Answer: The number of gold atoms per cubic centimeters in the given alloy is [tex]1.83\times 10^{22}[/tex]
Explanation:
To calculate the number of gold atoms per cubic centimeters for te given silver-gold alloy, we use the equation:
[tex]N_{Au}=\frac{N_AC_{Au}}{(\frac{C_{Au}M_{Au}}{\rho_{Au}})+(\frac{M_{Au}(100-C_{Au})}{\rho_{Ag}})}[/tex]
where,
[tex]N_{Au}[/tex] = number of gold atoms per cubic centimeters
[tex]N_A[/tex] = Avogadro's number = [tex]6.022\times 10^{23}atoms/mol[/tex]
[tex]C_{Au}[/tex] = Mass percent of gold in the alloy = 42 %
[tex]\rho_{Au}[/tex] = Density of pure gold = [tex]19.32g/cm^3[/tex]
[tex]\rho_{Ag}[/tex] = Density of pure silver = [tex]10.49g/cm^3[/tex]
[tex]M_{Au[/tex] = molar mass of gold = 196.97 g/mol
Putting values in above equation, we get:
[tex]N_{Au}=\frac{(6.022\times 10^{23}atoms/mol)\times 48\%}{(\frac{48\%\times 196.97g/mol}{19.32g/cm^3})+(\frac{196.97g/mol\times 58\%}{10.49g/cm^3})}\\\\N_{Au}=1.83\times 10^{22}atoms/cm^3[/tex]
Hence, the number of gold atoms per cubic centimeters in the given alloy is [tex]1.83\times 10^{22}[/tex]
