Question

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

Answer #1

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

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