Comprehensive Chemistry Lecture Notes: Matter, Measurements, and Atomic Theory

Administrative Updates and Course Resources

• The Chapter One PowerPoint and the first set of practice problems have been reuploaded with minor corrections.
• A second handout of practice problems was added recently. The instructor noted that the first handout focused more on concepts, whereas the specifically added second handout contains more math-intensive problems.
• Exams for this semester will be authored by the current instructor rather than the department head, Dr. Schwab. The current instructor believes Dr. Schwab's exams are excessively difficult and intends to create slightly easier assessments.
• Metric prefix conversion slides were updated with a corrected chart to ensure no prefixes were omitted and to improve clarity for decimal-shifting methods.

Metric Units and Prefix Conversions

• Metric Prefix Hierarchy: Prefixes represent orders of magnitude relative to a base unit.   - Giga (G): $10^9$   - Mega (M): $10^6$   - Kilo (k): $10^3$   - Hecto (h): $10^2$   - Base unit (e.g., meter, gram, liter): $10^0$
• Unit Timeline Strategy: The instructor recommends the "unit timeline" or decimal-moving method. Jumping one position to the right on the metric scale corresponds to moving the decimal point one place to the right.
• Practice Problem: 48 kilograms (kg) to hectograms (hg):   - Dimensional Analysis Approach:     - Equivalency: $1\,kg = 10\,hg$     - Calculation: $48\,kg \times \frac{10\,hg}{1\,kg} = 480\,hg$     - Alternative Equivalency: $1\,hg = 0.1\,kg$     - Calculation: $48\,kg \times \frac{1\,hg}{0.1\,kg} = 480\,hg$   - Decimal Movement Approach: Since hecto is one place to the right of kilo, move the decimal one place to the right.     - $48.0 \rightarrow 480$
• Memorization Requirement: Students must memorize all metric prefixes and their corresponding exponential values.
• Polyatomic Ions: Unlike lower-level courses, students are required to memorize polyatomic ions for the nomenclature section of the exam. The instructor will provide a list of the specific ions expected to be on the test.

Physical Properties of Matter: Temperature, Volume, and Density

• Temperature: An intensive property representing the degree of hotness or coldness.   - Kelvin ($K$): The official scientific (SI) unit. It uses the absolute zero scale ($0\,K$). No degree symbol is used with Kelvin.   - Celsius ($^{\circ}C$): Commonly used in science and the rest of the world.   - Fahrenheit ($^{\circ}F$): Primarily used in the United States. The instructor jokes that $100^{\circ}F$ is "100% hot."   - Key Conversions:     - Kelvin from Celsius: $T_{K} = T_{^{\circ}C} + 273.15$ (Note: Some courses use $273$, but $.15$ is more precise; the instructor will likely not test on specific conversions between Fahrenheit and Celsius).     - Fahrenheit from Celsius: $T_{^{\circ}F} = \frac{9}{5} \times T_{^{\circ}C} + 32$
• Volume: The amount of space an object occupies.   - Standard SI Unit: Cubic meters ($m^3$).   - Laboratory Units: Milliliters ($mL$), Liters ($L$), and Microliters ($\mu L$).   - Crucial Equivalency: $1\,mL = 1\,cm^3$
• Density: An intensive property defined as the mass-to-volume ratio ($D = \frac{m}{v}$).   - Standard SI Units: Kilograms per cubic meter ($kg/m^3$).   - Common Chemistry Units: Grams per milliliter ($g/mL$) or grams per cubic centimeter ($g/cm^3$).   - Reference Density (Water): $1.0\,g/cm^3$.   - Notes on Substances: Ice ($0.917\,g/cm^3$) is less dense than liquid water. Mercury ($13.6\,g/cm^3$) is very dense. Gold is extremely dense and valuable.
• Derived Units: Any unit formed by combining base SI units (e.g., density involving mass/volume or volume involving $length \times width \times height$).

