JEE Chemistry Classification Of Elements and Periodicity In Properties Notes Set 05

Early Attempts at Classification

With 118 known elements, a systematic classification makes it easier to study their chemistry and to predict new facts. Dobereiner's triads grouped three similar elements in which the middle atomic mass was close to the mean of the other two (Li 7, Na 23, K 39: \( (7+39)/2 = 23 \)); it worked only for a few elements. Newlands' law of octaves noted that every eighth element, when arranged by increasing atomic mass, resembled the first; it failed beyond the lighter elements. Lothar Meyer plotted atomic volume against atomic mass: alkali metals sit at the crests, transition elements in the troughs, halogens on the rising parts before the noble gases and alkaline earth metals near the middle of the falling parts.

Mendeleev's Table

Mendeleev stated that the properties of elements are periodic functions of their atomic masses. He placed similar elements in the same vertical column (nine groups, seven periods) and left gaps for undiscovered elements. His predictions for eka-aluminium (found later as gallium, predicted mass 68, found 70) and eka-silicon (germanium, predicted mass 72, found 72.6) matched experiment closely. He also corrected atomic masses, for example Be = 9 (valency 2 times equivalent mass 4.5), not 13.5.

Its defects: the position of hydrogen was uncertain; isotopes had no separate place; lanthanides and actinides had no proper place; strict mass order was broken (Ar before K, Te before I); dissimilar elements shared a group (alkali metals and coinage metals) while similar ones were separated (Cu and Hg); and the cause of periodicity was not explained.

The Modern (Long Form) Periodic Table

Moseley bombarded metals with fast electrons and found that the square root of the X-ray frequency is a straight-line function of atomic number, \( \sqrt{\nu} = a(Z-b) \), but not of atomic mass. Hence the modern periodic law: the properties of elements are periodic functions of their atomic numbers. Periodicity arises from the recurrence of similar valence-shell electronic configurations at regular intervals of 2, 8, 8, 18, 18 and 32 elements.

Periods. There are 7 periods; the period number equals the principal quantum number of the valence shell. Each period starts with an alkali metal (\( ns^1 \)) and ends with a noble gas (\( ns^2np^6 \); helium \( 1s^2 \)). The number of elements in a period is twice the number of orbitals filled in it: period 1 has 2, periods 2 and 3 have 8, periods 4 and 5 have 18, and periods 6 and 7 have 32. Period 3 has only 8 elements because 4s fills before 3d. Groups. There are 18 groups; elements of a group have the same valence-shell configuration.

Blocks and Prediction of Position

The block is set by the subshell that receives the last electron. The s-block (groups 1 and 2, \( ns^{1-2} \)); the p-block (groups 13 to 18, \( ns^2np^{1-6} \)), containing some metals, all non-metals and metalloids; the d-block (groups 3 to 12, \( (n-1)d^{1-10}ns^{1-2} \), palladium being \( 4d^{10}5s^0 \)); and the f-block (\( (n-2)f^{1-14}(n-1)d^{0-1}ns^2 \)), the lanthanides (Ce to Lu, 4f) and actinides (Th to Lr, 5f), all placed in group 3 and shown at the bottom to avoid an over-wide table. Zn, Cd and Hg are d-block elements but not transition elements, since they do not have partly filled d orbitals in the atom or in common ions. Helium is an s-block element placed with the noble gases because of its filled shell, and hydrogen is placed separately at the top.

Group number. s-block: number of valence electrons. p-block: 10 + number of valence electrons. d-block: electrons in (n-1)d plus electrons in ns. Example. Element 112 has the configuration \( [Rn]\,5f^{14}6d^{10}7s^2 \); it is a d-block element of group 12 (10 + 2) and period 7. Atoms with configurations \( 1s^22s^22p^1 \) and \( 1s^22s^22p^63s^23p^1 \) are in the same group (13) since both end in \( ns^2np^1 \). An element with configuration ending \( 3d^64s^2 \) is in group 8.

Metals, Non-metals, Metalloids and Diagonal Relationship

Metals (over 78% of the elements) lie on the left, are lustrous, conduct well, give basic oxides and lose electrons readily. Non-metals sit at the upper right, are poor conductors, form anions and give acidic oxides. Metalloids (typically B, Si, Ge, As, Sb, Te) lie on the border and show both behaviours; their oxides are generally amphoteric.

The second-period elements Li, Be and B resemble Mg, Al and Si of the next period diagonally. The reason is similar size (Li 1.23 and Mg 1.36 angstrom; Li+ 0.76 and Mg2+ 0.72) and similar electronegativity (Li 1.0, Mg 1.2; Be 1.5, Al 1.5; B 2.0, Si 1.8). For Be and Al the charge/radius ratio is similar (2+ and 3+ with sizes 0.45 and 0.535 angstrom).

