CHE-103 Chapter 2

Comprehensive Study Guide on Atomic Structure, Elements, and Periodic Trends

Fundamentals of Elements and Matter

• Definition of an Element: An element is a pure substance that cannot be broken down into simpler substances by a chemical reaction.

• Element Symbols: Each element is identified by a unique one- or two-letter symbol. The first letter is always capitalized, and the second letter is always lowercase.

• Common Elements and Their Symbols:

  | Element | Symbol | Element | Symbol |   | :--- | :--- | :--- | :--- |   | Bromine | $\text{Br}$ | Magnesium | $\text{Mg}$ |   | Calcium | $\text{Ca}$ | Manganese | $\text{Mn}$ |   | Carbon | $\text{C}$ | Molybdenum | $\text{Mo}$ |   | Chlorine | $\text{Cl}$ | Nitrogen | $\text{N}$ |   | Chromium | $\text{Cr}$ | Oxygen | $\text{O}$ |   | Cobalt | $\text{Co}$ | Phosphorus | $\text{P}$ |   | Copper | $\text{Cu}$ | Potassium | $\text{K}$ |   | Fluorine | $\text{F}$ | Sodium | $\text{Na}$ |   | Hydrogen | $\text{H}$ | Sulfur | $\text{S}$ |   | Iodine | $\text{I}$ | Zinc | $\text{Zn}$ |   | Lead | $\text{Pb}$ | | |

Classification of Elements in the Periodic Table

• Elements are arranged in the periodic table, where an element's position provides extensive information regarding its chemical properties.

• Elements are categorized into three main distinct classes: metals, nonmetals, and metalloids.

Metals

• Location: Situated on the left side of the periodic table.

• Properties: Good conductors of heat and electricity.

• Physical State: Shiny solids at room temperature, with the sole exception of mercury ($\text{Hg}$), which is a liquid.

Nonmetals

• Location: Situated on the right side of the periodic table.

• Properties: Have a dull appearance and are poor conductors of heat and electricity.

• Physical State: Can exist as solids, liquids, or gases at room temperature:

  • Solids: Examples include sulfur ($\text{S}$) and carbon ($\text{C}$).

  • Liquid: Bromine ($\text{Br}$).

  • Gases: Examples include nitrogen ($\text{N}_2$) and oxygen ($\text{O}_2$).

Metalloids

• Location: Located along the solid diagonal line that begins at boron ($\text{B}$) and angles down toward astatine ($\text{At}$).

• Properties: Possess intermediate properties between metals and nonmetals.

• Elements Included: Exactly seven elements are classified as metalloids:

  1. Boron ($\text{B}$)

  2. Silicon ($\text{Si}$)

  3. Germanium ($\text{Ge}$)

  4. Arsenic ($\text{As}$)

  5. Antimony ($\text{Sb}$)

  6. Tellurium ($\text{Te}$)

  7. Astatine ($\text{At}$)

Biological Roles of Elements in the Human Body

Building-Block Elements

• Comprise almost $96\%$ of the total mass of the human body.

• The four building-block elements are:

  • Oxygen ($\text{O}$)

  • Carbon ($\text{C}$)

  • Hydrogen ($\text{H}$)

  • Nitrogen ($\text{N}$)

• Muscle tissue contains all four building-block elements.

• Carbon, hydrogen, and oxygen form the framework for all four main classes of biological molecules: proteins, carbohydrates, lipids, and nucleic acids. Proteins and nucleic acids additionally contain nitrogen.

• The six elements of life ($\text{C}, \text{H}, \text{O}, \text{N}, \text{P}, \text{S}$) make up over $97\%$ of the total mass of living organisms.

  • Phosphorus ($\text{P}$): Forms the structural backbone of DNA and RNA; essential for energy transfer molecules such as adenosine triphosphate (ATP).

  • Sulfur ($\text{S}$): Assists proteins in maintaining stable three-dimensional configurations via specific chemical crosslinks.

Major Minerals

• Present in quantities of $0.1-2\%$ by mass in the body.

• A minimum daily dietary intake of at least $100\,\text{mg}$ of each major mineral is required.

• Body Fluids: Potassium ($\text{K}$), sodium ($\text{Na}$), and chlorine ($\text{Cl}$) are present in body fluids.