Density Calculations Practice

• Problem 1 (Finding Density): A metal block has a mass of $125\,g$ and a volume of $15\,cm^3$.   - $D = \frac{125\,g}{15\,cm^3} = 8.333...\,g/cm^3$   - Result (applying 3 sig figs): $8.33\,g/cm^3$
• Problem 2 (Finding Mass): A liquid has a density of $0.85\,g/mL$ and a volume of $250\,mL$.   - Isolate Mass: $m = D \times v$   - Calculation: $0.85\,g/mL \times 250\,mL = 212.5\,g$   - Result (applying 2 sig figs): $210\,g$ (Significant figure rounding requirements apply).

Measurement Uncertainty and Significant Figures (Sig Figs)

• Exact Numbers: Obtained by counting or definition (e.g., 12 eggs in a dozen, $1\,inch = 2.54\,cm$). They have infinite significant figures.
• Uncertain Numbers: Obtained via measurement tools; the last digit of any measured number is always considered an estimate (uncertain).
• Sig Fig Rules:   - Non-zero digits: Always significant.   - Middle Zeros: Always significant (e.g., 70.607 has 5 sig figs).   - Leading Zeros: Never significant; they are just placeholders (e.g., $0.00832$ has 3 sig figs).   - Trailing Zeros: Significant ONLY if a decimal point is explicitly present (e.g., $55.0$ has 3 sig figs, while $1300$ is ambiguous but generally treated as 2).
• Scientific Notation: Helpful for clarifying sig figs. In $1.23 \times 10^{-3}$, there are 3 sig figs.

Significant Figure Rounding Rules

• Addition and Subtraction: Round the answer to the same number of decimal places as the measurement with the fewest decimal places (least certain precision).   - Example: $1.023\,g + 4.383\,g = 5.406\,g$ (Both have three decimal places, so the result keeps three).   - Example: $486 + 421.23 = 907.23 \rightarrow$ round to ones place as $907$ (since 486 has no decimals).
• Multiplication and Division: Round the answer to match the factor with the fewest overall significant figures.   - Example: $421.23 / 486$ ($5\,sig\,figs / 3\,sig\,figs$) results in $0.867$ (3 sig figs).
• General Rounding Rules:   - If the first dropped digit is less than 5, round down.   - If the first dropped digit is greater than 5, round up.   - If exactly 5, use "banker's rounding" (round to the nearest even number) or round up per instructor preference.

Fundamental Concepts of Scientific Measurement

• Order of Operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Essential for multi-step chemistry calculations.
• Accuracy: How close a measurement is to the true or accepted value.
• Precision: How close repeated measurements are to each other (reproducibility).
• Experimental Outcomes:   - Accurate and Precise: Tight grouping near the target.   - Precise but not Accurate: Tight grouping in the wrong location.   - Neither: Scattered data Points.

Dimensional Analysis and Multi-Step Conversions

• Dimensional Analysis: A mathematical method where units are treated like numbers for cancellation purposes.
• Standard Conversion Factors to Know:   - $1\,inch = 2.54\,cm$   - $1\,kg \approx 2.2\,lbs$   - $1\,lb = 453.59\,g$   - $1\,L = 1.0567\,quarts$
• Case Study: Antifreeze Density:   - Given: $9.26\,lbs$ and $4\,quarts$. Goal: Grams per Milliliter ($g/mL$).   - Step 1 (Mass): $9.26\,lbs \times \frac{453.59\,g}{1\,lb} \approx 4200\,g$   - Step 2 (Volume): $4\,qts \times \frac{1\,L}{1.0567\,qts} \times \frac{1000\,mL}{1\,L} \approx 3785\,mL$   - Step 3 (Division): $\frac{4200\,g}{3785\,mL} = 1.11\,g/mL$
• Case Study: Usain Bolt World Record:   - 100 meters in 9.58 seconds.   - Distance over time: $\frac{100\,m}{9.58\,s}$   - Conversion to miles/hour: Use the equivalency $1\,mile = 1609\,m$ and $3600\,s = 1\,hr$.   - Result: $23.5\,mph$.

