Chemistry · Ch 9 — Elements of Group 13, 14 and 15
Trends in atomic and physical properties of elements of groups 13, 14 and 15
Trends in atomic and physical properties of elements of groups 13, 14 and 15
Physical and atomic properties vary widely within these three groups because each group spans nonmetals, metalloids and metals. In group 13, boron is a metalloid — a hard, glossy solid that nonetheless conducts electricity poorly, like a nonmetal — while aluminium, gallium, indium and thallium are reactive metals; aluminium is, in fact, the third most abundant element in the earth's crust. In group 14, carbon is a nonmetal; silicon and germanium are metalloids, brittle, hard solids with a metallic lustre; and tin and lead are corrosion-resistant, moderately reactive metals. In group 15, gaseous nitrogen and brittle phosphorus are nonmetals, arsenic and antimony are metalloids, and bismuth is a moderately reactive metal. Down each group the atomic radius generally increases (a new shell is added each period) and the first ionization enthalpy generally decreases (the outer electron sits farther from, and is more shielded from, the nucleus), but both trends show irregularities at gallium, indium/tin and thallium/lead/bismuth, because of the poor shielding offered by intervening d and f electrons. Problem 9.1 works through the resulting M3+ ionic-radius order for group 13; Problem 9.2 explains why gallium's atomic radius is smaller than aluminium's despite lyin …
B: atomic no. 5, mass 10.81, atomic radius 88 pm, M3+ ionic radius 27 pm, ionization enthalpies (1st/2nd/3rd) 801/2427/3659 kJ/mol, electronegativity 2.0, density 2.35 g/cm3, melting point printed in the source as "24.53" K (almost certainly a digit-order extraction glitch — real boron melts near 2453 K/2349°C, and the adjacent boiling point of 3923 K is consistent with real boron data, so "24.53" is flagged here as unreliable rather than silently corrected), boiling point 3923 K. Al: at. no. 13, mass 26.98, radius 143 pm, ionic radius 53.5 pm, IE 577/1816/2744 kJ/mol, electronegativity 1.5, density 2.70 g/cm3, melting point 933 K, boiling point 2740 K. Ga: at. no. 31, mass 69.72, radius 135 pm, ionic radius 62.0 pm, IE 579/1979/2962 kJ/mol, electronegativity 1.6, density 5.90 g/cm3, melting point 303 K, boiling point 2676 K. In: at. no. 49, mass 114.82, radius 167 pm, ionic radius 80.0 pm, IE 558/1820/2704 kJ/mol, electronegativity 1.7, density 7.31 g/cm3, melting point 430 K, boiling point 2353 K …
C: atomic no. 6, mass 12.01, atomic radius 77 pm, ionic radius not listed (carbon does not form a simple M4+ cation), ionization enthalpies (1st/2nd/3rd/4th) 1086/2352/4620/6220 kJ/mol, electronegativity 2.5, density 3.51 g/cm3, melting point not listed (diamond/graphite do not have an ordinary melting point at 1 atm — carbon sublimes/decomposes instead — so a blank cell here is chemically expected, not a data gap), boiling point 4373 K. Si: at. no. 14, mass 28.09, radius 118 pm, ionic radius 40 pm, IE 786/1577/3228/4354 kJ/mol, electronegativity 1.8, density 2.34 g/cm3, melting point 1693 K, boiling point 3550 K. Ge: at. no. 32, mass 72.60, radius 122 pm, ionic radius 53 pm, IE 761/1537/3300/4400 kJ/mol, electronegativity 1.8, density 5.32 g/cm3, melting point 1218 K, boiling point 3123 K. Sn: at. no. 50, mass 118.71, radius 140 pm, ionic radius 69 pm, IE 708/1411/2942/3929 kJ/mol, electronegativity 1.8, density 7.26 g/cm3, melting point 505 K, boiling point 2896 K. Pb: at. no. 82, mass 207.2, radius 146 pm, ionic radius 78 pm, IE 715/1450/3081/4082 kJ/mol, electronegativity 1.9, density 11.34 g/cm3, melting point 600 K, boiling point 2024 K. Note: the source's ionic-radius column header literally repeats the Group-13 table's label 'M3+' for this Group-14 table too, which is very lik …
N: atomic no. 7, mass 14.01, atomic radius 70 pm, ionic radius 171 pm (for the M3- anion — the source's charge symbol prints only faintly for N/P/As, but a negative, anion charge is the chemically sensible reading for these nonmetals, unlike Sb/Bi below where the source explicitly prints a + superscript), ionization enthalpies (1st/2nd/3rd) 1402/2856/4577 kJ/mol, electronegativity 3.0, density 0.879 g/cm3, melting point printed as "6.3" K (flagged as an extraction glitch: real N2 melts at about 63 K, so this is very likely "63" with a stray decimal point inserted, similar to the Table 9.2 boron melting-point issue — not silently corrected here), boiling point 77.2 K (this value matches real liquid nitrogen's boiling point closely, supporting the reading above). P: at. no. 15, mass 30.97, radius 110 pm, ionic radius 212 pm (M3-), IE 1012/1903/2910 kJ/mol, electronegativity 2.1, density 1.823 g/cm3, melting point 317 K, boiling point 554 K. As: at. no. 33, mass 74.92, radius 121 pm, ionic radius 222 pm (M3-), IE 947/1798/2736 kJ/mol, electronegativity 2.0, density 5.778 g/cm3, melting point 1089 K, boiling point not listed (consistent with the real chemistry: arsenic sublimes rather than boils at 1 atm, so a blank cell here is chemically expected). Sb: at. no. 51, mass 121.75, radius 141 pm, ionic radius 76 pm (M3+, as explicitly printed), IE 834/1595/2443 kJ/mol, electronegativity 1.9, density 6.697 g/cm3, melting point 904 K, boiling point 1860 K. Bi: at. no. 83, mass 208.98, radius 148 pm, ionic radius 103 pm (M3+, as explicitly printed), IE 703/1610/2466 kJ/mol, el …
Worked out. Worked problem: the atomic numbers of the group 13 elements increase in the order B < Al < Ga < In < Tl — arrange these elements in increasing order of the ionic radius of M3+. Solution: down group 13 the general outer electronic configuration is ns²np¹, and the M3+ ion of each element is formed by removing all three outer 'n'-shell electrons, so in M3+ the 'n−1' shell becomes the outermost shell. Since the size of this exposed 'n−1' shell increases steadily down the group, the ionic radius of M3+ also increases down the group, in the same order as a …
Worked out. Worked problem: why is the atomic radius of gallium less than that of aluminium? Solution: atomic radius normally increases down a group because a new shell is added, but gallium's atomic radius (135 pm) is actually smaller than aluminium's (143 pm) directly above it. Aluminium has no d-electrons, but going from Al down to Ga the nuclear charge increases by 18 units, and ten of those eighteen added electrons fill the inner 3d subshell. Because d-electrons shield the nucleus poorly, the outer electrons of Ga feel the increased nuclear charge more strongly than the shielding would suggest, pulling them inward and making Ga's atomic radius smaller th …
Worked out. Worked problem: the first ionization enthalpies of Al, Si and P are 577, 786 and 1012 kJ/mol respectively — explain the observed trend. Solution: Al, Si and P all belong to period 3 and share the same valence shell (n=3). Moving from Al to Si to P, the nuclear charge increases while the valence electrons stay in the same shell, so those electrons are held more tightly by the nucleus. Removing an electron therefore takes progressively more energy going from Al to Si to P, which is why the first ionization enthalpy rises steadily acr …