# Lecture 1: Matter, Measurement, and Significant Figures ## General Chemistry I --- ## Learning Objectives By the end of this lecture, students will be able to: 1. Classify matter as elements, compounds, or mixtures and distinguish between pure substances and mixtures 2. Differentiate among the three states of matter and describe phase transitions at the molecular level 3. Distinguish between physical and chemical properties, and between physical and chemical changes 4. Apply SI units and metric prefixes to express measurements in chemistry 5. Perform dimensional analysis (factor-label method) to convert between units 6. Apply the rules of significant figures in measurements and calculations 7. Distinguish between accuracy and precision and calculate percent error --- ## Lecture Content ### I. What Is Chemistry? Chemistry is the study of matter, its properties, and the changes it undergoes. Often called the "central science," chemistry bridges physics, biology, environmental science, medicine, and engineering. For pre-med students, a solid understanding of chemistry is essential because fields such as pharmacology, biochemistry, and physiology all rest squarely on chemical principles. ### II. Classification of Matter Matter is defined as anything that has mass and occupies space. It can be divided into two broad categories: pure substances and mixtures. #### A. Pure Substances An element is a substance that cannot be broken down into simpler substances by chemical means. Elements are represented by one- or two-letter symbols on the periodic table (for example, O for oxygen, Fe for iron, and Na for sodium). Of the 118 known elements, roughly 90 occur naturally. A compound, by contrast, consists of two or more elements that are chemically combined in a fixed ratio. Importantly, the properties of a compound differ from those of its constituent elements; sodium chloride (NaCl), for example, behaves nothing like metallic sodium or chlorine gas. Compounds can be broken apart by chemical methods but not by physical methods. #### B. Mixtures A homogeneous mixture, commonly called a solution, has a uniform composition throughout. Examples include saltwater, air, and brass (an alloy of copper and zinc). In such mixtures, the individual components are not visually distinguishable. A heterogeneous mixture, on the other hand, has a non-uniform composition with distinct regions or phases that can be seen. Granite, a combination of oil and water, and trail mix are all heterogeneous mixtures. Unlike compounds, mixtures can be separated by physical methods such as filtration, distillation, chromatography, and evaporation. A hierarchical flowchart classifying matter. At the top, "Matter" branches into "Pure Substances" and "Mixtures." Pure Substances branches into "Elements" (with examples: gold, oxygen, carbon) and "Compounds" (with examples: water, sodium chloride, glucose). Mixtures branches into "Homogeneous" (with examples: saltwater, air) and "Heterogeneous" (with examples: sand in water, granite). Arrows between levels indicate separation methods: chemical methods separate compounds into elements; physical methods separate mixtures into pure substances. ### III. States of Matter Matter exists in three familiar states. A solid has a fixed shape and volume because its particles are packed closely in an orderly arrangement, held in place by strong intermolecular forces, and limited to vibrational motion. A liquid retains a fixed volume but takes the shape of its container; its particles remain close together yet are disordered enough to slide past one another, reflecting moderate intermolecular forces. A gas has neither a fixed shape nor a fixed volume and will fill any container completely. Gas particles are far apart, experience negligible intermolecular forces, and move rapidly and randomly. Transitions between these states are called phase transitions. Melting (also called fusion) converts a solid to a liquid, while vaporization (boiling or evaporation) converts a liquid to a gas. Sublimation is the direct conversion of a solid to a gas, bypassing the liquid phase. The reverse processes are freezing, condensation, and deposition, respectively. A three-panel molecular-level illustration of the three states of matter for water. Panel A (Solid/Ice): molecules arranged in a regular crystalline lattice with hydrogen bonds shown as dashed lines, molecules vibrating in fixed positions. Panel B (Liquid Water): molecules close together but randomly arranged, some hydrogen bonds present but constantly breaking and reforming. Panel C (Gas/Steam): molecules widely spaced, moving rapidly in random directions with arrows showing velocity vectors, no persistent intermolecular interactions. Below all three panels, a horizontal arrow labeled "Increasing temperature / Increasing kinetic energy" runs left to right. ### IV. Physical and Chemical Properties and Changes #### A. Properties Physical properties can be observed or measured without changing the composition of a substance. These fall into two subcategories: intensive properties, which are independent of the amount of material present (such as density, boiling point, color, and