• Muscle Proteins: Magnesium ($\text{Mg}$) and sulfur ($\text{S}$) are present in muscle proteins.

• Bones and Teeth: Calcium ($\text{Ca}$) and phosphorus ($\text{P}$) form structural components of teeth and bones.

Trace Elements

• Each trace element is present in amounts less than $0.1\%$ by mass.

• Daily dietary requirements are small ($15\,\text{mg}$ or less for each element).

• Complete list of required trace elements: Arsenic ($\text{As}$), Boron ($\text{B}$), Chromium ($\text{Cr}$), Cobalt ($\text{Co}$), Copper ($\text{Cu}$), Fluorine ($\text{F}$), Iodine ($\text{I}$), Iron ($\text{Fe}$), Manganese ($\text{Mn}$), Molybdenum ($\text{Mo}$), Nickel ($\text{Ni}$), Selenium ($\text{Se}$), Silicon ($\text{Si}$), and Zinc ($\text{Zn}$).

Compounds and Molecular Representations

• Compound Definition: A pure substance formed by chemically combining two or more elements in a fixed ratio.

• Chemical Formula: Consists of element symbols identifying the constituent elements and numeric subscripts indicating the precise ratio of atoms.

  • Example 1: $\text{H}_2\text{O}$ contains 2 Hydrogen ($\text{H}$) atoms and 1 Oxygen ($\text{O}$) atom.

  • Example 2: $\text{C}_3\text{H}_8$ contains 3 Carbon ($\text{C}$) atoms and 8 Hydrogen ($\text{H}$) atoms.

Standard Spherical Color Designations for Elements

• In ball-and-stick and space-filling representations, specific color conventions represent individual elements:

• Carbon ($\text{C}$): Black

• Hydrogen ($\text{H}$): White

• Oxygen ($\text{O}$): Red

• Nitrogen ($\text{N}$): Blue

• Fluorine ($\text{F}$): Yellow-green / Light Yellow

• Chlorine ($\text{Cl}$): Green

• Bromine ($\text{Br}$): Brown / Dark Red

• Iodine ($\text{I}$): Purple

• Sulfur ($\text{S}$): Yellow

• Phosphorus ($\text{P}$): Orange

Structure of the Atom

• All matter is composed of basic building blocks called atoms.

• Atoms contain three subatomic particles: protons, neutrons, and electrons.

Subatomic Architecture

• Nucleus:

  • Dense core located at the center of the atom.

  • Contains protons and neutrons.

  • Accounts for virtually all of the atom's mass.

  • Approximate nuclear diameter: $10^{-15}\,\text{m}$.

• Electron Cloud:

  • Surrounds the nucleus and contains all electrons.

  • Comprises most of the atom's total volume.

  • Consists predominantly of empty space.

  • Approximate atomic diameter: $10^{-10}\,\text{m}$.

Electrostatic Principles

• Opposite charges attract; like charges repel.

• Protons ($+1$) and electrons ($-1$) attract one another.

• Like charges repel each other (protons repel protons; electrons repel electrons).

Atomic Number, Mass Number, and Isotopes

Atomic Number ($Z$)

• Equal to the number of protons contained within the nucleus of an atom.

• Every atom of a given element possesses the identical number of protons.

• Different elements have distinct atomic numbers.

• In a neutral atom, there is no overall net charge, establishing the relation:   $\text{Atomic Number }(Z) = \text{Number of Protons} = \text{Number of Electrons}$

Mass Number ($A$) and Isotopes

• Mass Number ($A$): Defined as the total sum of protons ($Z$) and neutrons in an atom's nucleus:   $\text{Mass Number }(A) = \text{Number of Protons }(Z) + \text{Number of Neutrons}$

• Isotopes: Atoms of the same element that contain the same number of protons but different numbers of neutrons.

• Example — Chlorine Isotopes:

• Chlorine-35 ($^{35}_{17}\text{Cl}$):

  • Protons = $17$

  • Electrons = $17$

  • Neutrons = $35 - 17 = 18$

• Chlorine-37 ($^{37}_{17}\text{Cl}$):

  • Protons = $17$

  • Electrons = $17$

  • Neutrons = $37 - 17 = 20$

Atomic Weight

• The atomic weight reported on the periodic table represents the weighted average mass of the naturally occurring isotopes of an element, expressed in atomic mass units ($\text{amu}$ or daltons).

