Question

In a sample of 18-karat gold, 75 percent of the total mass is pure gold, while the rest is typically 16 percent silver and 9 percent copper. If the density of pure gold is rhogold=19.3g/cm3, while the densitites of silver and copper are respectively rhosilver=10.5g/cm3 and rhocopper=8.90g/cm3, what is the overall density rho18kt of this alloy of 18-karat gold?

Answer 1

Answer:

15.57 g/cm³

Explanation:

$\rho_g$ = Density of gold = 19.3 g/cm³

$\rho_s$ = Density of silver = 10.5 g/cm³

$\rho_c$ = Density of copper = 8.9 g/cm³

Assuming total mass as 1000 g

Volume of gold

$V_g=\frac{0.75\times 1000}{19.3}\\\Rightarrow V_g=38.86\ cm^3$

Volume of silver

$V_g=\frac{0.16\times 1000}{10.5}\\\Rightarrow V_g=15.238\ cm^3$

Volume of copper

$V_c=\frac{0.09\times 1000}{8.9}\\\Rightarrow V_c=10.11\ cm^3$

Density of the alloy would be

$\rho=\frac{M}{V_g+V_s+V_c}\\\Rightarrow \rho=\frac{1000}{38.86+15.238+10.11}\\\Rightarrow \rho=15.57\ g/cm^3$

The overall density of this alloy is 15.57 g/cm³