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Definition: The Latin-speaking half of the Roman Empire, centered in Rome. Flashcard #2  Term: Eastern Roman Empire  Definition: The Greek-speaking half of the Roman Empire, also known as the Byzantine Empire, centered in Constantinople. Flashcard #3  Term: Catacombs  Definition: Underground burial chambers where early Christians worshipped privately due to persecution. Flashcard #4  Term: Appropriation  Definition: Using existing imagery or symbols in a new context, a common practice in early Christianity. Flashcard #5  Term: Orant figure  Definition: A standing figure with arms raised in prayer, derived from Roman gestures of duty. Flashcard #6  Term: Ichthys (fish)  Definition: A Christian symbol for Jesus Christ, Son of God. Flashcard #7  Term: Good Shepherd  Definition: A depiction of Jesus as a caring, protective, and pastoral caretaker, adapted from Roman pastoral scenes. Flashcard #8  Term: Cubicula  Definition: Mortuary chapels or rooms within catacombs used for small services. Flashcard #9  Term: Loculi  Definition: Shelves carved into catacomb walls for individual burials. Flashcard #10  Term: Wet plaster fresco (fresco buon)  Definition: A painting technique where pigment is applied to wet plaster. Flashcard #11  Term: Domus (community house)  Definition: Private homes converted for use as early Christian worship spaces. Flashcard #12  Term: Familia  Definition: A Roman core value emphasizing family loyalty. Flashcard #13  Term: Pietas  Definition: A Roman core value emphasizing duty to the state and gods. Flashcard #14  Term: Contra-posto  Definition: A naturalistic standing pose used in Roman art, where the body's weight is shifted to one leg. Flashcard #15  Term: Prefiguration  Definition: An Old Testament story or figure that foreshadows a New Testament event or figure. Flashcard #16  Term: Constantine  Definition: Roman Emperor (reigned 312–337 CE) who legalized Christianity and initiated widespread Christian architectural patronage. Flashcard #17  Term: Old St. Peter’s Basilica  Definition: An early Christian basilica built in Rome under Constantine over St. Peter’s tomb, serving as a pilgrimage site. Flashcard #18  Term: Basilican/Cross Plan  Definition: A Western church architectural plan characterized by a long nave, side aisles, transept forming a cross, and an apse. Flashcard #19  Term: Santa Sabina  Definition: A smaller, well-preserved example of a Western early Christian basilica in Rome. Flashcard #20  Term: Santa Costanza  Definition: Originally a royal mausoleum, later converted into a central-plan church, circular with a dome and ambulatory, showing Eastern influence in the West. Flashcard #21  Term: Atrium (Old St. Peter's)  Definition: The open courtyard leading into the narthex of Old St. Peter’s Basilica. Flashcard #22  Term: Narthex (Old St. Peter's)  Definition: The entrance hall or porch leading to the nave of Old St. Peter’s Basilica. Flashcard #23  Term: Nave (Old St. Peter's)  Definition: The central, main aisle of Old St. Peter's Basilica, accommodating the congregation. Flashcard #24  Term: Transept (Old St. Peter's)  Definition: The arm of the church that projects at right angles to the nave, forming the 'cross' in a cruciform plan, providing space for clergy. Flashcard #25  Term: Apse (Old St. Peter's)  Definition: A semicircular recession at the eastern end of the church, containing the altar. Flashcard #26  Term: Justinian I  Definition: Byzantine Emperor (527–565 CE) who expanded the empire, promoted Christianity, and commissioned major churches like Hagia Sophia and San Vitale. Flashcard #27  Term: Trinity  Definition: The Christian concept of God as Father, Son (Jesus), and Holy Spirit. Flashcard #28  Term: Nimubs  Definition: A halo around the head of a holy figure in art. Flashcard #29  Term: Mandorla  Definition: An almond-shaped aura surrounding the full-body depiction of Christ or other sacred figures, signifying divinity. Flashcard #30  Term: Icon  Definition: A religious image, often painted on wood, used in devotion, particularly in Eastern Christianity. Flashcard #31  Term: Iconoclasm  Definition: The deliberate destruction of religious images, notably during the Byzantine controversy of 726+ CE. Flashcard #32  Term: Dematerialization (Byzantine art)  Definition: An artistic and architectural goal in Byzantine art to create a divine space that transcends material reality, often achieved with light and shimmering mosaics. Flashcard #33  Term: Tesserae  Definition: Small pieces of glass, stone, or other material used to create a mosaic. Flashcard #34  Term: Hagia Sophia  Definition: Meaning 'Holy Wisdom,' a monumental Byzantine church in Istanbul built by Justinian (532–537 CE), known for synthesizing basilican and central plans with its massive dome. Flashcard #35  Term: Pendentives  Definition: Spherical triangular sections that transfer the weight of a circular dome to four piers or columns, allowing for a large, open space below. Flashcard #36  Term: San Vitale  Definition: An octagonal, central-plan Byzantine church in Ravenna, famous