CHEM 1411 Study Guide: Chapters E–3 (Units, Atoms, Quantum Model, Periodic Properties)

Chapter E: Essentials – Units, Measurement, and Problem Solving

Extensive and Intensive Properties; Chemical and Physical Properties

Properties of matter are classified as either extensive or intensive, and as chemical or physical. Understanding these distinctions is fundamental in chemistry.

• Extensive Properties: Depend on the amount of matter present (e.g., mass, volume).

• Intensive Properties: Independent of the amount of matter (e.g., density, temperature).

• Chemical Properties: Describe a substance's ability to undergo chemical changes (e.g., flammability, reactivity).

• Physical Properties: Can be observed without changing the substance's identity (e.g., color, melting point).

• Example: Water's boiling point (intensive, physical); mass of water (extensive, physical).

Periodic Table Regions, Groups, and Periods

The periodic table is organized into regions, groups (columns), and periods (rows).

• Groups: Vertical columns; elements in the same group have similar chemical properties.

• Periods: Horizontal rows; elements in the same period have the same number of electron shells.

• Regions: Main regions include metals, nonmetals, metalloids, transition metals, and noble gases.

• Example: Sodium (Na) is in Group 1 (alkali metals), Period 3.

Metric and English Unit Conversions

Converting between metric and English units is essential for laboratory and real-world applications.

• Mass: 1 kg = 2.2046 lb

• Length: 1 inch = 2.54 cm

• Volume: 1 L = 1.057 qt

• Example: To convert 10 inches to centimeters: $10 \times 2.54 = 25.4$ cm

Significant Figures in Measurement and Calculation

Significant figures reflect the precision of measured and calculated quantities.

• Measured Quantities: All nonzero digits are significant; zeros between nonzero digits are significant; leading zeros are not significant; trailing zeros are significant if there is a decimal point.

• Calculated Quantities: The result should reflect the least number of significant figures in the input data.

• Example: 0.00450 has three significant figures.

Density Calculations and Practical Interpretation

Density is a fundamental property used to identify substances and interpret observations.

• Definition: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Units: g/cm3 or kg/m3

• Example: If a block has a mass of 50 g and a volume of 25 cm3, its density is $\frac{50}{25} = 2$ g/cm3.

Chapter 1 and Sections 4.9–4.10: Atoms and Isotopes

Laws of Conservation of Mass, Definite Proportions, and Multiple Proportions

These laws form the foundation of chemical theory.

• Law of Conservation of Mass: Mass is neither created nor destroyed in a chemical reaction.

• Law of Definite Proportions: A compound always contains the same elements in the same proportion by mass.

• Law of Multiple Proportions: When two elements form more than one compound, the ratios of the masses of the second element that combine with a fixed mass of the first element are simple whole numbers.

• Example: CO and CO2 follow the law of multiple proportions.

Dalton’s Atomic Theory and Its Shortcomings

Dalton proposed a model for the atom, but it had limitations.

• Postulates: Elements are composed of atoms; atoms of the same element are identical; atoms combine in simple ratios; atoms are indivisible in chemical reactions.

• Shortcomings: Atoms are divisible (subatomic particles exist); isotopes show that atoms of the same element can differ.

Rutherford’s Experiments and Atomic Structure

Rutherford’s gold foil experiment revealed the nuclear model of the atom.

• Findings: Most of the atom is empty space; the nucleus is small, dense, and positively charged.

• Example: Alpha particles deflected by the nucleus.

Composition, Mass, and Volume of the Atom

The atom consists of a nucleus (protons and neutrons) and electrons.

• Nucleus: Contains most of the mass, but occupies very little volume.

• Electrons: Occupy most of the volume, but contribute little mass.

Atoms vs. Elements

An element is a substance made of one type of atom; an atom is the smallest unit of an element.

• Example: Oxygen element (O) consists of oxygen atoms.

Isotope Symbols and Calculations

Isotopes are atoms of the same element with different numbers of neutrons.

