Question

I have to find the overall density of the 18karat gold. In this alloy, it contains 75% gold, 16% silver and 9% copper. Im given the densities of gold, copper and silver, but I'm confused what to do with the percentages. It also told me that an " 18-karat gold alloy contains (at least) 18 parts (by mass) of gold out of 24 parts total."

What do I do with the percentages?

Answer 1

Seems certain the percentages are by mass so say you have a 1kg bar of the alloy....

That is made up of \(\begin{matrix}
Au & .750kg \\
Ag & .160kg \\
Cu & .090kg
\end{matrix}
\)

Key idea is density \(\rho = \dfrac{Mass}{Volume} \implies V = \dfrac{M}{\rho}\)

So the bar will have total volume: \(V_T = \dfrac{.750}{\rho_{Au}} + \dfrac{.160}{\rho_{Ag}} + \dfrac{.090}{\rho_{Cu}} \)

and so overall density \(= \dfrac{\mathbf{Tot ~ Mass} }{\mathbf{Tot ~ Volume} } = \dfrac{1}{ V_T}\)