for its lavish mosaics depicting Emperor Justinian and Empress Theodora. Flashcard #37  Term: Muhammad  Definition: The prophet of Islam (571–632 CE) who received revelations from Allah, forming the basis of the Qur’an. Flashcard #38  Term: Qur’an  Definition: The holy book of Islam, believed to be the literal word of God (Allah) revealed to Muhammad. Flashcard #39  Term: Calligraphy (Islam)  Definition: The art of beautiful writing, highly esteemed in Islamic culture as a manifestation of Allah's word. Flashcard #40  Term: Five Pillars of Islam  Definition: The fundamental practices of Islam: Shahada (faith), Salah (prayer), Sawm (fasting), Zakat (charity), Hajj (pilgrimage). Flashcard #41  Term: Geometric abstraction (Islamic art)  Definition: Complex patterns based on numbers and mathematics, developed in Islamic art due to the general avoidance of sentient figural imagery in religious contexts. Flashcard #42  Term: Tessellation  Definition: The repeating of geometric units to form an intricate pattern without gaps or overlaps, common in Islamic art to suggest eternity. Flashcard #43  Term: Symmetry (Islamic art)  Definition: The use of balanced proportions (e.g., fourfold, fivefold, sixfold) in geometric patterns to create visual harmony. Flashcard #44  Term: Masjid  Definition: An Arabic term meaning 'place of prostration,' referring to a mosque. Flashcard #45  Term: Minaret  Definition: A tall, slender tower, typically part of a mosque, from which the call to prayer (adhan) is issued. Flashcard #46  Term: Qibla wall  Definition: The wall in a mosque that faces the direction of the Kaaba in Mecca, which Muslims face during prayer. Flashcard #47  Term: Mihrab  Definition: A niche or recess in the qibla wall of a mosque, indicating the direction of prayer. Flashcard #48  Term: Dome of the Rock  Definition: Built 687–692 CE in Jerusalem, it is one of the earliest major Islamic monuments, an octagonal central-plan building sacred to Jews, Christians, and Muslims. Flashcard #49  Term: Horror vacui (Islamic art)  Definition: A design principle characterized by the filling of an entire surface with details and decoration, often seen in the Dome of the Rock's exterior. Flashcard #50  Term: Great Mosque of Córdoba  Definition: A significant example of Islamic architecture in Spain, featuring a massive hypostyle prayer hall with reused Roman columns and a distinctive double-arched system. Flashcard #51  Term: Siddhartha Gautama  Definition: The historical Buddha (5th century BCE) who founded Buddhism after renouncing luxury to seek an end to human suffering. Flashcard #52  Term: Four Noble Truths  Definition: The core teachings of Buddhism: 1. Life is suffering. 2. Suffering is caused by desire and ignorance. 3. Ending desire ends suffering. 4. The way to end suffering is to follow the Eightfold Path. Flashcard #53  Term: Eightfold Path  Definition: The Buddhist path to liberation from suffering, comprising right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, and right concentration. Flashcard #54  Term: Stupa  Definition: A hemispherical mound or reliquary housing Buddha's relics, symbolizing the cosmos (mandala), used as a pilgrimage site for circumambulation. Flashcard #55  Term: Circumambulation  Definition: The ritual act of walking around a sacred object, such as a stupa or shrine, in a clockwise direction as a form of devotion. Flashcard #56  Term: Toranas  Definition: Elaborately carved gateways at the entrances to a stupa, decorated with narrative scenes and symbolic representations of the Buddha. Flashcard #57  Term: Yakshi Figures  Definition: Female nature spirits associated with fertility, abundance, and life force, often shown in a sensuous tribhanga pose at stupa gateways. Flashcard #58  Term: Tribhanga pose  Definition: A triple-bent pose (at the neck, waist, and knee) often used in ancient Indian sculpture, especially for female figures like Yakshi. Flashcard #59  Term: Chaitya Halls  Definition: Rock-cut sanctuaries and congregation halls in Buddhist cave architecture, often containing stupa replicas, used for worship and by monks during monsoons. Flashcard #60  Term: Mudras  Definition: Symbolic hand gestures of the Buddha that convey specific meanings or states of mind in Buddhist iconography. Flashcard #61  Term: Mandala (Tibetan Buddhism)  Definition: A diagram of the universe, often intricately designed, used as a tool for meditation and ritual in Tibetan Buddhism. Flashcard #62  Term: Ottonian Period  Definition: A period in European art and architecture from c. 950–1050 CE, primarily in present-day Germany, marked by a continuation of Carolingian ideals and increased church building. Flashcard #63  Term: St. Michael’s, Hildesheim  Definition: A key Ottonian basilica plan church known for its double transept, strong symmetry, and wooden roof which posed a fire risk. Flashcard #64  Term: Codex  Definition: The modern book form, consisting of folded and bound pages, which replaced scrolls by the 5th–6th century CE and allowed for easier navigation of texts. Flashcard #65  Term: Migration Period  Definition: A period in