Question

A hypothetical element X forms a substantial solid solution with another Y. compute the number of X atoms per cubic centimeter for a X-Y alloy that contains 20.5 wt%X and 79.5 wt%Y, their densities are 8.35g/cm^3 and 17.90g/cm^3 and their atomic masses are 90.55g/mol and 126.80g/mol.

Answer 1

100 grams of X-Y alloy contains 20.5 grams of X and 79.5 grams of Y.

Volume of 20.5 grams of X = Mass / Density of X = 20.5 g / 8.35g/cm³ = 2.46 cm³

Volume of 79.5 grams of Y = Mass / Density of Y = 79.5 grams/ 17.90g/cm³ = 4.44 cm³

Total volume of 100 grams of alloy = 2.46 cm³ + 4.44 cm³ = 6.90 cm³

So, 6.90 cm³ of the alloy contains 20.5 grams of X atoms

1 cm³ of the alloy contains 20.5 grams * 1 cm³ / 6.90 cm³ of X atoms = 2.97 grams of X atoms = 2.97 grams/ (90.55g/mol ) = 0.0328 mole of X atoms

Number of X atoms in 0.0328 moles of X = 0.0328 * 6.023 * 10²³ = 1.98 * 10²²

Number of X atoms per cubic centimeter of the alloy is 1.98 * 10²²