Question

How much copper, in weight percent, is in an alloy consisting of 94.1 at.% Ag and 5.9 at.% copper? The atomic weights for Ag and Cu are 107.87 g/mol and 63.55 g/mol, respectively.

Answer 1

we know that

atomic percentage of Ag = ( number of atoms of Ag / total atoms in alloy ) x 100

similarly

atomic percentage of Cu = ( number of atoms of Cu / total atoms in alloy ) x 100

dividing both of them we get

atomic percentage of Ag / atomic percentage of Cu = number of atoms of Ag / number of atoms of Cu

so

94.1 / 5.9 = number of atoms of Ag / number of atoms of Cu

15.8949 = number of atoms of Ag / number of atoms of Cu

we know that

moles of Ag = number of atoms of Ag / avagadro number (NA)

moles of Ag = number of atoms of Ag / NA

also

mass of Ag = moles of Ag x atomci mass of Ag

so

mass of Ag = number of atoms of Ag x 107.87 / NA

similarly

mass of Cu = number of atoms of Cu x 63.55 / NA

dividing both of them we get

mass of Ag / mass of Cu = number of atoms of Ag x 107.37 / number of atoms of Cu x 63.55

but we got

15.8949 = number of atoms of Ag / number of atoms of Cu

so

mass of Ag / mass of Cu = 15.8949 x 107.37 / 63.55

mass of Ag / mass of Cu = 26.94

now

mass of alloy = mass of Ag + mass of Cu

so

mass of alloy = (26.94 x mass of Cu ) + mass of Cu

mass of alloy = 27.94 x mass of Cu

now consider weight percent

weight percent of Cu = ( mass of Cu / mass of alloy ) x 100

= mass of Cu x 100 / 27.94 x mass of Cu

= 3.578

so the weight percent of Copper in the alloy is 3.578 %