Answer:
Density of 18.0-karat gold mixture is [tex]15.58 g/cm^3[/tex].
Explanation:
A mixture of 18 parts gold, 5 parts silver, and 1 part copper.
Let mass of gold be 18x
Let the mass of silver be 5x
Let the mass of copper be 1x
The density of gold = [tex]19.32g/cm^3[/tex]
The density of silver = [tex]10.1g/cm^3[/tex]
The density of copper =[tex] 8.8g/cm^3[/tex]
[tex]Volume=\frac{Mass}{Density}[/tex]
Volume of the gold in the mixture = [tex]V_1=\frac{18x}{19.32 g/cm^3}[/tex]
Volume of the silver in the mixture = [tex]V_2=\frac{5x}{10.1 g/cm^3}[/tex]
Volume of the copper in the mixture = [tex]V_3=\frac{1x}{8.8 g/cm^3}[/tex]
Mass of the mixture = M = 18x+5x+1x =24x
Volume of the mixture = [tex]V_1+V_2+V_3[/tex]
Density of the mixture:
[tex]\frac{M}{V_1+V_2+V_3}=15.58 g/cm^3[/tex]
