Answer to Question #133326 in Inorganic Chemistry for Nisaa

Question #133326
A small bar of an unknown metal was left on the bench. The density of the metal is 11.5 g/cm3. An X-ray diffraction experiment was conducted to measures the edge of the face-centered cubic unit cell as 4.06 x 10-10 m. Find the atomic weight of this metal and tentatively identify this metal.
Expert's answer

"Density=" "Mass \\over Volume" "=11.5g\/cm^3"

"Volume(i^3)=" "(4.06\\times 10^{-8}cm^3)^3"

"=6.692\\times 10^{-23}cm^3"

"11.5g\/cm^3=" "Mass of unit cell \\over 6.692\\times 10^{-23}cm^3"

"\\therefore" Mass of unit cell"=7.696\\times 10^{-22}g"

Since there are "4" units per unit cell, the mass of one atom is mass of unit cell/ 4. Converting the mass of one atom to the mass of 1 mole therefore is;

"7.696\\times 10^{-22}g\\over 4atoms" "=" "1.924\\times 10^{-22}g\\over atom" "\\times 6.022\\times 10^{23} atoms"


The compound is thus "FeCO_3"

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