☰ Year plan · Chemistry

Properties, magnetism and catalysts of the first series

Week 3 · Chapter 1 (C): general properties of the first series (atomic mass, radius, density, metallic character), paramagnetic and diamagnetic substances and counting unpaired electrons, transition metals as catalysts · 3 lessons
1

Radius, mass and density across the first series

Chemistry Sec 3 Term 1, Chapter 1: pp. 12–15
GoalDescribe how atomic mass, atomic radius and density change across the first series, and explain each trend.
New words
atomic radius · half the distance between the centres of two neighbouring atoms in the metal, measured in pm (1 pm = 10⁻¹² m)density · mass per unit volume, ρ = m ÷ V, in g/cm³effective nuclear charge · the pull of the nucleus felt by the outer electrons, after the other electrons have shielded part of it
Explanation

Atomic mass rises with atomic number across the series, with one small break: the average atomic mass of nickel (about 58.7) is a little below that of cobalt (about 58.9), although nickel has one more proton. An average mass depends on the mixture of isotopes, and nickel’s mixture is dominated by its lighter isotopes. Atomic radius changes much less than you might expect. Going across, the pull of the nucleus grows, which draws the electrons in; but the added 3d electrons repel the other electrons, which pushes the atom outward. The two opposite effects nearly cancel, and from Cr to Cu the radius stays within about 124 to 128 pm. Because the atoms are about the same size, they can take each other’s places in a metal lattice, so these metals mix easily in alloys. Density is mass ÷ volume: each atom is heavier along the series but takes almost the same room, so density rises, from about 3 g/cm³ for Sc to about 9 g/cm³ for Cu, with zinc lower at about 7. The radius and density values here are rounded approximations, for illustration only.

050100150200ScTiVCrMnFeCoNiCuZnpmatomic radius, approximate
Worked examples
Density from a measurement. A block of an iron-like metal (invented numbers) has a mass of 100 g and a volume of 12.5 cm³. ρ = m ÷ V = 100 g ÷ 12.5 cm³ = 8.0 g/cm³, close to the density of iron.
MetalM (g/mol)ρ (g/cm³)V = M ÷ ρ (cm³/mol)
Cr527.27.2
Fe567.97.1
Cu63.59.07.1
Why density rises while atoms stay the same size. Take the volume of one mole, V = M ÷ ρ, using rounded densities of 7.2 g/cm³ for Cr, 7.9 for Fe and 9.0 for Cu. The molar mass rises from 52 to 63.5 g/mol, but the volume of a mole stays near 7 cm³/mol, so a heavier mole in the same space means a higher density.
ƒTwo opposite effects
more nuclear charge: pulls in · more 3d repulsion: pushes out
Cr to Cu: nearly cancel, so the radius is nearly constant
A tug of war inside the atom. From Sc to Cr the radius falls from about 162 to 128 pm: the nuclear charge grows and the few 3d electrons added push out little. From Cr to Cu the extra pull and the extra repulsion balance, so the radius changes by only about 4 pm.
Class activity

A paper tug of war. Draw a circle for an atom. Draw a long arrow pointing inward and a short arrow pointing outward, and write on them “nuclear charge” and “repulsion of 3d electrons”: that is Sc to Cr, where the atom shrinks. Draw the same atom again with two arrows of equal length: that is Cr to Cu, where the size hardly changes. Then, with a grown-up, fill a small cup with rice and another of the same size with sugar, level both with a spoon and weigh them on a kitchen scale. Same volume, different mass: say which has the higher density.

Practice
1
A copper-like block (invented numbers) has a mass of 134.4 g and a volume of 15.0 cm³. Find its density.
2
A titanium-like piece has density 4.5 g/cm³ and mass 36 g. What is its volume?
3
Zinc has a density of about 7.1 g/cm³. What is the mass of 20 cm³ of it?
4
Why does the atomic radius stay almost constant from chromium to copper?