• Determination of Atomic Weight Step-by-Step:

  1. List each naturally occurring isotope, its precise mass in $\text{amu}$, and its fractional abundance in nature.

  2. Multiply the fractional isotopic abundance by the corresponding mass for each isotope.

  3. Sum the calculated products to yield the atomic weight.

• Worked Example for Chlorine:

  • Isotope $\text{Cl-35}$: Mass = $34.97\,\text{amu}$, Abundance = $75.78\% = 0.7578$

  • Isotope $\text{Cl-37}$: Mass = $36.97\,\text{amu}$, Abundance = $24.22\% = 0.2422$

  • Calculations:     $34.97\,\text{amu} \times 0.7578 = 26.5003\,\text{amu}$     $36.97\,\text{amu} \times 0.2422 = 8.9541\,\text{amu}$

  • Sum of components:     $26.5003\,\text{amu} + 8.9541\,\text{amu} = 35.4544\,\text{amu} \approx 35.45\,\text{amu}$

Organization of the Periodic Table

• Periods: Horizontal rows in the periodic table (numbered 1 through 7).

• Groups: Vertical columns in the periodic table containing elements with shared chemical characteristics.

  • Main Group Elements: The tall columns situated on the left and right sides of the periodic table, numbered $1\text{A}$ to $8\text{A}$.

  • Transition Metal Elements: The 10 shorter central columns, numbered $1\text{B}$ to $8\text{B}$.

  • Inner Transition Elements: Consist of the lanthanides and actinides listed separately below the main table (no group numbers assigned).

Characteristics of Specific Groups

• Group 1A (Alkali Metals): Includes lithium, sodium, potassium, rubidium, cesium, and francium (excluding hydrogen).

  • Soft and shiny metals with low melting points.

  • Exceptional conductors of heat and electricity.

  • React vigorously with water to generate basic (alkaline) solutions.

• Group 2A (Alkaline Earth Elements): Includes beryllium, magnesium, calcium, strontium, barium, and radium.

  • Soft and shiny metals with low melting points.

  • Good conductors of heat and electricity.

  • React with water to form basic solutions.

• Group 7A (Halogens): Includes fluorine, chlorine, bromine, iodine, and astatine.

  • Exist in elemental form as diatomic molecules (two atoms bonded together, e.g., $\text{F}_2, \text{Cl}_2, \text{Br}_2, \text{I}_2$).

  • Highly reactive chemical species.

• Group 8A (Noble Gases): Includes helium, neon, argon, krypton, xenon, and radon.

  • Extremely stable and unreactive.

  • Rarely enter into chemical combination with other elements.

Electronic Structure of the Atom

• Electrons reside in designated regions around the nucleus, defining specific energy values.

• Principal Energy Levels (Shells, $n$):

  • Numbered sequentially $n = 1, 2, 3, 4, \dots$

  • Electrons in lower-numbered shells reside closer to the nucleus and possess lower energy.

  • Electrons in higher-numbered shells are situated further from the nucleus and possess higher energy.

• Maximum Shell Capacity:

  • The maximum number of electrons that can occupy a given principal shell $n$ is calculated using the formula:     $\text{Maximum Electrons} = 2n^2$

  • Shell Occupancy Table:

  • Shell $n = 1$: $2(1)^2 = 2$ electrons.

  • Shell $n = 2$: $2(2)^2 = 8$ electrons.

  • Shell $n = 3$: $2(3)^2 = 18$ electrons.

  • Shell $n = 4$: $2(4)^2 = 32$ electrons.

Subshells and Orbitals

• Shells are divided into subshells denoted by the letters $s, p, d,$ and $f$

• Orbital: A localized region of space wherein the probability of finding an electron is high. Every single orbital holds a maximum of 2 electrons.

• Subshell Breakdown:

  | Subshell | Number of Orbitals | Maximum Electron Capacity |   | :--- | :--- | :--- |   | $s$ | $1$ | $2$ |   | $p$ | $3$ | $3 \times 2 = 6$ |   | $d$ | $5$ | $5 \times 2 = 10$ |   | $f$ | $7$ | $7 \times 2 = 14$ |

Orbital Shapes

• $s$ Orbital: Spherical shape. The spherical volume expands in size as the principal quantum shell $n$ increases.

