High School Chemistry Unit 2: Data Analysis and Atomic Concepts Study Guide

Units and Measurements: Mass, Volume, and Density

• Definitions and Distinction     * Mass: A measure of the amount of matter contained within an object. Mass does not change based on location.     * Weight: A measure of the gravitational pull exerted on matter. Weight is dependent on gravity; as gravity changes, weight changes. For example, a person weighing $100\,kg$ on Earth would weigh approximately $16.6\,kg$ on the Moon, though their mass remains identical.     * Volume: The amount of three-dimensional space occupied by an object.     * Density: The ratio of mass to volume, calculated as mass divided by volume ($D = \frac{M}{V}$). Density is considered a constant for a specific substance and does not change regardless of the object's mass, shape, or volume (e.g., the density of water is always $1\,g/mL$).

• Density Units     * Standard units include: $kg/m^3$, $g/cm^3$, $g/mL$, and $g/L$.

• Calculations and Measurement Procedures     * Measuring Mass: Use a balance.         1. Place a weight boat or beaker on the scale.         2. Tare the balance (it should read $0.00\,g$).         3. Place the substance in the container.         4. Wait for the mass to stabilize and record results.     * Measuring Volume:         * Regular Solids: Use a ruler to measure in centimeters ($cm$).             * Cube/Rectangular Prism: $V = L \times W \times H$             * Cylinder: $V = \pi r^2 h$         * Liquids: Use a graduated cylinder and read the meniscus.         * Irregular Solids: Use the volume by displacement method. Measure the initial volume of water in a cylinder, submerge the object, and calculate the difference ($V_{final} - V_{initial}$).

Uncertainty, Accuracy, and Precision in Data

• Uncertainty in Measurement     * Error or uncertainty always exists in any measurement.     * Precision of equipment: Equipment presenting more decimal places typically has lower uncertainty. For example, a digital scale reading to the hundredths place has an uncertainty of $\pm 0.01\,g$, while a scale reading to the whole gram has an uncertainty of $\pm 1\,g$.

• Accuracy vs. Precision     * Accuracy: How close a measurement is to the correct or accepted value.     * Precision: How close a set of measurements are to each other when made in the same way.     * Physical Analogy (Darts):         * High Precision/High Accuracy: Darts clustered tightly in the bull's-eye.         * High Precision/Low Accuracy: Darts clustered tightly but far from the bull's-eye.         * Low Precision/High Accuracy: Darts spread out, but their average position is the bull's-eye.         * Low Precision/Low Accuracy: Darts spread out and far from the bull's-eye.

SI Units and Metric Conversions

• Le Systeme International d’Unites (SI)     * A standardized measurement system used globally by scientists. Consists of seven common base units:         1. Length: meter ($m$)         2. Mass: kilogram ($kg$)         3. Time: second ($s$)         4. Temperature: Kelvin ($K$)         5. Amount of Substance: mole ($mol$)         6. Electric Current: ampere ($A$)         7. Luminous Intensity: candela ($cd$)

• SI Prefixes and Factors     * Tera (T): $10^{12}$     * Giga (G): $10^9$     * Mega (M): $10^6$     * Kilo (k): $10^3$ ($1,000$)     * Hecto (h): $10^2$ ($100$)     * Deka (da): $10^1$ ($10$)     * Deci (d): $10^{-1}$ ($1/10$)     * Centi (c): $10^{-2}$ ($1/100$)     * Milli (m): $10^{-3}$ ($1/1,000$)     * Micro (\mu): $10^{-6}$     * Nano (n): $10^{-9}$     * Pico (p): $10^{-12}$

• Dimensional Analysis     * A method using conversion factors to change one unit of measurement to another. For example, converting $5.712\,g$ to $kg$ requires the factor $\frac{1\,kg}{1,000\,g}$.

Scientific Notation and Mathematical Operations

• Format: $M \times 10^n$     * $M$ is a number 1 \le M < 10.     * $n$ is the number of decimal spaces moved.     * Positive $n$: Decimal moves left (large numbers like $7,960,000 \rightarrow 7.96 \times 10^6$).     * Negative $n$: Decimal moves right (small numbers like $0.0000087 \rightarrow 8.7 \times 10^{-6}$).

• Arithmetic in Scientific Notation     * Addition/Subtraction: Powers ($n$) must be identical. Add/subtract coefficients and keep the power the same.     * Multiplication: Multiply coefficients and add exponents.         * Example: $(5.23 \times 10^6\,\mu m) \times (7.1 \times 10^{-2}\,\mu m) = 3.7133 \times 10^4 \rightarrow 3.7 \times 10^5\,\mu m^2$ (adjusted for sig figs).     * Division: Divide coefficients and subtract exponents.         * Example: $\frac{5.44 \times 10^7\,g}{8.1 \times 10^4\,mol} = 6.716 \times 10^2 \rightarrow 6.7 \times 10^2\,g/mol$.

Significant Figures and Rounding Rules

• Sig Fig Rules:     1. Non-zero digits are always significant.     2. Zeros between non-zero digits are significant (e.g., $9076$ has 4 sig figs).     3. Leading zeros are never significant (e.g., $0.0087$ has 2 sig figs).     4. Trailing zeros to the right of a decimal are significant (e.g., $85.00$ has 4 sig figs).     5. Trailing zeros with no decimal are generally not significant (e.g., $2000$ has 1 sig fig, but $2000.$ has 4).

