A-Level Properties and complexes of first-row transition metals: worked solution

Question

Table 4.2 records some physical data for calcium, cobalt and manganese (relative atomic masses 40.1, 58.9, 54.9; metallic atomic radii 0.197, 0.125, 0.132 nm; densities 1.53, 8.83 and x g cm−3 respectively). From these figures, propose a value of x for the density of manganese and justify it. No calculation is expected.

Density increases with atomic mass and decreases with atomic volume (radius³). Manganese is a transition metal with an atomic mass (54.9) and metallic radius (0.132 nm) very close to cobalt (58.9, 0.125 nm), and both are far denser and much smaller in radius than calcium (density 1.53, radius 0.197 nm). Since Mn has a slightly larger radius and slightly smaller mass than Co, its density should be a little lower than Co's 8.83. A value of about 7 g cm⁻³ is reasonable (density is roughly proportional to Ar/radius³, which gives ~7).