystalline solids (which have perfect repeating structures) and amorphous solids (which lack order), metals have free-moving electrons.

The three states of matter differ in particle arrangement and motion:

• Solids: Particles are close together with minimal movement (vibrational only)
• Liquids: Particles can slide past each other but remain close
• Gases: Particles move independently and can expand to fill containers

The Ideal Gas Law $PV = nRT$ helps predict gas behavior. Real gases behave most "ideally" under high temperature and low pressure conditions—where interactions between particles are minimal.

For gas mixtures, remember that Dalton's Law states that the total pressure equals the sum of partial pressures: P_total = P₁ + P₂ + ... + P_n

The Boltzmann distribution shows that at higher temperatures, more gas particles move at higher velocities and have greater kinetic energy.

Solutions are homogeneous mixtures with uniform composition throughout. Their concentration is typically measured as molarity (moles of solute per liter of solution).

🧪 When solving solution problems, remember this key relationship: Moles = Molarity × Liters

The principle "like dissolves like" explains solubility—polar molecules dissolve in polar solvents (water), while nonpolar molecules dissolve in nonpolar solvents (benzene).

Spectroscopy and Analytical Methods

Different regions of the electromagnetic spectrum interact with matter in different ways:

• UV/visible light causes electron transitions
• Infrared radiation causes molecular vibrations
• Microwave radiation causes molecules to rotate

The photoelectric effect relates light's properties using these equations:

• c = λν $speed of light = wavelength × frequency$
• E = hν $energy of a photon = Planck's constant × frequency$

The Beer-Lambert Law $A = εbc$ is crucial for spectroscopy and connects absorbance (A) to concentration (c), path length (b), and molar absorptivity (ε). This allows scientists to determine unknown concentrations using calibration curves.

Chemical Reactions

Chemical changes involve transforming substances by breaking and forming bonds. You can recognize reactions by observing:

• Light production
• Gas formation
• Heat changes
• Color changes
• Precipitate formation

When writing chemical equations, remember to balance them to show conservation of mass. For ionic reactions, you can write net ionic equations by removing spectator ions (those that don't participate in the reaction).

💡 Spectator ions appear in the same form on both sides of the equation, so they can be removed when writing the net ionic equation!

Different reaction types include:

• Acid-base reactions: Transfer of protons (H⁺)
• Redox reactions: Transfer of electrons (OILRIG: Oxidation Is Loss, Reduction Is Gain)
• Precipitation reactions: Formation of insoluble products

Acid-Base Chemistry

The Brønsted-Lowry definition describes acids as proton donors and bases as proton acceptors. When an acid donates a proton, it becomes a conjugate base; when a base accepts a proton, it becomes a conjugate acid.

These pairs have an inverse relationship: the stronger an acid, the weaker its conjugate base. Water is amphoteric—it can act as either an acid or a base depending on what it's reacting with!

Redox reactions involve electron transfers:

• Oxidation: increase in charge (loss of electrons)
• Reduction: decrease in charge (gain of electrons)

Kinetics

Reaction rates depend on several factors:

• Concentration of reactants (usually increases rate)
• Temperature $higher = faster$
• Particle size/surface area $smaller particles = faster$
• Presence of catalysts (speeds up reaction)

Relative rates relate to coefficients in the balanced equation. For example, in 2NO + O₂ → 2NO₂, NO disappears at the same rate NO₂ appears, while O₂ disappears at half that rate.

The rate law shows how concentration affects reaction rate: Rate = k$A$ˣ$B$ʸ

where k is the rate constant, and x and y are the reaction orders.

🔍 To determine reaction order, look at how rate changes when you change concentration. If doubling $A$ doubles the rate, the reaction is first order with respect to A.

The overall order equals the sum of the individual orders $x + y$. Different orders produce different concentration vs. time graphs:

• Zero order: $A$ vs. time gives a straight line down
• First order: ln$A$ vs. time gives a straight line down
• Second order: 1/$A$ vs. time gives a straight line up

Reaction Mechanisms

The collision model explains that for reactions to occur, molecules must:

1. Collide with sufficient energy (≥ activation energy)
2. Have the correct orientation to form new bonds

At higher temperatures, more molecules have enough energy to react when they collide.