Western Europe (c. 500–700 CE), formerly called the 'Dark Ages,' characterized by political decentralization, nomadic societies, and art primarily consisting of small, portable luxury objects. Flashcard #66  Term: Zoomorphic motifs  Definition: Stylized animal forms and designs, common in the metalwork and art of the Migration Period. Flashcard #67  Term: Cloisonné technique  Definition: An enameling technique where colored glass, enamel, or gemstones are separated by thin metal strips (cloisons) on a metal backing, seen in Migration Period jewelry. Flashcard #68  Term: Monasteries (Early Middle Ages)  Definition: Centers of learning, economic activity, and safe havens during the instability of the Early Middle Ages. Flashcard #69  Term: Illuminated Manuscripts  Definition: Hand-copied books, often religious texts, adorned with intricate decorations, illustrations, and ornamental initials by monks in scriptoria. Flashcard #70  Term: Vellum  Definition: A fine parchment made from calf or sheep skin, commonly used as pages for illuminated manuscripts. Flashcard #71  Term: Carpet pages  Definition: Purely decorative pages in illuminated manuscripts, often resembling textiles, used for meditation before reading the text (e.g., Lindisfarne Gospels). Flashcard #72  Term: Romanesque Period  Definition: An architectural and artistic style (c. 1050–1200 CE) meaning 'Roman-like,' characterized by a revival of large-scale stone construction, round arches, and barrel/groin vaults. Flashcard #73  Term: Crusades  Definition: A series of religious wars (1096–1204 CE) promoted by Pope Urban II, which led to increased East-West interaction and the recovery of ancient Roman knowledge in Western Europe. Flashcard #74  Term: Pilgrimage (Romanesque)  Definition: An act of devotion, healing, or penance involving travel to sacred sites like Santiago de Compostela, a driving force behind Romanesque church construction. Flashcard #75  Term: Relics  Definition: Body parts, clothing, or other objects associated with saints, believed to possess healing or miraculous powers, central to Romanesque pilgrimage. Flashcard #76  Term: Reliquaries  Definition: Elaborately crafted containers, often made of precious materials, designed to house and display relics. Flashcard #77  Term: Church of Saint-Sernin, Toulouse  Definition: An important Romanesque pilgrimage church (c. 1070–1120) known for its early stone vaulting and plan designed to accommodate large numbers of pilgrims. Flashcard #78  Term: Crossing square  Definition: The square space at the intersection of the nave and transept in a Romanesque church, which often served as the basic geometric unit for the church's proportions. Flashcard #79  Term: Ambulatory (Romanesque)  Definition: A walkway or aisle around the apse and altar of a Romanesque church, allowing pilgrims to circulate and visit radiating chapels without disturbing services. Flashcard #80  Term: Radiating chapels  Definition: Small chapels projecting outward from the ambulatory of a Romanesque church, designed to house relics. Flashcard #81  Term: Chevet (Romanesque)  Definition: The extended eastern end of a Romanesque church, comprising the apse, ambulatory, and radiating chapels. Flashcard #82  Term: Barrel-vaulted nave  Definition: A long, continuous semicircular vaulted ceiling over the nave, characteristic of many Romanesque churches. Flashcard #83  Term: Transverse arches  Definition: Arches that span the nave at regular intervals, reinforcing the barrel vaulting and dividing the nave into bays. Flashcard #84  Term: Massive stone piers  Definition: Large, solid columns or supports used in Romanesque architecture to bear the heavy weight of stone vaults. Flashcard #85  Term: Nave arcade (Romanesque)  Definition: The series of arches supported by columns or piers that separate the nave from the side aisles in a Romanesque church. Flashcard #86  Term: Gallery (Romanesque)  Definition: A second story built over the side aisles of a Romanesque church, opening onto the nave. Flashcard #87  Term: Westwork  Definition: A monumental, multi-storied stone façade located at the western end of a Romanesque church, often featuring towers and multiple portals. Flashcard #88  Term: Tympanum  Definition: The semicircular or triangular decorative wall surface over an entrance, door, or window, often filled with relief sculpture in Romanesque and Gothic architecture. Flashcard #89  Term: Lintel  Definition: A horizontal architectural support spanning the top of a door or window opening, often sculpted in Romanesque portals. Flashcard #90  Term: Trumeau  Definition: The central column or post supporting the lintel and tympanum of a large portal, often carved with a figure. Flashcard #91  Term: Jambs  Definition: The side posts or vertical elements of a doorway or window frame, often adorned with sculpted figures in Romanesque and Gothic architecture. Flashcard #92  Term: Voussoirs  Definition: Wedge-shaped stones that form an arch, found in Romanesque portals. Flashcard #93  Term: Historiated Capitals  Definition: Sculpted capitals on columns or piers that depict narrative