Question

Gold has a density of 19.3 g/cm³, and quartz has a density of 2.65 g/cm³. A sample of quartz contains gold. If the quartz sample has a mass of 10 g and a volume of 3 cm³, what is the mass in grams of gold in the quartz sample?

Answer 1

Sample density ρs = 10 gr/3 cm^3 = 3.333 g/cm^3
If we call x the gold in per unit (p.u.) and (1-x) the quartz in p.u., then the following statement is true :
(Gold density ρg*x+quartz density ρq*(1-x) = Sample density ρs
19.3x+2.65(1-x) = 3.333
19.3x+2.65-2.65x = 3.333
16.65x = 0.683
x = 0.683/16.65 = 0.04102 in p.u. or 100*0.04102 = 4.102 %
4.102 % of the volume is gold ..so :
3*0.04102*19.3 = 2.375 gr .....mass of gold
check :
3*(1.00-0.04102)*2.65 = 7.625 gr.....mass of quartz
2.375+7.625 = 10.00 gr...total sample mass