• $p$ Orbitals: Dumbbell shape. Three orthogonal orientations exist ($p_x, p_y, p_z$) aligned at $90^\circ$ angles to one another along perpendicular Cartesian axes.

Electron Configurations

• Definition: Description of how electrons are distributed among available atomic orbitals.

• Ground State: The lowest energy electronic arrangement of an atom.

Governing Filling Rules

1. Aufbau Principle: Electrons occupy the lowest available energy orbital starting with $1s$. Orbitals fill in strict order of increasing energy:    $1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 5s \rightarrow 4d \rightarrow 5p \rightarrow 6s \rightarrow 4f \rightarrow 5d \rightarrow 6p \rightarrow 7s \rightarrow 5f \rightarrow 6d$    Note: The $4s$ subshell is lower in energy than the $3d$ subshell and is filled prior to filling $3d$

2. Pauli Exclusion Principle: An orbital can contain a maximum of 2 electrons. To occupy the same orbital, two electrons must possess paired (opposite) spins.

3. Hund's Rule: When orbitals of equal energy (degenerate orbitals) are available, 1 electron is added to each orbital with parallel spins until all orbitals in the subshell are half-filled before any orbital receives a second electron.

Orbital Diagrams

• Uses boxes to represent individual orbitals and arrows to depict electrons.

  • An empty box represents an empty orbital.

  • A single upward arrow ($\uparrow$) represents a single unpaired electron.

  • Antiparallel arrows ($\uparrow\downarrow$) represent a fully occupied electron pair with opposite spins.

Electron Configurations across Periods

• Period 1 Elements:

  • Hydrogen ($\text{H}, Z = 1$): $1s^1$

  • Helium ($\text{He}, Z = 2$): $1s^2$

• Period 2 Examples:

  • Lithium ($\text{Li}, Z = 3$): $1s^2 2s^1$

  • Carbon ($\text{C}, Z = 6$): $1s^2 2s^2 2p^2$

  • Neon ($\text{Ne}, Z = 10$): $1s^2 2s^2 2p^6$

Noble Gas Notation

• Shortened notation format wherein the electron configuration of the preceding noble gas is represented by its symbol in brackets, followed by the configuration of the outer electrons.

  • Carbon ($\text{C}$): $1s^2 2s^2 2p^2 \rightarrow [\text{He}] 2s^2 2p^2$

  • Calcium ($\text{Ca}, Z = 20$): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 \rightarrow [\text{Ar}] 4s^2$

Subshell Blocks in the Periodic Table

• $s\text{-Block}$: Consists of Groups $1\text{A}$ and $2\text{A}$ (plus Helium).

• $p\text{-Block}$: Consists of Groups $3\text{A}$ through $8\text{A}$ (except Helium).

• $d\text{-Block}$: Transition metals.

• $f\text{-Block}$: Inner transition metals (Lanthanides and Actinides).

Valence Electrons and Lewis Structures

• Valence Shell: The outermost principal quantum shell (highest numerical value of $n$).

• Valence Electrons: Electrons located within the valence shell. These electrons dictate the chemical reactivity and bonding behavior of an element.

  • Beryllium ($\text{Be}$): Valence shell $n = 2$; possesses 2 valence electrons.

  • Chlorine ($\text{Cl}$): Valence shell $n = 3$; possesses 7 valence electrons.

• Group Number Relationship: For main group elements (Groups $1\text{A}-8\text{A}$), the group number equals the exact number of valence electrons (Helium is the exception, possessing 2 valence electrons despite being in Group $8\text{A}$).

Electron-Dot (Lewis) Symbols

• Consists of the element symbol surrounded by dots representing individual valence electrons placed on four sides (top, bottom, left, right).

• Single dots are used for 1 to 4 valence electrons; dots are paired when more than 4 valence electrons are present.