Effective Nuclear Charge and Shielding

Inner electrons repel an outer electron and partly cancel the attraction of the nucleus. The net pull is the effective nuclear charge: \( Z_{\text{eff}} = Z - \sigma \), where \( \sigma \) is the screening (Slater) constant. Shielding falls in the order s > p > d > f for a given shell because of their penetration. Down a group, \( Z_{\text{eff}} \) stays almost constant while n rises; along a period, \( Z_{\text{eff}} \) increases steadily.

Oxidation States and Inert Pair Effect

The oxidation state is the charge an atom would carry if the bonding electrons were assigned to the more electronegative atom; the sum over a species equals its charge, and every atom in an element is zero. Usual rules: F is -1; alkali metals +1; alkaline earths +2; Al and Ga +3; H is +1 except in metal hydrides (-1); O is -2 except in peroxides (-1), superoxides (-1/2) and with fluorine (+1 in \( \ce{O2F2} \), +2 in \( \ce{OF2} \)); Cl, Br and I are -1 except when combined with more electronegative atoms; when rules conflict the more electronegative atom has priority. The average oxidation number can be fractional, as for S in \( \ce{S4O6^{2-}} \) and Fe in \( \ce{Fe3O4} \). In \( \ce{NH4NO2} \), N is -3 in the cation and +3 in the anion.

The inert pair effect is the reluctance of the ns2 pair of the heavier p-block elements to take part in bonding, because it penetrates the d and f shells and is held tightly. The state two lower than the group state becomes more stable down groups 13 to 15: \( \ce{Ga^{3+} > In^{3+} > Tl^{3+}} \) but \( \ce{Ga^+ < In^+ < Tl^+} \); \( \ce{Ge^{4+} > Sn^{4+} > Pb^{4+}} \) with \( \ce{Ge^{2+} < Sn^{2+} < Pb^{2+}} \); \( \ce{As^{5+} > Sb^{5+} > Bi^{5+}} \). Hence Pb(IV) and Bi(V) compounds are strong oxidising agents. High oxidation states persist only with F or O: TlF3, PbF4, PbCl4, BiF5 and NaBiO3 exist, while PbI4, PbBr4 and BiCl5 do not, and TlI3 is really \( \ce{Tl^+I3^-} \).

Atomic Radius

Four kinds of radius are used. The covalent radius is half the distance between two singly bonded like atoms (Cl2: 198 pm gives 99 pm); for unlike atoms of nearly equal electronegativity the bond length is the sum of the radii (C-I 213 pm and C 77 pm gives I = 136 pm), but a large electronegativity difference shortens the bond. The metallic radius is half the distance between neighbouring atoms in the metal lattice and exceeds the covalent radius. The van der Waals radius is half the distance between non-bonded neighbouring atoms in a solid and is the largest of the three; noble gases have only this radius. Hence van der Waals radius > metallic radius > covalent radius.

Trends. Along a period the radius falls because \( Z_{\text{eff}} \) rises while the shell number is fixed (Li > Be > B > C > N > O > F). Down a group it rises because the added shells outweigh the nuclear charge (Li < Na < K < Rb < Cs). In the first transition series the radii fall from Sc (144 pm) to Cr (117 pm), stay almost constant from Cr to Cu, and rise slightly at Zn (125 pm), because added d electrons shield poorly yet repel each other. The lanthanide contraction (poor shielding by 4f electrons) makes the second and third row d-block elements almost equal in size, so there is hardly any increase from the second to the third member of a group.

Ions. A cation is smaller than its atom (more protons per electron, and often one fewer shell), and the radius falls as the charge rises: Fe > Fe2+ > Fe3+; Pb2+ > Pb4+; Mn > Mn2+ > Mn3+ and so on. An anion is larger than its atom (\( Z_{\text{eff}} \) falls and repulsion grows), more so with higher charge: O < O^- < O^2-. In an isoelectronic series the radius falls as the nuclear charge increases: \( \ce{N^{3-} > O^{2-} > F^- > Na^+ > Mg^{2+} > Al^{3+}} \) and \( \ce{S^{2-} > Cl^- > K^+ > Ca^{2+}} \). Mg2+ is smaller than O2- for this reason (12 protons against 8 for the same 10 electrons). Radius also falls with bond order: N-N > N=N > N triple N.

Worked example. The fraction of the volume of Li occupied by its 2s electron: volume of Li (r = 1.23 angstrom) = 7.79 cubic angstrom; volume of Li+ (r = 0.76 angstrom) = 1.84 cubic angstrom; difference = 5.95; fraction = 5.95/7.79 = 76.4%. Increasing size order for \( \ce{Be^{2+}, Cl^-, S^{2-}, Na^+, Mg^{2+}, Br^-} \): \( \ce{Be^{2+} < Mg^{2+} < Na^+ < Cl^- < S^{2-} < Br^-} \).

