You have a piece of gold weighing 9.36g. Its volumes is .657 cm^3 Assume that the metal is an mixture of gold and silver. which have densities of 19.3 g/cm^3 and 10.5 cm^3, respectively. Assume that there is no change in volume when the pure metals are mixed.How to calculate the percentage of gold (by mass) in the mixture?
Let g stands for gold and s stands for silver. therefore
g+s =9.36...................i
v1 and v2 are their volumes and d1 and d2 are their densities
v1 +v2= 0.657............ii
v1d1+v2 d2=9.36
19.3v1 +10.5v2=9.36.....iii
Multiply ii by 19.3 and solve with iii
19.3v1 +19.3v2 =12.6801........iv
subtract iii from iv
8.8v2=3.3201
v2 =0.37728409..............v
Using ii and v
v1=0.27971591..............vi
g=v1xd1=0.27971591x19.3=5.398517063gm.鈥?br>
s =0.37728409x10.5=3.961482945 gm......................viii
Therefore gold is ={5.398517063/9.36}x100=57.676%
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