scenes, biblical stories, or fantastic beasts, common in Romanesque interiors. Flashcard #94  Term: Last Judgment Portal — Autun Cathedral  Definition: A famous Romanesque tympanum sculpture at the Church of Saint-Lazare in Autun, France, depicting Christ in Majesty presiding over the Last Judgment, designed to inspire fear and moral instruction. Flashcard #95  Term: Christ in Majesty  Definition: An iconic depiction of Christ enthroned within a mandorla, often flanked by the symbols of the four Evangelists, symbolizing his divine authority. Flashcard #96  Term: Evangelist symbols  Definition: Representations of the four Evangelists: Matthew (man or angel), Mark (lion), Luke (ox), and John (eagle), often surrounding Christ in Majesty. Flashcard #97  Term: Charlemagne  Definition: Frankish king crowned Holy Roman Emperor in 800 CE, who initiated the Carolingian Renaissance, reviving Roman art, architecture, and learning. Flashcard #98  Term: Carolingian Renaissance  Definition: A period of intellectual, cultural, and artistic revival in the Carolingian Empire under Charlemagne, marked by a conscious effort to restore Roman imperial glory. Flashcard #99  Term: Coronation Gospels  Definition: An example of Carolingian manuscript art known for its naturalistic figures, gold text on purple vellum, reflecting imperial power and Roman influence. Flashcard #100  Term: Palatine Chapel, Aachen  Definition: Charlemagne's personal chapel, inspired by San Vitale, representing the first vaulted stone building north of the Alps since Rome and fusing Roman, Byzantine, and Christian symbolism. Flashcard #101  Term: Gothic Art & Architecture  Definition: An architectural and artistic style (c. 1140–1400) originating in the Paris region, characterized by unprecedented height, abundant light, and a sense of dematerialization. Flashcard #102  Term: Abbot Suger  Definition: The Abbot of Saint-Denis and advisor to French kings, credited with conceptually inventing Gothic architecture through his renovation of the Abbey Church of Saint-Denis. Flashcard #103  Term: Saint-Denis (Gothic)  Definition: The burial church of French kings and the birthplace of Gothic architecture, renovated by Abbot Suger to embody his vision of Lux Nova and anagogy. Flashcard #104  Term: Pseudo-Dionysius  Definition: A 6th-century Byzantine mystic whose Neoplatonic texts, mistakenly attributed to Saint Denis, profoundly influenced Abbot Suger's ideas about the symbolism of light in architecture. Flashcard #105  Term: Lux Nova  Definition: 'New Light,' Abbot Suger’s key theological concept, referring to the divine, spiritual light that filled Gothic churches through stained glass, facilitating anagogical ascent. Flashcard #106  Term: Anagogy  Definition: A spiritual ascent from the material to the immaterial, a key concept for Abbot Suger, who believed architecture could lift the soul toward God through physical beauty. Flashcard #107  Term: Pointed arch  Definition: A key Gothic structural innovation that directs weight more vertically downwards than a round arch, allowing for taller structures and lighter walls. Flashcard #108  Term: Ribbed cross vault  Definition: A Gothic vaulting technique where stone ribs form a skeletal framework, reducing the weight of the vault and allowing lighter materials to fill the spaces between. Flashcard #109  Term: Slender columns  Definition: A Gothic innovation where massive Romanesque piers are replaced by more delicate columns, directing weight vertically and contributing to a sense of openness. Flashcard #110  Term: Flying buttresses  Definition: Exterior skeletal supports, characteristic of Gothic architecture, that transfer the outward thrust of the nave vaults across the side aisles to piers, allowing for thinner walls and larger windows. Flashcard #111  Term: Tripartite Nave Elevation  Definition: The three-story vertical division of the Gothic nave interior, consisting of the nave arcade, triforium, and clerestory. Flashcard #112  Term: Nave arcade  Definition: The lowest level of the Gothic nave elevation, composed of a series of arches supported by columns or piers separating the nave from the side aisles. Flashcard #113  Term: Triforium  Definition: The middle level of the Gothic nave elevation, often a narrow passageway or decorative arcade below the clerestory. Flashcard #114  Term: Clerestory  Definition: The uppermost level of the Gothic nave elevation, featuring large stained-glass windows that flood the interior with light. Flashcard #115  Term: Chartres Cathedral  Definition: A prominent High Gothic cathedral in France, largely rebuilt after a fire in 1194, known for its unified design, extensive stained glass (including rose and lancet windows), and preservation of the Virgin Mary's tunic. Flashcard #116  Term: Sainte-Chapelle  Definition: A royal chapel in Paris, considered the ultimate realization of the Gothic Lux Nova concept, with walls almost entirely composed of stained glass, creating an overwhelming ethereal light. Flashcard #117  Term: 3rd–4th century CE  Definition: Development of early Christian art. Flashcard #118  Term: 270 CE  