Question

What is likely identity of a metal, if a sample has a mass of 67.5g when measured in air and an apparent mass of 59.5g when submerged in water?

Answer 1

By Archimedes principle, the weight of a submerged object is reduced by the weight of liquid it displaces.

Weight of metal in air = 67.5 g
Weight in water = 59.5
weight of water displaced =67.5-59.5=8 g
density of water = 1.0 g / ml
volume of water displaced = 8 / 1.0 ml = 8 ml
volume of metal = 8 ml
density of metal = 67.5/8 = 8.44 g/ml
From a list of density of elements, we find, in ascending order:

7.87 Iron, Fe
7.9 Gadolinium, Gd
8.23 Terbium, Tb
8.55 Dysprosium, Dy
8.57 Niobium, Nb
8.65 Cadmium, Cd
8.8 Holmium, Ho
8.9 Nickel, Ni
8.9 Cobalt, Co

Make your choice from the list depending on the likelihood of weighing exotic metals. To me, likely choices are among Iron, Cadmium, Nickel and Cobalt.

Ref: http://www.lenntech.com/periodic-chart-elements/density.htm#ixzz0pVbYQMDV