Valence Electrons, the Octet Rule, and Oxidation Numbers

Overview of Module 4 Lesson 1: Electrons and the Periodic Table

• This content serves as a continuation of previous lessons in Module 4, specifically Lesson 1, focusing on the relationship between electron configuration and the periodic table.
• Fundamental goals include identifying valence electrons, understanding reactivity, applying the octet rule, and determining oxidation numbers.
• Electron configurations can be written in full or in a shortened noble gas configuration, which directly correlates to an element's chemical behavior.

Anatomy of the Atom: Inner Cores vs. Valence Electrons

• Every atom is composed of an inner core of electrons and an outer shell of electrons.
• Inner Core Electrons (Noble Gas Core):
  • These electrons are not very reactive.
  • They do not participate in chemical reactions or bonding with other atoms.
  • This core is often called the "noble gas core" because noble gases are inert.
• Outer Electrons (Valence Electrons):
  • These are the electrons located in the outermost energy shell.
  • They are more reactive and are typically involved in chemical reactions with other elements.
  • Behavior: These electrons can be lost to another atom, gained from another atom, or shared between atoms during the formation of chemical compounds.
  • Significance: The specific number of valence electrons determines the reactivity and chemical properties of the atom.

Determining Valence Electrons for Non-Transition Metals

• The Highest $n$ Rule: For non-transition metals (main group elements), all electrons inhabiting the highest value of $n$ (the energy level) are counted as valence electrons.
• Example: Potassium ($K$)
  • Electron Configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1$
  • Highest $n$ value: $4$
  • Wait: There is only one electron in the $4s$ subshell.
  • Total valence electrons: $1$
• Example: Krypton ($Kr$)
  • Electron Configuration ends in $4p^6$.
  • Highest $n$ value: $4$
  • Distribution: There are $2$ electrons in the $4s$ subshell and $6$ electrons in the $4p$ subshell.
  • Calculation: $2 + 6 = 8$
  • Total valence electrons: $8$
• Example: Sulfur ($S$)
  • Noble Gas Configuration: $[Ne]3s^2 3p^4$
  • Highest $n$ value: $3$
  • Calculation: $2 + 4 = 6$
  • Total valence electrons: $6$
• Example: Astatine ($At$)
  • Noble Gas Configuration: $[Xe]6s^2 5d^{10} 6p^5$
  • Highest $n$ value: $6$
  • Note: While $5d$ is present, we only count subshells with the highest $n$ ($6$).
  • Calculation: $2 + 5 = 7$
  • Total valence electrons: $7$

Determining Valence Electrons for Transition and Inner Transition Metals

• Transition and inner transition metals are more complex. The valence count is found by taking the electrons in the highest energy level ($n$) and adding any electrons in unfilled $d$ or $f$ subshells.
• Example: Manganese ($Mn$)
  • Electron Configuration ends in $4s^2 3d^5$.
  • Highest $n$ value: $4$ (contains $2$ electrons).
  • Unfilled subshell: $3d^5$ (contains $5$ electrons; it is unfilled because a full $d$ subshell holds $10$).
  • Calculation: $2 + 5 = 7$
  • Total valence electrons: $7$
• Example: Silver ($Ag$)
  • Configuration ends in $5s^2 4d^9$.
  • Highest $n$ value: $5$ (contains $2$ electrons).
  • Unfilled subshell: $4d^9$ (contains $9$ electrons).
  • Calculation: $2 + 9 = 11$
  • Total valence electrons: $11$
• Example: Titanium ($Ti$)
  • Configuration: $[Ar]4s^2 3d^2$
  • Highest $n$ value: $4$ (contains $2$ electrons).
  • Unfilled subshell: $3d^2$ (contains $2$ electrons).
  • Calculation: $2 + 2 = 4$
  • Total valence electrons: $4$
• Example: Plutonium ($Pu$)
  • Configuration: $[Rn]7s^2 5f^5$
  • Highest $n$ value: $7$ (contains $2$ electrons).
  • Unfilled subshell: $5f^5$ (contains $5$ electrons; it is unfilled because a full $f$ subshell holds $14$).
  • Calculation: $2 + 5 = 7$
  • Total valence electrons: $7$

Main Group Practice: Arsenic and Copper

• Arsenic ($As$):
  • Ends in $4p^3$.
  • Not a transition metal.
  • Highest $n$ is $4$. Subshells include $4s^2$ and $4p^3$.
  • Calculation: $2 + 3 = 5$
  • Total valence electrons: $5$
• Copper ($Cu$):
  • Ends in $3d^9$.
  • Identified as a transition metal in the periodic table.
  • Highest $n$ is $4$. Subshell is $4s^2$.
  • Unfilled subshell: $3d^9$.
  • Calculation: $2 + 9 = 11$
  • Total valence electrons: $11$

The Periodic Table Hack for Valence Electrons

• Elements within the same group (column) share the same number of valence electrons because they have identical ending subshell configurations (e.g., all alkali metals end in $s^1$).
• The Sequential Order (Skipping Transition Metals):
  • Group 1: $1$ valence electron.
  • Group 2: $2$ valence electrons.
  • (Skip Transition Metals).
  • Group 13: $3$ valence electrons.
  • Group 14: $4$ valence electrons.
  • Group 15: $5$ valence electrons.
  • Group 16: $6$ valence electrons.
  • Group 17: $7$ valence electrons.
  • Group 18: $8$ valence electrons (Noble Gases).
• Exceptions:
  • Helium ($He$): Located in Group 18 with noble gases but only has $2$ valence electrons. This is because its only energy level ($n=1$) is full to capacity with only $2$ electrons.