Definition: Date of the Santa Maria Antiqua sarcophagus. Flashcard #119  Term: 70 CE  Definition: Destruction of the Jewish Temple by the Romans, leading to the split of Judaism and the emergence of Christianity. Flashcard #120  Term: 571–632 CE  Definition: Life of Muhammad, the prophet of Islam. Flashcard #121  Term: 622 CE  Definition: The Hijra, when Muhammad fled Mecca to Medina, marking the beginning of the Islamic calendar. Flashcard #122  Term: 687–692 CE  Definition: Construction period of the Dome of the Rock in Jerusalem. Flashcard #123  Term: 5th century BCE  Definition: Approximate time when Siddhartha Gautama founded Buddhism. Flashcard #124  Term: 250 BCE  Definition: Approximate date of the Great Stupa at Sanchi, built by Emperor Ashoka. Flashcard #125  Term: c. 950–1050 CE  Definition: The Ottonian Period in European art and architecture. Flashcard #126  Term: 476 CE  Definition: Traditional date for the Fall of the Western Roman Empire. Flashcard #127  Term: c. 500–900 CE  Definition: The Early Middle Ages. Flashcard #128  Term: c. 500–700 CE  Definition: The Migration Period (formerly 'Dark Ages'). Flashcard #129  Term: 742 CE  Definition: Birth of Charlemagne. Flashcard #130  Term: 800 CE  Definition: Charlemagne crowned Holy Roman Emperor. Flashcard #131  Term: c. 1050–1200 CE  Definition: The Romanesque Period. Flashcard #132  Term: 1096–1204 CE  Definition: The period encompassing the Four Official Crusades. Flashcard #133  Term: c. 1070–1120 CE  Definition: Construction period of the Church of Saint-Sernin in Toulouse. Flashcard #134  Term: c. 1140–1400 CE  Definition: The period of Gothic Art & Architecture. Flashcard #135  Term: 1194 CE  Definition: Date of the devastating fire at Chartres Cathedral, which led to its High Gothic rebuilding. Flashcard #136  Term: 532–537 CE  Definition: Construction period of Hagia Sophia under Emperor Justinian. Flashcard #137  Term: 527–565 CE  Definition: Reign of Emperor Justinian I. Flashcard #138  Term: 312–337 CE  Definition: Reign of Emperor Constantine, during which Christianity was legalized

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Chapters 1 and 2 Study Guide 1.1 Classifying matter (what it is and how we name it) Physical state Solid: fixed shape and volume (particles tightly packed; strong intermolecular forces). Liquid: fixed volume but shape adapts to container (particles close but can move past each other). Gas: no fixed shape or volume — fills container (particles far apart; weak interactions). Pure substance vs mixture Pure substance: one type of “stuff” with fixed composition. Element: pure substance that cannot be chemically broken into simpler substances (e.g., O₂ gas consists of oxygen atoms). Compound: pure substance made of two or more elements chemically bonded in fixed ratio (e.g., H₂O). Mixture: two or more substances physically combined; components keep their chemical identities. Homogeneous mixture: uniform throughout (solution like salt water). Heterogeneous mixture: non-uniform (e.g., sand in water). Particles Atom: smallest unit of an element that retains element identity (e.g., one carbon atom). Molecule: two or more atoms bonded together (could be same element, e.g., O₂, or different, e.g., CO₂). Ion: atom or group of atoms with net electric charge (cation = positive, anion = negative). How to classify — short checklist Is composition fixed? yes → pure substance (element or compound). no → mixture. Is it made of single type of atom? yes → element. If different elements bonded → compound. Is it uniform? yes → homogeneous; no → heterogeneous. 1.2 SI units & common prefixes Base SI units you need: Length: meter (m) Mass: kilogram (kg) — note: kg is base unit (not g), but we often use grams (g). Time: second (s) Temperature: kelvin (K) Amount of substance: mole (mol) Common prefixes (multipliers): kilo- (k) = 10³ = 1,000 e.g., 1 km = 1,000 m centi- (c) = 10⁻² = 0.01 e.g., 1 cm = 0.01 m milli- (m) = 10⁻³ = 0.001 e.g., 1 mm = 0.001 m Tip: memorize that kilo = 1000, centi = 1/100, milli = 1/1000. 1.3 Scientific notation Why: makes very large or very small numbers easier and reduces error. Format: a \times 10^n where 1 ≤ |a| < 10 and n is integer. Examples 0.000345 = 3.45 \times 10^{-4}. 6,200,000 = 6.2 \times 10^{6}. To convert: move decimal left for positive exponent, right for negative. 1.4 Significant figures (sig figs) & uncertainty What sig figs mean: digits in a measurement that are known reliably plus one uncertain digit (last digit). Rules for counting sig figs Nonzero digits are always significant: 245 → 3 sig figs. Zeros between nonzero digits are significant: 2005 → 4 sig figs. Leading zeros (to left of first nonzero) are NOT significant: 0.0072 → 2 sig figs. Trailing zeros in a number with a decimal are significant: 2.300 → 4 sig figs. Trailing zeros in a whole number without a decimal are ambiguous — use scientific notation to show significance: 1200 (ambiguous) → write 1.200×10³ to show 4 sig figs or 1.2×10³ to show 2. Relationship to uncertainty: the last sig fig is the estimated digit — it indicates the measurement’s uncertainty level. 