Copper forms a substitutional solid solution with silver (known as sterling silver) where copper and silver exist in lattice point positions. If the densities of pure Cu and Ag are 8.96 and 10.49 g/cm3, respectively, compute the number of copper atoms required to create a 1 cm3 sterling silver alloy with 7.5 wt% copper.

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mickymike92 mickymike92 · Answer 1 · 2022-02-17T21:11:10+01:00

Based on the density of Sterling silver, there are 7.32 × 10^21 atoms of Cu in 1 cm^3 of Sterling silver.

Density is defined as the ratio of mass and densityof the substance.

The density of the sterling silver mixture is calculated with the formula below:

Density of Sterling silver = (Mass fraction of Cu * Density of Cu) + (Mass fraction of Ag * Density of Ag)

Density of Sterling silver = 7.5% × 8.96 + 92.5% × 10.49

Density of Sterling silver = 10.38 g/cm^3

The mass of the 1 cm^3 is determined with the formula below:

Mass of Sterling silver = 10.38 × 1

Mass of Sterling silver = 10.38 g

Mass of Cu = 0.075 × 10.38

Mass of Cu = 0.7785 g

The number of atoms is then calculated as follows:

I mole of Cu = 64.0 g

64.0 g contains 6.02 × 10^23 atoms of Cu

0.7785 g will contain 0.7785 × 6.02 × 10^23/64

Number of atoms = 7.32 × 10^21 atoms of Cu.

Therefore, there are 7.32 × 10^21 atoms of Cu in 1 cm^3 of Sterling silver.

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