Chapter 2: Early Atomic Theory and History

• Pre-Scientific Ideas:   - Aristotle: Believed matter was comprised of four elements (earth, air, fire, water). This held precedence for 2,000 years despite lack of evidence.   - Democritus: Proposed matter is made of "atomos" (tiny, indivisible particles).
• John Dalton (1807): Developed the first evidence-based atomic theory. Known for laws regarding weather and color blindness study despite messy lab habits.
• Dalton's Five Postulates:   1. Matter is composed of atoms (the smallest unit of an element).   2. An element consists of one type of atom (identical in mass/properties).   3. Atoms of different elements differ in properties.   4. Compounds form via small, whole-number ratios (e.g., $H_2O$ always has a 2:1 ratio).   5. Atoms are conserved (not created or destroyed) during chemical change—they are merely rearranged.
• Law of Definite Proportions: All samples of a pure compound contain the same elements in the same proportion by mass regardless of source or sample size.
• Law of Multiple Proportions: When two elements form more than one compound, a fixed mass of one element will react with masses of the other in a ratio of small whole numbers.   - Example: Copper and Chlorine forming Copper(I) Chloride ($CuCl$) (green) vs. Copper(II) Chloride ($CuCl_2$) (brown).

Evolution of the Atomic Model

• JJ Thompson (1897): Used the Cathode Ray Tube experiment. Observed that the beam deflected toward a positive plate, proving the existence of the negatively charged electron. He proposed the "Plum Pudding" model (negative charges embedded in a positive sphere).
• Robert Millikan (1909): Oil Drop Experiment. Determined the charge of a single electron ($1.602 \times 10^{-19}\,C$). Combined with Thompson's data to find the mass of the electron: $9.107 \times 10^{-31}\,kg$.
• Ernest Rutherford (1911): Gold Foil Experiment. Fired alpha particles ($p^+$) at gold foil. Most passed through, but some deflected sharply back.   - Conclusions: The atom is mostly empty space with a tiny, dense, positively charged center called the nucleus. Coined the term proton.
• James Chadwick (1932): Discovered the neutron (uncharged particle in the nucleus). This explained isotopes and the "missing" mass of the nucleus.
• Isotopes: Atoms of the same element with the same number of protons but different numbers of neutrons.   - Example: Hydrogen ($0\,n$), Deuterium ($1\,n$), and Tritium ($2\,n$).

Atomic Structure and Notation

• Subatomic Particles:   - Proton ($p^+$): Positive charge ($+1$). Found in the nucleus. Mass $≈ 1\,amu$.   - Neutron ($n^0$): Neutral charge. Found in the nucleus. Mass $≈ 1\,amu$.   - Electron ($e^-$): Negative charge ($-1$). Found in orbitals outside the nucleus. Mass negligible ($\approx 0\,amu$).
• Notation Standard:   - Atomic Number ($z$): Number of protons. Defines the element's identity.   - Mass Number ($A$): Total number of protons + neutrons.   - Chemical Symbol ($X$): Represented as ${}^A_Z X$.
• Ions: Atoms that have gained or lost electrons.   - Cation: Positive ion (lost electrons). Usually metals.   - Anion: Negative ion (gained electrons). Usually nonmetals.
• Oxidation States Trends:   - Group 1: $+1$   - Group 2: $+2$   - Group 13: $+3$   - Group 14: $\pm 4$ (C and Si are flexible)   - Group 15: $-3$   - Group 16: $-2$   - Group 17 (Halogens): $-1$   - Group 18 (Noble Gases): $0$ (Stable, full octet)

Questions & Discussion

• Q: Do we have to know the polyatomic ions?
• A: Yes, they will not be provided on the exam. You must memorize them for nomenclature.
• Q: How should we treat sig figs for exact definitions like "12 eggs in a dozen"?
• A: Exact numbers are irrelevant for sig fig calculations because they have an infinite number of significant figures; you do not round based on them.
• Q: Is the charge always equal for protons and electrons?
• A: In a neutral atom, yes. They differ only when the atom becomes an ion (cation or anion).
• Q: What about group 14 oxidation numbers?
• A: They can be positive or negative four. Carbon is unique and doesn't care much about whether it gains or loses; it is often found in covalent chains.