An archaeologist at an excavation discovers a crown that looks like gold. It has a mass of 546 g and a volume of 34.6 cm³. However, chemical analysis shows that the crown consists of a mixture of gold and silver. Unfortunately the analysis is unable to give the proportions without removing a sample. The problem is to find the mass of gold in the crown. We assume that the volume of the crown is equal to the initial volumes of gold and silver of which it is composed.
Density of gold, ρg=19.3 g cm−3
Density of silver, ρs=10.5 g cm−3
a) Write down an equation relating the masses mg and ms of gold and silver in the crown and an equation for the corresponding volumes Vg and Vs. [2]
b) Write down an equation for the total mass in terms of the volumes Vg, Vs and densities ρg, ρs of the gold and silver in the crown. [1]
c) In the equation from (b) substitute for Vs and then substitute for Vg to obtain a relation between ρg, ρs and mg. [3]
d) Determine the value of the mass of gold, mg. [1]