Ionisation Enthalpy

The first ionisation enthalpy is the energy needed to remove the most loosely held electron from an isolated gaseous atom: \( \ce{M(g) -> M^+(g) + e^-} \); successive values rise, \( IE_1 < IE_2 < IE_3 \ldots \), because fewer electrons feel the same nuclear charge. The energy to form M2+ is \( IE_1 + IE_2 \). Factors: larger atomic size lowers it; higher nuclear charge raises it; more shielding lowers it; better penetration raises it (s > p > d > f); and filled or half-filled subshells raise it. Hence Be > B (2s2 against 2p1), Mg > Al (3s against 3p), and noble gases have the highest values in each period. Down a group the value falls generally, with exceptions: group 13 B > Tl > Ga > Al > In and group 14 C > Si > Ge > Pb > Sn, because of poor shielding by d and f electrons. A low ionisation enthalpy means strong metallic and reducing character in the gas phase.

Worked examples. (1) The largest IE among F, O, N is F (smallest size, highest \( Z_{\text{eff}} \)); among Mg, P, Ar it is Ar (stable octet). (2) For Mg, \( IE_1 = 7.646 \) eV and \( IE_2 = 15.035 \) eV, total 22.681 eV = 2188.7 kJ/mol (1 eV = 96.5 kJ/mol); 12 mg of Mg is 0.5 mmol, so the energy is 1.094 kJ. (3) If \( M \rightarrow M^+ + e^- \) needs 100 eV and \( M \rightarrow M^{2+} + 2e^- \) needs 250 eV, then \( IE_1(M) = 100 \) eV, \( IE_2(M) = IE_1(M^+) = 150 \) eV. (4) For three elements with \( IE_1/IE_2 \) of 403/2640, 549/1060 and 1142/2080 kJ/mol: the first is an alkali metal (huge jump to \( IE_2 \)), the second an alkaline earth metal (small gap) and the third a non-metal (highest values). Na (period 3) has an IE below that of Li.

Electron Gain Enthalpy

Electron gain enthalpy \( \Delta_{eg}H \) is the enthalpy change when a gaseous atom takes up an electron; it is negative (exothermic) for most elements and equals minus the electron affinity. Halogens have the most negative values, because one electron completes the octet. Along a period the values become more negative and down a group less negative. Exceptions: Cl (-349) is more negative than F (-328), and S more than O, because the small second-period atoms suffer greater electron repulsion; N has a low value because the electron must enter a half-filled p subshell; alkaline earth metals and noble gases have positive or near-zero values (the electron goes into a filled ns or into a new shell). The second electron gain is always endothermic (O: -141 kJ then +744 kJ), because the electron is repelled by the negative ion. The order N < P < O < S shows increasing negative gain enthalpy, and an atom has a higher affinity than its anion.

Worked example. If 5.0 x 10^-13 J is released when a million iodine atoms are converted to iodide, per atom this is 5.0 x 10^-19 J, and for a mole it is 301 kJ, so \( \Delta_{eg}H \) = -301 kJ/mol = -3.12 eV per atom.

Electronegativity

Electronegativity measures how strongly an atom attracts shared electrons in a bond. It increases across a period and decreases down a group (with the same size and \( Z_{\text{eff}} \) reasoning), increases with the oxidation state of the atom, and increases with s-character of the hybrid orbital (sp3 25%, sp2 33%, sp 50%). Pauling values: H 2.1, Li 1.0, Be 1.5, B 2.0, C 2.5, N 3.0, O 3.5, F 4.0, P 2.1, S 2.5, Cl 3.0, Br 2.8, I 2.5. Pauling's relation is \( \chi_A - \chi_B = 0.208\sqrt{E_{A-B} - \sqrt{E_{A-A}E_{B-B}}} \) (energies in kcal/mol), and Mulliken's definition is \( \chi_M = (IE + EA)/2 \), with \( \chi_P = \chi_M/2.8 \) when IE and EA are in eV. For fluorine, IE = 17.42 eV and EA = 3.45 eV, so \( \chi_M = 10.435 \) and \( \chi_P = 3.73 \).

Applications: the more electronegative element is written last and ends in -ide (OF2, oxygen difluoride; Cl2O, dichlorine oxide; ICl, iodine chloride); a larger electronegativity difference gives a shorter, more polar bond (bond length HF < HCl < HBr < HI).

Points to Remember

Group number from configuration: s-block = valence electrons; p-block = 10 + valence electrons; d-block = (n-1)d + ns electrons. Radius: anion > atom > cation; isoelectronic radius falls with rising Z. IE order exceptions: Be > B, Mg > Al, N > O, P > S. Electron gain enthalpy exceptions: Cl > F, S > O, N is low, and the second gain is endothermic. Inert pair effect gives strong oxidants Tl(III), Pb(IV) and Bi(V).