Question

Convert the composition of the following alloy from atom percent to weight percent (a) 45.0 at% of silver, (b) 46.2 at% of gold, and (c) 8.8 at% of copper. The atomic weights for silver, gold, and copper are 107.87, 196.97, and 63.55 g/mol, respectively.

Answer 1

Basis 100 atoms of alloy

Number of atoms in silver = 45 atoms

Moles of silver = 45/NA

Where NA = Avogadro number

Mass of silver = moles x molecular weight

= (45/NA) mol x 107.87 g/mol

= 4854.15/NA g

Similarly

Moles of gold = 46.2/NA

Mass of gold = moles x molecular weight

= (46.2/NA) mol x 196.97 g/mol

= 9100.014/NA g

Moles of copper = 8.8/NA

Mass of copper = moles x molecular weight

= (8.8/NA) mol x 63.55  g/mol

= 559.24/NA g

Total mass of alloy = (1/NA) (4854.15 + 9100.014 + 559.24)

= 14513.404 /NA g

Part a

Weight % of silver = mass of silver x 100 / mass of alloy

= ( 4854.15/NA) x 100 / (14513.404 /NA)

= 33.45 %

Part b

Weight % of gold = mass of gold x 100 / mass of alloy

= ( 9100.014/NA) x 100 / (14513.404 /NA)

= 62.70 %

Part c

Weight % of copper = mass of copper x 100 / mass of alloy

= ( 559.24/NA) x 100 / (14513.404 /NA)

= 3.85%