let G equal volume of gold , and S equal volume of silver
G + S = 0.685 cm^3
19.3 G + 10.5 S = 9.50 g
solve the system for the volume of gold (G)
... multiply by the density to find the mass
Consider a piece of gold jewelry that weighs 9.50 g and has a volume of 0.685 cm^3 . The jewelry contains only gold and silver, which have densities of 19.3 g/cm^3 and 10.5 g/cm^3, respectively. If the total volume of the jewelry is the sum of the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry.
3 answers
Let x = mass Au,
then 9.50-x = mass Ag.
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(1)--volume Au = m/d = x/19.3
(2)--volume Ag = m/d = (9.50-x)/10.5
(3)--volume Au + volume Ag = 0.685
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Substitute (1) and (2) into (3), solve for x and 9.50-x, then
mass % Au = (mass Au/9.50)*100 = ?
mass % Ag = (mass Ag/9.50)*100 = ?
then 9.50-x = mass Ag.
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(1)--volume Au = m/d = x/19.3
(2)--volume Ag = m/d = (9.50-x)/10.5
(3)--volume Au + volume Ag = 0.685
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Substitute (1) and (2) into (3), solve for x and 9.50-x, then
mass % Au = (mass Au/9.50)*100 = ?
mass % Ag = (mass Ag/9.50)*100 = ?
You have the system. Work it to find the answer. You should be thankful you have been given the equations to solve the problem.
2 answers