The Octet Rule and Chemical Stability

• Stability Definition: Atoms with a full outer shell are stable and "happy." They do not react easily because they are in a state of high stability.
• Capacity Thresholds:
  • First energy level atoms ($n=1$): Stable with $2$ valence electrons.
  • Atoms with more than one energy level ($n > 1$): Stable with $8$ valence electrons in the outer shell.
• The Octet Rule: Chemical compounds tend to form so that each atom, by gaining, losing, or sharing electrons, achieves an octet (8 electrons) in its highest occupied energy level.
• Noble gases (except Helium) naturally possess $8$ valence electrons, making them inert.

Ion Formation and Electron Transfer

• Atoms will take the path of least resistance to reach stability. This involves either losing few electrons or gaining few electrons to reach a full shell.
• Sodium ($Na$) Example:
  • Neutral state: $11$ protons, $11$ electrons ($2$ in level 1, $8$ in level 2, $1$ in level 3).
  • Option: Lose $1$ electron from level 3 or gain $7$ to fill level 3.
  • Path: Sodium tends to lose the single electron.
  • Result: Level 2 becomes the new outer shell (with $8$ electrons). The charge becomes $1+$ due to having $11$ protons and only $10$ electrons.
• Chlorine ($Cl$) Example:
  • Neutral state: $17$ protons, $17$ electrons ($2$ in level 1, $8$ in level 2, $7$ in level 3).
  • Option: Lose $7$ electrons or gain $1$ to fill level 3.
  • Path: Chlorine tends to gain $1$ electron.
  • Result: Level 3 achieves an octet ($8$ electrons). The charge becomes $1-$ due to having $17$ protons and $18$ electrons.

Valence Electron versus Electron Transaction Patterns

• Valence $1$: Lose $1$ electron.
• Valence $2$: Lose $2$ electrons (Exception: Helium is already stable).
• Valence $3$: Lose $3$ electrons.
• Valence $4$: Gain or lose $4$ electrons (depends on the specific situation/bonding environment).
• Valence $5$: Gain $3$ electrons.
• Valence $6$: Gain $2$ electrons.
• Valence $7$: Gain $1$ electron.
• Valence $8$: No change; already stable.

Oxidation Numbers and Periodic Patterns

• Oxidation Number: A number indicating how many electrons an atom will gain or lose when forming a chemical bond. Its sign indicates the resulting charge: "+" means electrons were lost, "-" means electrons were gained.
• Main Group Pattern (The Hack):
  • Group 1: Oxidation number of $1+$ (lose $1$ electron).
  • Group 2: Oxidation number of $2+$ (lose $2$ electrons).
  • Group 13: Oxidation number of $3+$ (lose $3$ electrons).
  • Group 14: Oxidation number of $4+$ or $4-$ (halfway point).
  • Group 15: Oxidation number of $3-$ (gain $3$ electrons).
  • Group 16: Oxidation number of $2-$ (gain $2$ electrons).
  • Group 17: Oxidation number of $1-$ (gain $1$ electron).
  • Group 18: Oxidation number of $0$ (no change).

Comprehensive Practice for Oxidation Numbers

• Argon ($Ar$):
  • Highest $n=3$. Electrons: $3s^2 3p^6 = 8$.
  • Oxidation: Already has an octet, therefore $0$.
• Beryllium ($Be$):
  • Highest $n=2$. Electrons: $2s^2 = 2$.
  • Oxidation: Easier to lose $2$ than gain $6$. Becomes $2+$.
• Phosphorus ($P$):
  • Noble gas notation: $[Ne]3s^2 3p^3$
  • Highest $n=3$. Electrons: $2 + 3 = 5$.
  • Oxidation: Easier to gain $3$ to reach octet ($8$). Becomes $3-$.
• Iodine ($I$):
  • Location: 5p5 slot on the table.
  • Highest $n=5$. Electrons: $5s^2 5p^5 = 7$.
  • Oxidation: Easier to gain $1$ than lose $7$. Becomes $1-$.
• Carbon ($C$):
  • Configuration: $1s^2 2s^2 2p^2$.
  • Valence Count: $2 + 2 = 4$.
  • Oxidation: Located halfway; can be $4+$ or $4-$.
• Bromine ($Br$):
  • Configuration ends in $4p^5$.
  • Valence Count: $2 (4s) + 5 (4p) = 7$.
  • Oxidation: Needs $1$ more for octet. Becomes $1-$.
• Cesium ($Cs$):
  • Notation starts with $[Xe]$ followed by $6s^1$.
  • Valence Count: $1$.
  • Oxidation: Loses that single electron. Becomes $1+$.