The foundation of chemistry relies on precise measurements and understanding significant figures. When conducting measurements, accuracy refers to how close a value is to the accepted value, while precision indicates how close repeated measurements are to each other. A critical formula in determining measurement accuracy is percent error = $experimental - true$ / true × 100.

Proper measurement techniques require recording one decimal place beyond the smallest marked increment on measuring tools. For volume measurements, graduated cylinders provide the most accurate results compared to beakers or flasks. Temperature measurements in chemistry utilize Celsius or Kelvin scales exclusively.

Significant figures represent measurement precision through specific rules. All nonzero integers are always significant, while zeros follow three classifications: leading zeros $never significant$, captive zeros $always significant$, and trailing zeros $significant only with decimal points$. When performing calculations, multiplication and division results should have the same number of significant figures as the least precise measurement, while addition and subtraction results are limited by the least number of decimal places.

Definition: Significant figures are digits in a number that carry meaning and represent the precision of a measurement.

Laws of definite and multiple proportions form fundamental principles in chemistry. The law of definite proportions states that compounds always contain elements in fixed mass ratios. The law of multiple proportions explains that when elements form multiple compounds, the mass ratios of these elements will be small whole numbers.

Matter classification involves understanding different types of mixtures and pure substances. Heterogeneous mixtures show visible boundaries between components, while homogeneous solutions appear uniform throughout. Various separation techniques exist for mixtures:

• Decanting separates solids from liquids
• Filtration separates particles of different sizes
• Chromatography separates components based on absorption rates
• Distillation separates liquids with different boiling points

Example: In water $H₂O$, hydrogen and oxygen always combine in a 1:8 mass ratio, demonstrating the law of definite proportions.

The modern understanding of atomic structure evolved through numerous scientific discoveries. Dalton's atomic theory proposed indivisible atoms, while Thomson's cathode ray experiments revealed electrons. Rutherford's gold foil experiment demonstrated the nucleus's existence, and Bohr introduced electron energy levels.

Atomic structure fundamentals include:

• Atomic number equals proton count
• Mass number represents total protons and neutrons
• Isotopes differ in neutron count but maintain identical chemical properties

Highlight: The stability of atomic nuclei depends on the neutron-to-proton ratio, with heavier elements requiring more neutrons for stability.

Nuclear chemistry explores atomic nucleus changes through radioactive decay and nuclear reactions. Different types of radiation include alpha particles $helium nuclei$, beta particles $electrons or positrons$, and gamma rays $electromagnetic radiation$.

Radioactive decay processes follow predictable patterns measured by half-life, which is the time required for half of a radioactive sample to decay. The equation m$remaining$ = m$initial$$0.5$^n calculates remaining mass after n half-lives.

Nuclear reactions include:

• Fission: splitting heavy nuclei
• Fusion: combining light nuclei
• Transmutation: converting one element to another

Vocabulary: Radioisotopes are unstable atomic nuclei that undergo spontaneous decay to achieve stability.

The quantum mechanical model explains how electrons behave within atoms, providing crucial insights into atomic structure and chemical bonding. Electrons exist in specific energy levels around the nucleus, never occupying the space between levels. When electrons absorb energy, they become excited and jump to higher energy states. Upon returning to their ground state, they release energy in the form of light with specific wavelengths.

Definition: Quantum theory describes energy as discrete packets called photons that exhibit both wave and particle properties. This wave-particle duality applies to both light and electrons, as demonstrated by the Heisenberg Uncertainty Principle.

The arrangement of electrons follows specific rules governed by quantum numbers. Electron orbitals represent probability regions where electrons are likely found, organized into energy levels $1-7$ and sublevels $s, p, d, f$. Each orbital can hold a maximum of two electrons with opposite spins, following the Pauli Exclusion Principle. The Aufbau Principle dictates that electrons fill lower energy levels first, while Hund's Rule states that electrons in orbitals of the same energy must be unpaired before pairing begins.

Valence electrons, found in the outermost shell, are particularly important as they participate in chemical bonding. These electrons determine an atom's chemical properties and how it forms ionic or covalent bonds. Understanding electron configuration helps predict chemical behavior and explains periodic trends. For transition metals, multiple oxidation states are possible due to their unique electron arrangements in d-orbitals.

Atomic properties follow systematic trends across the periodic table, providing valuable insights into chemical behavior. Atomic radius generally decreases across periods due to increasing nuclear charge, while it increases down groups as additional electron shells are added. The shielding effect, described by effective nuclear charge $Zeff$, influences these trends by reducing the attraction between outer electrons and the nucleus.

Highlight: Electronegativity, the tendency to attract electrons in bonds, generally increases across periods and decreases down groups. Fluorine is the most electronegative element due to its small size and high nuclear charge.