refractive index), and extensive properties, which depend on the amount of material (such as mass, volume, length, and energy content). Chemical properties, by contrast, describe a substance's ability to undergo chemical change. Flammability, reactivity with acids, and the tendency to corrode or oxidize are all chemical properties. #### B. Changes A physical change alters the form or appearance of a substance without producing a new substance. Melting ice, dissolving sugar in water, and crushing a can are all physical changes. A chemical change, or chemical reaction, produces one or more new substances with different compositions and properties. Common indicators of a chemical change include a color change, the production of gas, the formation of a precipitate, an energy change (release or absorption of heat or light), or a new odor. ### V. Units of Measurement and the SI System Chemistry relies on the International System of Units (SI). The SI base units most relevant to chemistry include the meter (m) for length, the kilogram (kg) for mass, the second (s) for time, the kelvin (K) for temperature, the mole (mol) for amount of substance, the ampere (A) for electric current, and the candela (cd) for luminous intensity. Common metric prefixes scale these units up or down: giga (G, 10^9), mega (M, 10^6), and kilo (k, 10^3) denote large multiples, while deci (d, 10^-1), centi (c, 10^-2), milli (m, 10^-3), micro (u, 10^-6), nano (n, 10^-9), and pico (p, 10^-12) denote small fractions. Several derived units are essential in chemistry. Volume is commonly expressed in liters (L), where 1 L equals 1 dm^3, which equals 1000 cm^3 or 1000 mL. Density is reported as g/mL or g/cm^3 for solids and liquids, and g/L for gases. The joule (J), defined as kg*m^2/s^2, is the SI unit of energy; one calorie equals 4.184 J. Temperature conversions follow the relationships K = C + 273.15 and F = (9/5)C + 32. ### VI. Dimensional Analysis (Factor-Label Method) Dimensional analysis is a systematic approach to unit conversions that uses conversion factors -- fractions equal to 1 (for example, 1 km / 1000 m). By arranging these factors so that unwanted units cancel and desired units remain, even complex conversions become straightforward. For instance, to convert 5.0 miles to kilometers, one multiplies 5.0 mi by the factor (1.609 km / 1 mi) to obtain 8.0 km. Multi-step conversions simply chain several conversion factors in sequence. Density itself can serve as a conversion factor linking mass and volume, since d = m/V can be rearranged to interconvert the two quantities. ### VII. Significant Figures Significant figures reflect the precision of a measurement. Several rules govern which digits count as significant. All nonzero digits are significant, so 453 has three significant figures. Zeros between nonzero digits are significant, giving 1002 four significant figures. Leading zeros are not significant; 0.0045 has only two. Trailing zeros after a decimal point are significant, so 2.300 has four significant figures. Trailing zeros in a whole number without a decimal point are ambiguous and should be clarified with scientific notation (for example, writing 1.500 x 10^3 instead of 1500). When performing calculations, the treatment of significant figures depends on the operation. In multiplication and division, the result should carry the same number of significant figures as the measurement with the fewest significant figures. In addition and subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places. Exact numbers, which arise from definitions or counting, have unlimited significant figures and do not limit the result. ### VIII. Accuracy vs. Precision Accuracy describes how close a measurement is to the true or accepted value, while precision describes how close repeated measurements are to each other, reflecting reproducibility. A measurement can be precise but not accurate (indicating a systematic error), accurate but not precise (reflecting random scatter), both, or neither. The percent error quantifies accuracy: percent error = |(experimental value - accepted value)| / accepted value x 100%. A target-analogy diagram with four targets illustrating accuracy vs. precision. Target A (High accuracy, high precision): all darts clustered tightly at the bullseye. Target B (High precision, low accuracy): all darts clustered tightly but off-center from the bullseye. Target C (High accuracy, low precision): darts scattered broadly but centered around the bullseye. Target D (Low accuracy, low precision): darts scattered broadly and off-center. Each target is clearly labeled beneath with its accuracy/precision classification. ### IX. Scientific Notation Scientific notation expresses very large or very small numbers in the form N x 10^n, where 1 <= N < 10. For example, 602,200,000,000,000,000,000,000 becomes 6.022 x 10^23, and 0.000000001 m becomes 1 x 10^-9 m. When multiplying numbers in scientific notation, multiply the coefficients and add the exponents. When dividing, divide the coefficients and subtract the exponents. For addition and subtraction, first adjust the numbers to the same power of 10, then add or subtract the coefficients.