Gold forms a substitutional solid solution with silver. calculate the number of gold atoms per cubic centimeter (in atoms/cm3) for a silver-gold alloy that contains 29 wt% au and 71 wt% ag. the densities of pure gold and silver are 19.32 and 10.49 g/cm3, respectively, and their respective atomic weights are 196.97 and 107.87 g/mol.

Gold: 1.1 x 10²² atoms/cm³

Silver: 4.8 x 10²² atoms/cm³

Explanation:

100 g of the alloy will have 29 g of Au and 71 g of Ag.

19.32 g Au 1 cm³

29 g Au  x

x = 1.5 cm³

10.49 g Ag 1 cm³

71 g Ag   y

y = 6.8 cm³

The total volume of 100g of the alloy is x+y = 8.3 cm³.

Gold:

196.97 g Au 6.022 x 10²³ atoms Au

29 g Au w

w = 8.9 x 10²² atoms Au

8.9 x 10²² atoms Au 8.3 cm³

           A                     1 cm³

A = 1.1 x 10²² atoms Au

Silver:

107.87 g Ag 6.022 x 10²³ atoms Ag

71 g Ag w

w = 4.0 x 10²³ atoms Ag

4.0 x 10²³ atoms Ag 8.3 cm³

          B                     1 cm³

B = 4.8 x 10²² atoms Ag

6.4 cm (max) - 25 cm (min)