You have a piece of gold jewelry that weighs 9 g. Its volume is 0.74 cm3 Assume that the metal is an alloy (a mixture of solids) of gold and silver, which have densities of 19 g/cm3 and 10 g/cm3 respectively. Also assum that there is no change in volume when the pure metals are mixed. The relative amount of gold in an alloy is measured in karats. Pure gold is 24 karats; an alloy of 50% gold is 12 carats. State the proportion of gold in the jewelry in karats.
Answers
Answer:
the percentage o gold by mass has to be calculated and the proportion of gold in the jewelry in carats has to be given.
mass per unit volume of any object is known as its density. Density can be calculated if the mass and volume of the object are known. The SI units of density are kg/m^3.
d=m/v
where
d is the density
m is the mass
v is the volume.
Explanation:
the total mass of the jewelry is given as 9.35g and volume is 0.654cm^3
let us consider mass of gold be "x" and the mass of silver be "y".
therefore
x+y=9.35g
from the above equation, the mass of the silver is 9.35g - x
Total volume= mass of gold/density of gold + mass of silver/density of sliver
substituting the values in the above equation, we get
0.654 cm^3= x/19.3/cm^3+9.35g-x/10.5g/cm^3
rearranging the above equation we get,
(19.3)(10.5)(0.654) g=10.5x + 19.3(9.35g-x)
132.53g=10.5x+180.45g -19.3x
=8.8x+180.45g
8.8x=180