Question

Common brass is a copper and zinc alloy containing 37.0% zinc by mass and having a density of 8.48 g/cm3. A fitting composed of common brass has a total volume of 126.5 cm3 . How many atoms of copper does the fitting contain? How many atoms of zinc does the fitting contain?

Answer 1

Volume of the brass = 126.5 cm3

Density of brass = 8.48 g/cm3

Therefore, the mass of the brass = volume of brass x density of brass

                                                     = 126.5 cm³ x 8.48 g/cm³

                                                     = 1072.72 g

Mass of zinc in the brass = 1072.72 g x 37.0/100

                                        = 396.9064 g

Molar mass of Zn = 65.38 g/mol

Hence, mol of Zn in the brass = mass of Zn/molar mass of Zn

                                                = 396.9064 g / 65.38 g/mol

                                                = 6.071 mol

1 mol of Zn = 6.02 x 10²³ atoms of Zn

Therefore, 6.071 mol of Zn = 6.071 mol x 6.02 x 10²³ atoms/1 mol = 3.65 x 10²⁴ atoms of Zn

Percent of copper in the alloy = (100 - 37.0) = 63.0 %

Mass of copper in the brass = 1072.72 g x 63.0/100

                                             = 675.8136 g

Molar mass of Cu = 63.546 g/mol

Hence, mol of Cu in the brass = mass of Cu/molar mass of Cu

                                                = 675.8136 g / 63.546 g/mol

                                                = 10.64 mol

1 mol of Cu= 6.02 x 10²³ atoms of Cu

Therefore, 10.64 mol of Cu = 10.64 mol x 6.02 x 10²³ atoms/1 mol = 6.41 x 10²⁴ atoms of Cu

Hence, the copper fitting contains 6.41 x 10²⁴ atoms of copper and the zinc fitting contains 3.65 x 10²⁴ atoms of zinc.