The Periodic Table: Trends and Properties

Learning Outcomes

• Recognise the arrangement of elements in the periodic table according to increasing atomic number.

• Differentiate between various classes and groups: periods and groups, metals, non-metals, metalloids, alkali metals, alkaline earth metals, transition metals, halogens, inert (noble) gases, lanthanides, and actinides.

• Define the concept of "effective nuclear charge" ($Z_{eff}$).

• Define and describe the periodic trends (variation across a period and down a group) for:

  • Atomic radius

  • Ionic radius

  • Ionisation energy

  • Electron affinity

  • Electronegativity

Historical Context: Mendeleev’s Periodic Table

• Dmitri Mendeleev (1834 – 1907) published the first arrangement of elements in 1869.

• Characteristics of Mendeleev's work:

  • He had no knowledge of what atoms were made of or why they behaved as they did (discovery of subatomic particles came later).

  • He organised elements primarily in order of increasing atomic mass.

  • He noticed gaps in his table and used them to predict the existence and properties of several undiscovered elements.

The Modern Periodic Table

• Elements are arranged according to increasing atomic number ($Z$), representing the number of protons.

• Periods: Horizontal rows that indicate the energy levels being filled.

• Groups: Vertical columns grouping elements that show similar chemical properties.

• Metals: Good conductors of heat and electricity.

• Non-metals: Usually poor conductors of heat and electricity.

• Elements within a group show great variety but maintain similarities in physical and chemical properties. For example, Group I (Alkali Metals) and Group VII (Halogens) are among the most reactive elements.

Valence Electrons and Nuclear Attraction

• The attraction between the positive nucleus and the outermost negative electrons (valence electrons) is determined by three factors:

  1. The number of protons in the nucleus (nuclear charge).

  2. The distance from the nucleus to the valence shell.

  3. The shielding effect of inner-shell electrons that are closer to the nucleus.

• Valence electrons are crucial because they participate in the sharing and exchange processes responsible for chemical reactions.

Effective Nuclear Charge ($Z_{eff}$)

• Definition: The effective nuclear charge is the net nuclear charge felt by an electron when both the actual nuclear charge ($Z$) and the repulsive effects (shielding) of other electrons are taken into account.

• Formula: $Z_{eff} = Z - \sigma$

• Variables:

  • $Z$ = actual nuclear charge (number of protons).

  • $\sigma$ (sigma) = shielding constant (also called the screening constant).

• The shielding constant $\sigma$ is always greater than zero but smaller than $Z$.

Trends in Effective Nuclear Charge

• Across a Period (Left to Right):

  • $Z_{eff}$ increases.

  • While $Z$ increases, the added electrons are valence electrons. Valence electrons do not shield each other effectively.

  • Therefore, the outermost electrons feel a greater pull from the nucleus.

• Down a Group:

  • $Z_{eff}$ increases as calculated per Slater's rules.

  • Slater's rules account for the shielding of electrons in each specific orbital "shell."

Atomic Radius

• Definition: The atomic radius is defined as half the distance between the nuclei of two adjacent atoms of the same element.

Periodic Trends

• Across a Period:

  • As atomic number ($Z$) increases, the number of protons in the nucleus increases.

  • Electrons are added to the same main energy level.

  • Effective nuclear charge ($Z_{eff}$) increases.

  • This results in a "Bigger attraction," pulling electrons closer and causing the atomic radius to decrease.

• Down a Group:

  • Electrons enter higher/additional energy levels.

  • This creates a greater physical distance between the nucleus and the outermost shell.

  • As a result, the atomic radius increases.

Ionic Radius

• Definition: The radius of a cation (positive ion) or an anion (negative ion).

Formation of Anions ($X^-$)

• An extra electron is added to the atom.

• The nuclear charge remains the same.

• There is greater repulsion among the electrons.

• Example: Chlorine atom ($Cl$) has a radius of $99\,pm$ (17 protons, 17 electrons), while the Chloride ion ($Cl^-$) has a radius of $181\,pm$ (17 protons, 18 electrons).

• Result: Size increases; ionic radius is larger than the parent atom.

Formation of Cations ($X^+$)

• Electrons are removed from the atom.

• The nuclear charge remains the same.

• There is less repulsion among the remaining electrons.

• Example: Sodium atom ($Na$) has electronic configuration $1s^2 2s^2 2p^6 3s^1$ and a radius of $186\,pm$. The Sodium ion ($Na^+$) has configuration $1s^2 2s^2 2p^6$ and a radius of $99\,pm$.

• Result: Size decreases; ionic radius is smaller than the parent atom.

Isoelectronic Species and Comparison

• Definition: Species with the same number of electrons (e.g., $Na^+$ and $Mg^{2+}$ both have 10 electrons).

• Comparison of $Na^+$ vs $Mg^{2+}$:

  • $Na^+$: 11 protons, 10 electrons ($Radius = 99\,pm$).

  • $Mg^{2+}$: 12 protons, 10 electrons ($Radius = 65\,pm$).

  • Higher nuclear charge in $Mg^{2+}$ creates a stronger attraction, making it smaller.

  • Rule: Radius of a dipositive ion < Radius of a unipositive ion.

• Comparison of $O^{2-}$ vs $F^-$:

  • $O^{2-}$: 8 protons, 10 electrons.

  • $F^-$: 9 protons, 10 electrons.

  • $F^-$ has a higher nuclear charge, leading to a smaller size.