Ionization energy, the energy required to remove an electron, shows interesting patterns and exceptions. It typically increases across periods and decreases down groups. Notable exceptions occur with magnesium $due to its full subshell$ and phosphorus $due to half-filled p orbitals$, which show unexpectedly high ionization energies. Subsequent ionizations require progressively more energy, with sharp increases when removing core electrons.

Physical properties like melting points, boiling points, and density also follow periodic trends. Metals generally become more reactive down groups but less reactive across periods, while nonmetals show opposite trends. These patterns arise from electronic structure and help predict chemical behavior and reactivity patterns.

Understanding chemical bonding requires knowledge of both ionic and covalent interactions. Ionic bonds form between metals and nonmetals through electron transfer, creating charged particles called ions. These compounds form crystal lattices with high melting and boiling points, and conduct electricity when dissolved in water as electrolytes.

Example: In Fe₂O₃ $iron(III$ oxide), iron loses electrons to become Fe³⁺ while oxygen gains electrons to become O²⁻, forming a stable ionic compound through charge balance.

Covalent bonds form between nonmetals through electron sharing, creating molecular compounds with distinct properties. These compounds typically have lower melting and boiling points than ionic compounds and don't conduct electricity. The strength and characteristics of covalent bonds depend on electronegativity differences between atoms and the number of shared electron pairs.

Lewis structures help visualize electron arrangements in molecules, following the octet rule for main group elements. Some elements can violate this rule, particularly those in period 3 and below. VSEPR theory predicts molecular geometry based on electron domain arrangements, considering both bonding and nonbonding electron pairs. These geometric arrangements influence molecular polarity and chemical reactivity.

Chemical reactions involve the rearrangement of atoms to form new substances, following the law of conservation of mass. Different types of reactions include synthesis, decomposition, single replacement, double replacement, and combustion. Each type follows specific patterns and can be predicted using activity series and solubility rules.

Vocabulary: Redox reactions involve electron transfer, where oxidation represents electron loss $increase in oxidation number$ and reduction represents electron gain $decrease in oxidation number$.

Net ionic equations show the essential components of reactions by removing spectator ions that don't participate in the chemical change. Understanding oxidation numbers helps identify redox reactions and determine oxidizing and reducing agents. The substance being reduced acts as the oxidizing agent, while the substance being oxidized serves as the reducing agent.

Energy changes in reactions involve both bond breaking $endothermic$ and bond formation $exothermic$. The overall energy change depends on the balance between these processes. Endothermic reactions absorb energy from the surroundings, while exothermic reactions release energy. Reversible reactions demonstrate how one direction can be endothermic while the reverse is exothermic, highlighting the relationship between reaction direction and energy changes.

The foundation of chemical calculations lies in stoichiometry, which governs the quantitative relationships between reactants and products in chemical reactions. This essential concept helps chemists predict reaction outcomes and optimize industrial processes.

Definition: Stoichiometry is the mathematical study of the mass relationships between reactants and products in a chemical reaction, based on balanced equations and mole ratios.

Understanding limiting reactants is crucial for accurately predicting reaction yields. When two or more reactants are present, the limiting reactant determines the maximum amount of product that can form. Consider the reaction between sodium and chlorine gas: 2Na + Cl₂ → 2NaCl. If we have 79.1g Na and 158.0g Cl₂, we must calculate which reactant limits product formation.

Let's break down the process of identifying limiting reactants:

1. Convert all given masses to moles
2. Compare the molar ratios from the balanced equation
3. Calculate theoretical yield from each reactant
4. The smaller yield indicates the limiting reactant

Example: In the sodium chloride formation reaction:

• From Na: 79.1g Na × $1 mol Na/23.0g$ × $2 mol NaCl/2 mol Na$ × $58.44g NaCl/1 mol NaCl$ = 201g NaCl
• From Cl₂: 158.0g Cl₂ × $1 mol Cl₂/70.9g$ × $2 mol NaCl/1 mol Cl₂$ × $58.44g NaCl/1 mol NaCl$ = 260g NaCl

When working with limiting reactants, determining the amount of excess reactant remaining is equally important. Two methods can be used to calculate excess reactant quantities, providing valuable information for reaction optimization and cost analysis.

Highlight: Percent yield compares actual experimental results to theoretical calculations using the formula: $actual yield/theoretical yield$ × 100

The first method for calculating excess reactant involves:

1. Calculate theoretical yield from limiting reactant
2. Subtract this from the initial amount of excess reactant
3. Convert the difference back to grams of excess reactant

Example: Consider the reaction CaCO₃ + 2HCl → CO₂ + CaCl₂ + H₂O With 3.00g CaCO₃ and 0.100 mol HCl:

1. Calculate limiting reactant yields
2. Determine excess HCl remaining
3. Final calculation shows 1.46g HCl excess

This comprehensive understanding of stoichiometry, limiting reactants, and excess calculations is fundamental for honors chemistry final exam preparation and practical laboratory work. These concepts form the backbone of quantitative chemistry and are essential for honors chemistry semester 1 final exam success.