• Calculations with Sig Figs:     * Multiplication/Division: The answer must have the same number of sig figs as the measurement with the fewest total sig figs.     * Addition/Subtraction: The answer must have the same number of decimal places as the measurement with the fewest digits to the right of the decimal point.

• Scientific Rounding Rules:     * If the digit following the last retained digit is > 5, increase by 1.     * If the digit is < 5, stay the same.     * If the digit is exactly $5$:         * If followed by non-zero digits: Increase by 1.         * If not followed by non-zero digits and preceded by an odd digit: Increase by 1 (e.g., $4.635 \rightarrow 4.64$).         * If not followed by non-zero digits and preceded by an even digit: Stay the same (e.g., $78.65 \rightarrow 78.6$).

Evolution of Atomic Theory

• Democritus (400 BC): Proposed the "atomos," indivisible particles that cannot be destroyed or compressed.

• John Dalton (1803): Proposed the first testable atomic theory; atoms are hard spheres, atoms of the same element are identical, and atoms combine to form compounds.

• J.J. Thomson (1897): Used cathode ray tubes to discover electrons. Proposed the "Plum Pudding Model," where negative electrons are dispersed in a positive "pudding."

• Ernest Rutherford (1911): Conducted the Gold Foil Experiment with alpha particles. Concluded that the atom is mostly empty space with mass concentrated in a tiny, positively charged nucleus.

• Niels Bohr (1913): The "Planetary Model." Electrons exist in specific circular energy levels or shells. Valence electrons (outermost) determine chemical properties.

• James Chadwick (1932): Discovered neutrons in the nucleus to explain missing atomic mass.

• Erwin Schrödinger (1926): The "Wave Mechanical Model" (Electron Cloud). Electrons occupy orbitals, which are regions of space where there is a high probability ($90\%$) of finding an electron.

Atomic Structure, Isotopes, and Ions

• Subatomic Particles (Table O):     * Protons ($p$): Charge $+1$, Mass $1\,amu$, located in Nucleus.     * Neutrons ($n$): Charge $0$, Mass $1\,amu$, located in Nucleus.     * Electrons ($e^-$): Charge $-1$, Mass $\approx 0\,amu$, located in Orbitals.

• Atomic Number ($Z$): Identifies the element; equals the number of protons.

• Mass Number ($A$): The sum of protons and neutrons ($A = p + n$).

• Isotopes: Atoms of the same element (same number of protons) but with a different number of neutrons, resulting in different mass numbers.     * Notation: ${}^{A}_{Z}\text{X}$ or Element-Mass (e.g., C-14).

• Average Atomic Mass: The weighted average of all naturally occurring isotopes of an element.     * Calculation: Multiply each isotope's mass by its decimal abundance and add the results.

Electrons and Advanced Configurations

• Energy States:     * Ground State: Electrons occupy the lowest possible energy levels; most stable state.     * Excited State: Electrons absorb energy and move to higher levels (temporary/unstable). When dropping back to the ground state, energy is released as light, creating a bright-line spectrum (emission spectrum).

• Principal Energy Levels ($n$): Maximum electrons per level is $2n^2$.     * $n=1$ (2 e-), $n=2$ (8 e-), $n=3$ (18 e-), $n=4$ (32 e-).

• Sublevels and Orbitals:     * s sublevel: 1 orbital, max 2 electrons.     * p sublevel: 3 orbitals, max 6 electrons.     * d sublevel: 5 orbitals, max 10 electrons.     * f sublevel: 7 orbitals, max 14 electrons.

• Quantum Numbers:     * Principal ($n$): Designates size/energy level.     * Angular Momentum ($l$): Describes shape ($s=0, p=1, d=2, f=3$).     * Magnetic ($m_l$): Specifies orientation ($-l$ to $+l$).     * Spin ($m_s$): Specifies electron spin ($+1/2$ or $-1/2$).

• Electron Configuration Rules:     1. Aufbau Principle: Electrons fill sublevels of lowest energy first.     2. Pauli Exclusion Principle: Max 2 electrons per orbital with opposite spins.     3. Hund's Rule: Electrons fill orbitals of a sublevel singly before pairing up.

Questions & Discussion

• Bell Work (9/6 - 9/7):     * Question: Identify if the following are observations, inferences, or predictions: A. Lab counters are flame resistant (Inference); B. Projector is on (Observation); C. Wall is green (Observation); D. We will take a quiz (Prediction).     * Question: What equipment heats to a specific temperature? (Answers vary by context, likely an incubator or specialized heater).     * Question: List Aristotle's 5 principles. (Included for historical context in unit 1 review).

• Bell Work (9/11 - 9/13):     * Question: If mass is $120\,kg$ on Earth, what is it on the moon? (Answer: $120\,kg$; mass does not change).     * Question: What is the density of an object with mass $1.5\,g$ and volume $20\,mL$? (Answer: $0.075\,g/mL$).

• Bell Work (10/11 - 10/13):     * Question: How do you find the volume of an irregular object? (Answer: Displacement method).     * Question: Difference between Independent and Dependent variables? (Answer: Independent is changed by the scientist; Dependent is measured/affected).     * Question: As mass and volume increase, what happens to density? (Answer: Density remains constant for the same substance because the ratio $M/V$ stays the same).

• Bright-Line Spectrum Interaction:     * Question: How is light produced in terms of electrons and energy states? (Answer: Electrons in an excited state drop to a lower energy state/ground state, releasing energy in the form of photons/light).