1.5 Sig figs in calculations Multiplication / Division: answer has same number of sig figs as factor with fewest sig figs. Example: 2.5 \times 3.42 = 8.55 → 2 sig figs → round to 8.6. Addition / Subtraction: align decimal places; answer has decimal places equal to the quantity with fewest decimal places. Example: 12.11 + 0.3 = 12.41 → fewest decimals = 1 decimal → round to 12.4. Always follow these rules and only round at the end of multi-step calculations (keeping extra guard digits during intermediate steps). 1.6 Accuracy vs precision Accuracy: how close a measurement is to the true/accepted value. Precision: how repeatable measurements are (how close they are to each other). Illustration (dartboard): All darts close to bullseye → accurate and precise. All darts clustered but far from bullseye → precise but not accurate. Darts spread out but centered on bullseye on average → accurate but not precise. 1.7 Derived units: volume & density Volume: for regular shapes use geometry (e.g., m³ or L = dm³). Common lab units: mL (1 mL = 1 cm³). Density: \rho = \dfrac{\text{mass}}{\text{volume}}. Common units: g/mL or g/cm³ for solids/liquids; kg/m³ in SI. Rearrangements \text{mass} = \text{density} \times \text{volume} \text{volume} = \dfrac{\text{mass}}{\text{density}} Example (lab / irregular object): Object mass = 12.43 g. Volume by displacement = 3.10 mL. Density = 12.43 g ÷ 3.10 mL = 4.0097 g/mL → with sig figs: three sig figs (3.10 has 3 sig figs; 12.43 has 4) → 4.01 g/mL. 1.8 Dimensional analysis (unit conversions) Key idea: multiply by conversion factors that equal 1 (units cancel). Worked example: convert 2.50 miles → meters. 1 mile = 1609.34 m. 2.50\ \text{mi}\times \frac{1609.34\ \text{m}}{1\ \text{mi}} = 4023.35\ \text{m}. Sig figs: 2.50 has 3 sig figs → answer must have 3 sig figs → 4.02 × 10³ m. 1.9 Practice problems (with steps + sig figs) Problem A — Scientific notation Convert 0.000462 to scientific notation. Move decimal 4 places right: 4.62 \times 10^{-4}. Problem B — Multiplication with sig figs Compute (3.60 \times 2.1). Raw: 3.60\times2.1 = 7.56. Sig figs: 3.60 (3 sig figs), 2.1 (2 sig figs) → result 2 sig figs → 7.6. Problem C — Addition with sig figs Compute 12.11 + 0.3 + 0.042. Align decimals; fewest decimal places = 1 (from 0.3) → round final to 1 decimal place. Sum = 12.11 + 0.3 + 0.042 = 12.452 → round to 12.5. Problem D — Density (irregular object) Mass = 24.68 g; initial water in graduated cylinder = 15.0 mL; final = 17.35 mL. Volume displaced = 17.35 − 15.0 = 2.35 mL (note: 15.0 has 3 sig figs so difference has 3 sig figs). Density = 24.68 ÷ 2.35 = 10.500 ≈ 4 sig figs? But check sig figs: mass 24.68 (4 sig figs), volume 2.35 (3 sig figs) → result to 3 sig figs → 10.5 g/mL. Chapter 2 — Atomic structure, periodic table, bonding, naming 2.1 Historic experiments — what they showed and why they matter J.J. Thomson (late 1800s) — cathode ray experiment What he did: passed a beam (cathode ray) through electric & magnetic fields and measured deflection. Observation: beam deflected toward positive plate → beam composed of negatively charged particles. Discovery: existence of the electron — a very small, negatively charged particle present in atoms. Model implication: atoms are not indivisible; they contain subatomic particles. Thomson proposed the “plum pudding” model: a positive “soup” with embedded electrons. Significance: first discovery of subatomic particle; proved atoms have internal structure. Ernest Rutherford (early 1900s) — gold foil experiment What he did: fired alpha particles (positively charged) at very thin gold foil and detected scattering angles. Observation: most alpha particles passed straight through, but a small fraction deflected at large angles; some bounced back. Conclusion: atom is mostly empty space with a tiny, dense, positively charged nucleus that contains most mass — electrons orbit around that nucleus. Model implication: replaced plum pudding with nuclear model (nucleus + orbiting electrons). Why this matters: Rutherford explained the large-angle deflections that Thomson’s model couldn’t; introduced the nucleus concept — foundation for modern atomic structure. 2.2 Atomic number, mass number, isotopes Atomic number (Z): number of protons in nucleus → defines the element. Mass number (A): total number of protons + neutrons in nucleus (integer). Isotopes: atoms of same element (same Z) with different numbers of neutrons (different A). Example: carbon-12 (^12C) and carbon-14 (^14C). Isotopic notation: {}^{A}{Z}X^{\text{charge}} Example: an ion of chlorine with 17 protons and 18 neutrons and −1 charge → {}^{35}{17}\text{Cl}^{-} (35 = 17+18). Average atomic mass: weighted average of isotopic masses using natural abundances (found on periodic table). The periodic table lists average atomic mass (not integer mass numbers) because natural samples are mixtures of isotopes. 2.3 Example: average atomic mass (Neon) Given isotopes (typical values): ^20Ne mass = 19.992440 amu, abundance = 90.48% (0.9048) ^21Ne mass = 20.993847 amu, abundance = 0.27% (0.0027) ^22Ne mass = 21.991386 amu, abundance = 9.25% (0.0925) Average atomic mass: (19.992440)(0.9048) + (20.993847)(0.0027) + (21.991386)(0.0925) = 20.1800\ \text{amu (approx.)