• Representative Examples:

  • Hydrogen ($\text{H}$): $\text{H}\cdot$ (1 valence electron)

  • Carbon ($\text{C}$): $\cdot\dot{\text{C}}\cdot$ (4 valence electrons placed singly)

  • Oxygen ($\text{O}$): $\cdot\ddot{\text{O}}\cdot$ (6 valence electrons: 2 pairs and 2 single dots)

  • Chlorine ($\text{Cl}$): $\cdot\ddot{\text{Cl}}\mathbf{:}$ (7 valence electrons: 3 pairs and 1 single dot)

Periodic Trends

Atomic Size (Atomic Radius)

• Down a Group: Atomic size increases down a column because additional principal shells ($n$) are added, placing valence electrons progressively further from the nucleus.

• Across a Period: Atomic size decreases from left to right across a row because the nuclear charge increases (more protons), pulling electrons closer toward the nucleus.

Ionization Energy

• Definition: The minimum quantity of energy required to remove an electron from a neutral gaseous atom.

• Chemical Equation Representation:   $\text{Na} + \text{energy} \rightarrow \text{Na}^+ + e^-$

• Down a Group: Ionization energy decreases down a column because valence electrons reside further from the positively charged nucleus and are held less tightly.

• Across a Period: Ionization energy increases across a row due to increasing effective nuclear attraction.

Practical Problems and Applied Calculations

Patient Unit Conversion Problem

• Problem Statement: On admission to the hospital, a patient weighed $60.6\,\text{kg}$ and was $67\,\text{in.}$ tall.

  • (a) What is the weight of the patient in pounds ($\text{lbs}$)?

  • (b) What is the height of the patient in centimeters ($\text{cm}$)?

• Calculations:

  • (a) Conversion factor: $1\,\text{kg} = 2.20462\,\text{lbs}$     $\text{Weight} = 60.6\,\text{kg} \times 2.20462\,\text{lbs/kg} = 133.6\,\text{lbs} \approx 134\,\text{lbs}$

  • (b) Conversion factor: $1\,\text{in.} = 2.54\,\text{cm}$     $\text{Height} = 67\,\text{in.} \times 2.54\,\text{cm/in.} = 170.18\,\text{cm} \approx 170\,\text{cm}$

Graduated Cylinder Density Identification and Mass Problem

• Problem Statement: A graduated cylinder contains three liquids: water ($\text{density} = 1.00\,\text{g/mL}$), corn syrup ($\text{density} = 1.37\,\text{g/mL}$), and corn oil ($\text{density} = 0.93\,\text{g/mL}$).

  • (a) Identify the liquid that corresponds to layers A, B, and C in the cylinder.

  • (b) Determine how many grams of each liquid are present given the cylinder volume readings.

• Solutions:

  • (a) Identification by Density Stratification (Lowest density floats on top; highest density sinks to the bottom):

  • Layer A (Top): Corn oil (lowest density = $0.93\,\text{g/mL}$).

  • Layer B (Middle): Water (intermediate density = $1.00\,\text{g/mL}$).

  • Layer C (Bottom): Corn syrup (highest density = $1.37\,\text{g/mL}$).

  • (b) Mass Determinations (using $\text{Mass} = \text{Density} \times \text{Volume}$):

  • Volume Readings from Diagram:

    • Layer C ($0\,\text{mL}$ to $100\,\text{mL}$): Volume = $100\,\text{mL}$.

    • Layer B ($100\,\text{mL}$ to $150\,\text{mL}$): Volume = $50\,\text{mL}$.

    • Layer A ($150\,\text{mL}$ to $180\,\text{mL}$): Volume = $30\,\text{mL}$.

  • Mass Calculations:

    • Layer A (Corn oil): $30\,\text{mL} \times 0.93\,\text{g/mL} = 27.9\,\text{g}$

    • Layer B (Water): $50\,\text{mL} \times 1.00\,\text{g/mL} = 50.0\,\text{g}$

    • Layer C (Corn syrup): $100\,\text{mL} \times 1.37\,\text{g/mL} = 137\,\text{g}$

Mass Identification Question

• Question: Which element possesses an atomic mass of approximately $40\,\text{daltons}$ ($\text{Da}$)?

  • Options: A: $\text{H}$, B: $\text{O}$, C: $\text{Ca}$, D: $\text{Cl}$

• Answer: C: Calcium ($\text{Ca}$), which possesses an atomic weight of $40.08\,\text{Da}$.