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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?

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    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

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