• Isotope Symbol: $^{A}_{Z}\text{X}$, where A = mass number, Z = atomic number, X = element symbol.

• Protons: Equal to atomic number (Z).

• Neutrons: $\text{Neutrons} = A - Z$

• Electrons: Equal to protons in a neutral atom.

• Example: $^{14}_{6}\text{C}$ has 6 protons, 8 neutrons, 6 electrons.

Average Atomic Mass Calculations

The average atomic mass is calculated using isotopic masses and their relative abundances.

• Formula: $\text{Average Atomic Mass} = \sum (\text{Isotopic Mass} \times \text{Fractional Abundance})$

• Example: If $^{35}\text{Cl}$ is 75% and $^{37}\text{Cl}$ is 25%, average mass = $0.75 \times 34.97 + 0.25 \times 36.97$

Calculations with Atoms, Moles, and Mass

Relating mass, moles, and number of atoms is essential for stoichiometry.

• Mass of a Single Atom: $\text{Mass} = \frac{\text{Molar Mass}}{N_A}$, where $N_A = 6.022 \times 10^{23}$

• Moles of Atoms: $\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$

• Number of Atoms: $\text{Atoms} = \text{Moles} \times N_A$

• Example: 12 g of C contains $\frac{12}{12} = 1$ mole, or $6.022 \times 10^{23}$ atoms.

Molar Mass of Compounds

The molar mass is the sum of the atomic masses of all atoms in a compound.

• Formula: $\text{Molar Mass} = \sum \text{Atomic Masses}$

• Example: H2O: $2 \times 1.01 + 16.00 = 18.02$ g/mol

Chapter 2: The Quantum-Mechanical Model of the Atom

Wavelength, Frequency, and Energy of Electromagnetic Radiation

Electromagnetic radiation is characterized by wavelength ($\lambda$), frequency ($\nu$), and energy ($E$).

• Relationship: $c = \lambda \nu$, where $c$ is the speed of light.

• Energy: $E = h \nu$, where $h$ is Planck’s constant.

• Example: If $\lambda = 500$ nm, $\nu = \frac{c}{\lambda}$

Bohr Model and Its Deficiencies

The Bohr model explains quantized energy levels but fails for multi-electron atoms.

• Bohr Model: Electrons orbit the nucleus in fixed energy levels.

• Deficiencies: Cannot explain spectra of atoms with more than one electron; does not account for electron wave behavior.

Hydrogen Emission Spectrum and Electron Transitions

Lines in the hydrogen emission spectrum are due to electron transitions between energy levels.

• When an electron drops to a lower energy level, a photon is emitted.

• Example: $n=3 \rightarrow n=2$ transition emits visible light.

Balmer-Rydberg Equation for Photon Calculations

The Balmer-Rydberg equation calculates the wavelength or energy of photons absorbed or emitted.

• Equation: $\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$, where $R$ is the Rydberg constant.

• Example: Calculate $\lambda$ for $n_1=2$, $n_2=3$.

Energy Required to Remove an Electron from Hydrogen

The energy to remove an electron from hydrogen is its ionization energy.

• Formula: $E = -2.18 \times 10^{-18} \left( \frac{1}{n^2} \right)$ J

• Example: For $n=1$, $E = -2.18 \times 10^{-18}$ J

Quantum Numbers and Their Meaning

Quantum numbers describe the properties of electrons in atoms.

• Principal Quantum Number ($n$): Energy level (shell).

• Angular Momentum Quantum Number ($l$): Subshell (shape).

• Magnetic Quantum Number ($m_l$): Orientation.

• Spin Quantum Number ($m_s$): Electron spin.

• Mathematical Limitations: $l$ ranges from 0 to $n-1$; $m_l$ from $-l$ to $+l$; $m_s$ is $+\frac{1}{2}$ or $-\frac{1}{2}$.

Assigning Quantum Numbers

Each electron in an atom has a unique set of quantum numbers.