  • Rule: Radius of a dinegative ion > Radius of a uninegative ion.

Biological Application

• Ions move through channels in cell membranes. Selectivity in these channels is often based on size; for instance, some channels allow $Na^+$ passage but exclude the larger $K^+$ ion.

Ionisation Energy (IE)

• Definition: The minimum energy ($kJ\,mol^{-1}$) required to remove an electron from a gaseous atom in its ground state.

• First Ionisation Energy ($IE_1$): $M(g) \rightarrow M^+(g) + e^-$

• Second Ionisation Energy ($IE_2$): $M^+(g) \rightarrow M^{2+}(g) + e^-$

• Third Ionisation Energy ($IE_3$): $M^{2+}(g) \rightarrow M^{3+}(g) + e^-$

Periodic Trends

• Across a Period:

  • Nuclear charge ($Z$) and $Z_{eff}$ increase.

  • Attraction between nucleus and electrons becomes stronger.

  • Ionisation energy increases.

• Down a Group:

  • Electrons enter higher energy levels, increasing distance from the nucleus.

  • Nuclear attraction weakens due to distance.

  • Ionisation energy decreases.

• Group Specifics: Alkali metals generally have the lowest ionisation energies, while Noble gases have the highest.

Exceptions in Ionisation Energy

• Dips are observed in specific Period 2 pairs due to electronic stability:

  • $Be$ vs $B$: $Be$ ($1s^2 2s^2$) has a full s-subshell, making it harder to remove an electron than from $B$ ($1s^2 2s^2 2p^1$).

  • $N$ vs $O$: $N$ ($1s^2 2s^2 2p^3$) has a half-filled p-subshell, which provides stability compared to the pairing repulsion in $O$ ($1s^2 2s^2 2p^4$).

Electron Affinity (EA)

• Definition: The negative of the energy change ($\Delta H$) that occurs when an electron is accepted by an atom in the gaseous state to form an anion.

• Equation: $X(g) + e^- \rightarrow X^-(g)$

• Sign Convention: If energy is released, $\Delta H$ is negative. The more positive the Electron Affinity, the greater the affinity of the atom for the electron.

• Example: $F(g) + e^- \rightarrow F^-(g)$, $\Delta H = -328\,kJ\,mol^{-1}$. The Electron Affinity is therefore $+328\,kJ\,mol^{-1}$.

Electronegativity

• Definition: The ability of an atom to attract toward itself the electrons in a chemical bond.

• Bonding implications:

  • Shared equally ($H:H$): No dipole.

  • Shared unequally ($H:F$): Fluorine is more electronegative, pulling electrons toward itself, creating a dipole ($H^{\delta+} - F^{\delta-}$).

Trends in Electronegativity

• Fluorine ($F$): The most electronegative element.

  • High nuclear charge with minimal shielding.

  • Related to high electron affinity (picks up electrons easily) and high ionisation energy (does not lose electrons easily).

• Mnemonic: "Front Office Never Closes" for the most electronegative elements: $F > O > N > C$.

• Across a Period: Electronegativity increases.

• Down a Group: Electronegativity decreases.

Summary of Periodic Trends

• Recognise the arrangement of elements in the periodic table according to increasing atomic number:

  • Elements are organized from left to right, starting with hydrogen (atomic number 1) and proceeding sequentially through the table based on their atomic numbers, which reflects the number of protons in the nucleus of each atom.

• Differentiate between various classes and groups: periods and groups, metals, non-metals, metalloids, alkali metals, alkaline earth metals, transition metals, halogens, inert (noble) gases, lanthanides, and actinides:

  • Periods are horizontal rows that represent the principal energy levels being filled with electrons. Each period corresponds to the filling of a new electron shell.

  • Groups are vertical columns that categorize elements based on shared chemical and physical properties. For instance, Group I contains alkali metals, which are highly reactive, while Group VIII contains noble gases, which are inert.

  • Elements can also be classified into three broad categories: metals (good conductors of heat and electricity, typically malleable and ductile), non-metals (poor conductors, often brittle, and diverse in physical properties), and metalloids (exhibit properties intermediate between metals and non-metals).

• Define the concept of "effective nuclear charge" ($Z_{eff}$):

  • Effective nuclear charge represents the net positive charge experienced by an electron in a multi-electron atom. It takes into account both the actual nuclear charge (the total charge of the nucleus due to protons) and the shielding or screening effect of other electrons that repel the outer electrons.

  • This concept helps explain trends in atomic size, ionization energy, and electronegativity across the periodic table.

• Define and describe the periodic trends for:

  • Atomic radius - The size of an atom generally decreases across a period from left to right due to increased effective nuclear charge. Conversely, it increases down a group due to the addition of electron shells.

  • Ionic radius - The size of ions is affected by electron gain or loss. Anions are larger than their parent atoms due to increased electron-electron repulsion, while cations are smaller due to the loss of electrons and reduced repulsion among the remaining electrons.

  • Ionisation energy - The energy required to remove an electron from an atom. It increases across a period due to increased nuclear charge and decreases down a group as electrons are further from the nucleus.

  • Electron affinity - The energy change when an electron is added to a neutral atom in its gaseous state. Generally, this energy release becomes more negative across a period and less negative down a group.

  • Electronegativity - The tendency of an atom to attract electrons in a chemical bond. It increases across a period due to higher nuclear charge and decreases down a group due to increased distance between the nucleus and bonding electrons.