} This is the kind of number you’ll see on the periodic table: 20.180 amu. Procedure (general): multiply each isotope mass × its fractional abundance, then sum. 2.4 Writing atomic/ionic symbols and counting particles Given: protons, neutrons, electrons, and charge — decide isotope notation or ion symbol. Example 1: 17 protons, 18 neutrons, 17 electrons → neutral chlorine atom ^35Cl (since A = 17 + 18 = 35). Symbol: {}^{35}_{17}\text{Cl}. Example 2: 11 protons, 12 neutrons, 10 electrons → net charge +1 (lost 1 electron) → sodium ion {}^{23}_{11}\text{Na}^{+} (A = 23). How to check: protons = atomic number (Z) → identifies element. electrons = protons − charge (if charge positive, fewer electrons). mass number A = protons + neutrons. 2.5 Ionic vs covalent (molecular) compounds Ionic compounds Formed when electrons are transferred from a metal to a nonmetal (forming cations and anions). Bonding characterized by electrostatic attraction between oppositely charged ions. Usually full formula is a formula unit (empirical ratio). Often solids with high melting points and conduct electricity when molten or dissolved. Example: NaCl (Na⁺ and Cl⁻). Covalent (molecular) compounds Formed when two nonmetals share electrons to achieve noble gas configuration. Bonds are electron-sharing; molecules have discrete units. Example: H₂O, CO₂. Rule of thumb: metal + nonmetal → usually ionic. nonmetal + nonmetal → usually covalent. 2.6 Using the periodic table to get information From an element’s location: Atomic number → number of protons (top of box). Atomic mass (average) → usually decimal number beneath symbol. Group (column) number → similar chemical behavior and valence electrons. Period (row) → number of electron shells occupied. Metals/Nonmetals/Metalloids: left side metals, right side nonmetals; staircase demarcates metalloids. Common ion charges: Groups 1A → +1, 2A → +2, 7A (halogens) → −1, 6A → −2, etc. Transition metals: central block (d-block). Halogens: Group 17 (F, Cl, Br, I…). Noble gases: Group 18 (He, Ne, Ar…). 2.7 Writing chemical formulas Ionic compounds (simple) Balance total positive and negative charges to get neutral compound. Example: Al³⁺ and O²⁻ → least common multiple of 3 and 2 = 6 → need 2 Al³⁺ (2×+3=+6) and 3 O²⁻ (3×−2=−6) → formula Al₂O₃. With polyatomic ions Treat polyatomic ion as a unit; balance charges. Use parentheses when more than one polyatomic unit is needed: e.g., calcium nitrate = Ca²⁺ + NO₃⁻ → need two NO₃⁻ → Ca(NO₃)₂. Naming Ionic: cation name (metal) first, then anion name (nonmetal with −ide ending) or polyatomic ion name. For transition metals that can have multiple charges, use Roman numeral for charge (iron(III) chloride = FeCl₃). Molecular (binary nonmetal compounds): use prefixes (mono-, di-, tri-, etc.) to show number of each atom (CO₂ = carbon dioxide). Common polyatomic ions (memorize these) NH₄⁺ ammonium NO₃⁻ nitrate SO₄²⁻ sulfate CO₃²⁻ carbonate OH⁻ hydroxide PO₄³⁻ phosphate ClO₄⁻ perchlorate 2.8 Hydrates Definition: a compound that contains water molecules in its crystalline structure: written as \text{salt} \cdot x\text{H}_2\text{O}. Example: copper(II) sulfate pentahydrate = CuSO₄·5H₂O. Naming: name ionic compound then add prefix for water number + “hydrate” (e.g., decahydrate, pentahydrate). Finding empirical hydrate formula (lab procedure) Mass of hydrate (before heating) — measured. Heat to remove water → mass of anhydrous salt measured. Mass of water lost = mass hydrate − mass anhydrous. Convert both masses to moles: moles anhydrous = mass anhydrous ÷ molar mass of anhydrous salt. moles water = mass water ÷ 18.015 g/mol. Compute mole ratio: moles water ÷ moles anhydrous → round to nearest small whole number → that’s x in salt·x H₂O. Worked lab example (complete): (This matches labs you described.) Given: Mass hydrate = 2.564 g Mass anhydrous = 1.622 g Assume the anhydrous formula is CuSO₄ (molar mass = 159.609 g/mol) Steps: Mass water = 2.564 − 1.622 = 0.942 g. Moles anhydrous CuSO₄ = 1.622 g ÷ 159.609 g/mol = 0.010162 mol. Moles water = 0.942 g ÷ 18.015 g/mol = 0.052290 mol. Mole ratio water : salt = 0.052290 ÷ 0.010162 = 5.15 ≈ 5 → formula CuSO₄·5H₂O. Why rounding to whole number: water molecules must be whole; experimental values near whole numbers are rounded to the nearest integer (if close enough — e.g., 2.99 → 3). 2.9 Stoichiometry & dimensional analysis reminders Always write units and let them cancel. Carry at least one extra guard digit through calculations; only round final answer to correct sig figs. For atomic/molecular calculations you’ll often use Avogadro’s number: 6.022\times10^{23} particles/mol. Calculations and practice problems from your list — solved Identifying sig figs — quick answers 0.004500 → 4 significant figures (4500 with leading zeros not significant; trailing zeros after decimal are significant). 1200 → ambiguous; writing as 1.200×10³ shows 4 sig figs; 1.2×10³ shows 2. Example: Putting numbers into/out of scientific notation 7,890,000 → 7.89 \times 10^{6} (3 sig figs if original had 3 sig figs). 