• Example: For 2p electron: $n=2$, $l=1$, $m_l=-1,0,1$, $m_s=\pm\frac{1}{2}$

Shapes and Names of Subshells

Subshells are designated as s, p, d, f, each with characteristic shapes.

• s: Spherical

• p: Dumbbell-shaped

• d: Cloverleaf

• f: Complex

Electromagnetic Radiation Regions

Different regions of electromagnetic radiation are classified by wavelength and frequency.

• Gamma rays: Shortest wavelength, highest frequency

• X-rays, UV, Visible, IR, Microwave, Radio: Increasing wavelength, decreasing frequency

Pauli Exclusion Principle, Hund’s Rule, and Aufbau Principle

These principles govern electron arrangements in atoms.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers.

• Hund’s Rule: Electrons fill degenerate orbitals singly before pairing.

• Aufbau Principle: Electrons fill lowest energy orbitals first.

Ground-State Electron Configurations

Electron configurations show the arrangement of electrons in an atom’s orbitals.

• Example: Oxygen: 1s2 2s2 2p4

Chapter 3: Periodic Properties of the Elements

Mendeleev’s Construction of the Periodic Table

Mendeleev organized elements by increasing atomic mass and predicted properties of missing elements.

• Predictions: Properties of elements like gallium, scandium, and germanium.

Metallic vs. Nonmetallic Properties

Elements are classified as metals, nonmetals, or metalloids based on their properties.

• Metals: Shiny, conductive, malleable

• Nonmetals: Dull, poor conductors, brittle

• Example: Sodium (metal), sulfur (nonmetal)

Effective Nuclear Charge (Zeff)

Effective nuclear charge is the net positive charge experienced by an electron.

• Formula: $Z_{eff} = Z - S$, where $Z$ is atomic number, $S$ is shielding constant.

• Trend: Increases across a period, decreases down a group.

Electron Configurations for Atoms and Ions

Electron configurations differ for neutral atoms and ions.

• Example: Na: 1s2 2s2 2p6 3s1; Na+: 1s2 2s2 2p6

Orbital Diagrams and Magnetic Properties

Orbital diagrams show unpaired electrons, which determine magnetic properties.

• Paramagnetic: Atoms/ions with unpaired electrons

• Diamagnetic: Atoms/ions with all electrons paired

Anomalous Electron Configurations

Some elements have electron configurations that deviate from expected patterns.

• Example: Chromium: [Ar] 4s1 3d5 instead of [Ar] 4s2 3d4

Valence-Shell Electron Configurations

Valence electrons are those in the outermost shell, important for chemical reactivity.

• Main Group Elements: s and p electrons in the highest energy level

• Transition Metals: d electrons may also be considered

Ranking Atoms and Ions by Radius

Atomic and ionic radii vary based on electron configuration and charge.

• Trend: Decreases across a period, increases down a group

• Cations: Smaller than parent atom

• Anions: Larger than parent atom

Formation of Cations and Anions

Elements tend to lose or gain electrons to achieve stable electron configurations.

• Metals: Lose electrons to form cations

• Nonmetals: Gain electrons to form anions

Ionization Energy Trends

Ionization energy is the energy required to remove an electron from an atom.

• First Ionization Energy: Increases across a period, decreases down a group

• Successive Ionization Energies: Each removal requires more energy

Electron Affinity and Electronegativity

Electron affinity is the energy change when an atom gains an electron; electronegativity is the tendency to attract electrons in a bond.

• Trend: Both increase across a period, decrease down a group

• Example: Fluorine has the highest electronegativity

Electrons Gained or Lost in Ion Formation

The number of electrons gained or lost depends on the element’s group.

• Example: Group 1 elements lose 1 electron; Group 17 elements gain 1 electron

Property	Trend Across Period	Trend Down Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Increases	Decreases
Electronegativity	Increases	Decreases

Additional info: These notes expand on the learning goals by providing definitions, examples, and formulas for each topic, making them suitable for exam preparation in a general chemistry course.