Reaction mechanisms show the individual steps a reaction takes. The rate-determining step is the slowest step and controls the overall reaction rate. Reaction intermediates appear in early steps and are used up in later steps (not in the final equation).

A catalyst speeds up a reaction without being consumed. It works by lowering the activation energy, often by providing an alternative reaction pathway. Catalysts are present at both the beginning and end of a reaction.

Energy profiles for multistep reactions have multiple peaks (transition states). The highest peak represents the rate-determining step with the highest activation energy.

Thermodynamics

Endothermic processes absorb heat from surroundings (feel cold to touch), while exothermic processes release heat to surroundings (feel warm to touch). Remember:

• Forming bonds releases heat (exothermic)
• Breaking bonds requires heat (endothermic)

Heat transfer can be calculated using: Q = mcΔT where Q is heat energy, m is mass, c is specific heat capacity, and ΔT is temperature change.

💡 In calorimetry, the heat gained by one system equals the heat lost by another: -Q_{warmer object} = +Q_{cooler object}

During phase changes (melting, freezing, boiling), temperature remains constant as energy is used to change the state rather than increase molecular motion.

Chemical Equilibrium

Many chemical reactions are reversible—they can go in both forward and reverse directions. A reaction reaches equilibrium when the rates of forward and reverse reactions become equal.

The equilibrium constant (K) tells us which direction is favored:

• K > 1: Products are favored
• K < 1: Reactants are favored

The equilibrium expression is written as products over reactants, each raised to the power of their coefficients:

K_c = $C$^c$D$^d/$A$^a$B$^b

Remember that solids and pure liquids are omitted from equilibrium expressions!

When manipulating equilibrium equations:

• Reversing an equation: K = 1/K
• Doubling all coefficients: K = K²
• Adding two equations: K = K₁ × K₂

Le Châtelier's Principle helps predict how equilibrium systems respond to changes:

• Adding a substance shifts away from that substance
• Removing a substance shifts toward that substance
• Decreasing volume shifts toward fewer gas molecules
• Increasing volume shifts toward more gas molecules
• Adding heat to exothermic reactions shifts toward reactants
• Adding heat to endothermic reactions shifts toward products

🔄 To determine which direction a non-equilibrium system will shift, calculate Q and compare to K:

• If Q > K: System shifts left (toward reactants)
• If Q < K: System shifts right (toward products)

Solubility equilibria involve dissolved ions and follow the same principles. The common ion effect decreases solubility when a common ion is already present in solution.

Thermodynamics and Equilibrium

Entropy (S) measures the disorder or randomness in a system. The greater the possible arrangements of a system's components, the higher its entropy.

Generally:

• Solids have the lowest entropy
• Liquids have medium entropy
• Gases have the highest entropy
• Dissolving increases entropy

Gibbs free energy (G) determines whether a process is thermodynamically favorable:

• ΔG < 0: Process is favorable (spontaneous)
• ΔG > 0: Process is unfavorable $non-spontaneous$
• ΔG = 0: System at equilibrium

The equation ΔG = ΔH - TΔS shows that both enthalpy and entropy contribute to favorability:

• ΔH negative (exothermic) and ΔS positive (increasing disorder): Favorable at all temperatures
• ΔH positive (endothermic) and ΔS negative (decreasing disorder): Never favorable
• ΔH positive, ΔS positive: Favorable only at high temperatures
• ΔH negative, ΔS negative: Favorable only at low temperatures

💡 The Gibbs free energy relates to the equilibrium constant: ΔG = -RT ln(K)

• Large K > 1: ΔG negative (favorable)
• Small K < 1: ΔG positive (unfavorable)

Some reactions that are thermodynamically favorable occur extremely slowly due to high activation energy barriers. This is called kinetic control and explains phenomena like the slow rusting of iron.