3.40\times10^{-5} → 0.0000340. Dimensional analysis multistep example (CH1 style) Problem: Convert 45.0 km/h to m/s. 1 km = 1000 m, 1 h = 3600 s. 45.0\ \text{km/h} \times \dfrac{1000\ \text{m}}{1\ \text{km}} \times \dfrac{1\ \text{h}}{3600\ \text{s}} = \dfrac{45.0\times1000}{3600}\ \text{m/s} = 12.5\ \text{m/s} (sig figs: 45.0 has 3 sig figs → answer 3 sig figs → 12.5 m/s). Given isotopic data — calculate average atomic mass (worked) (Neon example shown earlier; result 20.180 amu). Using periodic table data to find p, n, e and determine if atom or ion Problem: Given symbol: {}^{37}_{17}\text{Cl}^{-}. Protons = 17 (by atomic number). Mass number = 37 → neutrons = 37 − 17 = 20. Charge −1 → electrons = protons + 1 = 18. This is an anion (ion). Not a neutral atom. Lab hydrate calculations — general example (walkthrough) (We already did CuSO₄·5H₂O example; follow same steps for your lab values.) Density equation & rearrangements (reminder) \rho = \dfrac{m}{V},\qquad m=\rho V,\qquad V=\dfrac{m}{\rho}. Essay-style questions (short, clear answers + reasoning) 1) Classify a substance as element/compound/mixture, pure or mixture, molecules or ions (how to explain) Example substance: Table salt (NaCl) from a bag. Is it pure substance or mixture? If chemically pure NaCl sample → pure substance (compound). If table salt has additives (iodide, anti-caking agents), it’s a mixture. Element/compound? NaCl is a compound (sodium + chlorine chemically bonded). Molecules or ions? Ionic compound made of Na⁺ and Cl⁻ ions (not discrete molecules), so it consists of ions in a crystal lattice. Why: composition fixed for compound; ionic bonding indicates ions rather than molecules. 2) Explain why some elements form cations and others form anions (use noble gas concept) Atoms tend to reach a lower energy, more stable electron configuration. Many atoms achieve stability by adopting the electron configuration of the nearest noble gas: Metals (left side): have few valence electrons; losing them gives a noble gas configuration → form cations (positive). Nonmetals (right side): have more valence electrons but are short of an octet; gaining electrons gives a noble gas configuration → form anions (negative). Example: Na (1 valence electron) loses 1 → Na⁺ (like Ne). Cl (7 valence electrons) gains 1 → Cl⁻ (like Ar). 3) Describe J.J. Thomson and Rutherford experiments (short) Thomson: cathode ray deflection → discovered electrons → atom contains negative particles → plum pudding model. Rutherford: gold foil scattering → most of atom empty; tiny dense positive nucleus deflects alpha particles → nuclear model of atom. Worked examples you specifically asked (Example 1 & 2) Example 1: Using cations: Li⁺ and Ba²⁺; anions: O²⁻ and ClO₄⁻ (perchlorate). Create four neutral ionic compounds and explain subscripts. We want neutral compounds (total positive charge = total negative charge). Possible pairings: Li⁺ + O²⁻ → Li₂O. Reason: O²⁻ has −2, Li⁺ is +1. Need two Li⁺ to balance one O²⁻ → Li₂O. Ba²⁺ + O²⁻ → BaO. Reason: Ba²⁺ (+2) and O²⁻ (−2) already balance 1:1 → BaO. Li⁺ + ClO₄⁻ → LiClO₄. Reason: perchlorate has −1, Li⁺ has +1 → 1:1 ratio. Ba²⁺ + ClO₄⁻ → Ba(ClO₄)₂. Reason: Ba²⁺ (+2) needs two ClO₄⁻ to neutralize → use parentheses for two polyatomic anions. How subscripts determined: cross-balance charges to get net zero; the smallest whole-number ratio is used. Example 2: Write formula or name for each I’ll give the correct formula or name and a brief explanation. K₂S — Name: potassium sulfide. K⁺ and S²⁻ → need two K⁺ to balance one S²⁻. (NH₄)₂SO₄ — Name: ammonium sulfate. NH₄⁺ is +1; sulfate is SO₄²⁻ → need two ammonium to balance sulfate. OBr₂ — Name: oxygen dibromide? Wait — check elements: O + Br is unusual: oxygen normally forms −2, bromine usually −1; a neutral binary molecular compound OBr₂ would be better thought as dibromine monoxide? This is a tricky one. But the formula given is OBr₂; if treated as a binary molecular compound (two elements, both nonmetals), use prefixes: oxygen dibromide (but molecule uncommon). Important note: In practice, more common bromine-oxygen compounds have different formulas (e.g., BrO₂⁻ is chlorite analogs). For classwork, accept oxygen dibromide as name for OBr₂ (prefix naming: mono/di). If the intended was phosphorus triiodide etc., the list might have mixed types; follow molecular naming rules for two nonmetals. Na₂CO₃ · 10H₂O — Name: sodium carbonate decahydrate. Sodium carbonate with ten waters attached. Strontium phosphate — Formula: Sr₃(PO₄)₂. Strontium is Sr²⁺; phosphate is PO₄³⁻. LCM of 2 and 3 is 6 → need three Sr²⁺ (3×+2=+6) and two PO₄³⁻ (2×−3=−6). Gold(III) bromide — Formula: AuBr₃. Gold (III) = Au³⁺, bromide = Br⁻ → need three Br⁻ to neutralize. Beryllium sulfate tetrahydrate — Formula: BeSO₄·4H₂O. Beryllium is Be²⁺, sulfate SO₄²⁻ → BeSO₄, plus 4 waters. Phosphorous triiodide — Formula: PI₃. Binary molecular: phosphorus (P) + iodine (I) → prefixes: phosphorus triiodide. Aluminum hydroxide — Formula: Al(OH)₃. Al³⁺ and OH⁻ → need three OH⁻ to balance one Al³⁺

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