Atomic radius and ionic radius
An atom has no sharp edge, so its size is taken from distances between nuclei.
- Covalent radius: half the distance between two bonded nuclei of the same element (Cl₂: 198 pm ÷ 2 = 99 pm).
- Metallic radius: half the distance between neighbouring nuclei in a metal crystal.
Trends
- Across a period: decreases. Electrons go into the same shell but the nuclear charge grows by +1 each step. The effective nuclear charge (Zeff), the pull actually felt by outer electrons after inner electrons shield part of it, rises, so the cloud is pulled closer.
- Down a group: increases. A new shell is added each time; the outer electrons are further away and more shielded.
Ionic radius
- A cation is smaller than its atom: fewer electrons feel the same nuclear charge (and often a whole shell is lost). Na 186 pm → Na⁺ 102 pm.
- An anion is bigger than its atom: extra electrons repel one another and the same nucleus pulls each one less. Cl 99 pm → Cl⁻ 181 pm.
- Isoelectronic species have the same number of electrons (for example O²⁻, F⁻, Na⁺, Mg²⁺, all with 10). The one with more protons is smaller: O²⁻ > F⁻ > Na⁺ > Mg²⁺.
Ionisation enthalpy
Ionisation enthalpy (ΔiH) is the energy needed to remove the most loosely held electron from an isolated gaseous atom in its ground state: X(g) → X⁺(g) + e⁻. Unit kJ mol⁻¹. It is always positive (energy is taken in).
The second ionisation enthalpy is always larger than the first, because the electron is being removed from a positive ion.
Trends
- Across a period: generally increases (higher Zeff, smaller atom). Alkali metals have the lowest values, noble gases the highest.
- Down a group: decreases (larger atom, more shielding).
Two famous breaks
- Be (899) > B (801): boron's electron is removed from 2p, which is higher in energy and better shielded than beryllium's 2s.
- N (1402) > O (1314): nitrogen has a stable half-filled 2p³. In oxygen (2p⁴) two electrons share one orbital and repel, so one is easier to remove.
Electron gain enthalpy
Electron gain enthalpy (ΔegH) is the enthalpy change when an electron is added to an isolated gaseous atom: X(g) + e⁻ → X⁻(g). If energy is released, it is negative.
- Across a period: becomes more negative (a smaller atom with higher Zeff attracts the new electron more).
- Down a group: becomes less negative (the added electron is further away).
- Halogens have the most negative values: one more electron completes their octet.
- Noble gases have large positive values: the extra electron must enter a new, higher shell.
- Exceptions: Cl (−349) is more negative than F (−328), and S more than O. F and O are so small that the incoming electron is crowded by the electrons already in the small 2p shell.
Electron affinity is a related term (energy released, taken at 0 K); in this course we use electron gain enthalpy.
Electronegativity
Electronegativity is the ability of an atom in a chemical bond to attract the shared electron pair towards itself. It is not a measured energy; it has no unit. The Pauling scale gives F = 4.0 (highest), O = 3.5, N = 3.0, Cl = 3.0, C = 2.5, H = 2.1, Na = 0.9, Cs = 0.7.
- Across a period: increases (smaller atom, higher Zeff).
- Down a group: decreases.
- High electronegativity means non-metallic character; low means metallic character. So metals are on the left and non-metals on the right.
Valence (valency)
Valence is the combining capacity of an element. For main-group elements it is usually equal to the number of outer electrons (groups 1, 2, 13, 14) or 8 minus the number of outer electrons (groups 15, 16, 17).
| Group | 1 | 2 | 13 | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|---|---|---|
| Outer e⁻ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Valence | 1 | 2 | 3 | 4 | 3, 5 | 2, 6 | 1, 7 | 0, 8 |
So formulas follow from the table: Na (1) and Cl (1) → NaCl; Al (3) and O (2) → Al₂O₃. Transition and inner transition elements show variable valence.
Anomalous second-period elements and diagonal relationship
Li, Be, B, C, N, O, F differ from the rest of their groups because they are very small, highly electronegative and have only four valence orbitals (2s, 2p), so their maximum covalence is 4. Some of them resemble the element diagonally below-right: Li–Mg, Be–Al, B–Si. This is called the diagonal relationship.
Chemical reactivity and nature of oxides
Reactivity is highest at the two far ends of a period and lowest in the middle.
- Left side (metals): low ionisation enthalpy → they lose electrons easily → strong reducing agents. Reactivity increases down the group (Cs > Rb > K > Na > Li).
- Right side (non-metals): very negative electron gain enthalpy → they gain electrons easily → strong oxidising agents. Reactivity decreases down the group (F > Cl > Br > I).
- Oxides: left-side oxides are basic (Na₂O + H₂O → 2NaOH), right-side oxides are acidic (Cl₂O₇ + H₂O → 2HClO₄), and middle ones such as Al₂O₃ are amphoteric (react with both acids and bases). CO, NO, N₂O are neutral.
Key formulas and definitions
- X(g) → X⁺(g) + e⁻ ; Δ_iH (always positive)
- X(g) + e⁻ → X⁻(g) ; Δ_egH (usually negative)
- Covalent radius = ½ × internuclear distance in X₂
- Isoelectronic ions: more protons → smaller size
- Across a period: radius ↓, IE ↑, EGE more negative, EN ↑
- Down a group: radius ↑, IE ↓, EGE less negative, EN ↓
- Valence = outer electrons, or 8 − outer electrons
Worked examples
1. The Cl–Cl bond length is 198 pm. Find the covalent radius of chlorine.
Covalent radius = 198 ÷ 2 = 99 pm.
2. Arrange Mg, Al, Si, Na in increasing atomic radius.
All in period 3; radius falls left to right (Na > Mg > Al > Si). Increasing order: Si < Al < Mg < Na.
3. Arrange the isoelectronic ions N³⁻, O²⁻, F⁻, Na⁺, Mg²⁺ in decreasing size.
All have 10 electrons. Protons: N 7, O 8, F 9, Na 11, Mg 12. More protons pull the same 10 electrons tighter. Decreasing size: N³⁻ > O²⁻ > F⁻ > Na⁺ > Mg²⁺.
4. First ionisation enthalpies: Na 496, Mg 737, Al 577 kJ/mol. Why is Al lower than Mg?
Mg: [Ne] 3s²; Al: [Ne] 3s² 3p¹. Al loses a 3p electron, which is higher in energy and shielded by the 3s pair, so it is easier to remove than Mg's 3s electron.
5. How much energy is needed to ionise 0.5 mol of gaseous sodium atoms? (Δ_iH of Na = 496 kJ/mol)
Energy = moles × Δ_iH = 0.5 × 496 = 248 kJ.
6. How much energy is released when 2 mol of Cl(g) atoms each gain one electron? (Δ_egH of Cl = −349 kJ/mol)
Energy change = 2 × (−349) = −698 kJ, so 698 kJ is released.
7. The first four ionisation enthalpies of an element are 738, 1451, 7733 and 10 540 kJ/mol. Find its group and valence.
Big jump between the 2nd (1451) and 3rd (7733): after 2 electrons, the next must come from a full inner shell. So it has 2 outer electrons → group 2, valence 2 (this is magnesium).
8. Predict the formula of the compound of Al with S, and say whether aluminium oxide is acidic or basic.
Al valence 3 (3 outer electrons); S valence 2 (8 − 6). Cross over: Al₂S₃. Al₂O₃ lies in the middle of the period, so it is amphoteric (reacts with both HCl and NaOH).
Common mistakes
- Saying atoms grow across a period because Z grows. More protons pull harder, so they shrink.
- Mixing up electron gain enthalpy and electronegativity. The first is an energy of an isolated atom; the second is a pull inside a bond and has no unit.
- Writing F as having the most negative electron gain enthalpy. Chlorine has; fluorine is too small and crowded.
- Forgetting the exceptions in ionisation enthalpy: Be > B and N > O.