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.

Question

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.

Answer 1

To calculate the percentage of gold (by mass) in the jewelry, we need to determine the mass of gold and the mass of silver in the jewelry.

Let's start by finding the volume of silver in the jewelry. Since the total volume of the jewelry is the sum of the volumes of gold and silver, we can subtract the volume of gold from the total volume to get the volume of silver:

Volume of Silver = Total Volume - Volume of Gold = 0.685 cm^3 - Volume of Gold

Now, let's find the mass of gold and silver:

Mass of Gold = Density of Gold * Volume of Gold
Mass of Silver = Density of Silver * Volume of Silver

We know the density of gold (19.3 g/cm^3), but we still need to determine the volume of gold. Since the total volume of the jewelry is the sum of the volumes of gold and silver, we can rearrange the equation to solve for the volume of gold:

Volume of Gold = Total Volume - Volume of Silver

Now we have all the information we need to calculate the mass of gold and silver.

Mass of Gold = Density of Gold * (Total Volume - Volume of Silver)
Mass of Silver = Density of Silver * Volume of Silver

Finally, we can calculate the percentage of gold (by mass) in the jewelry:

Percentage of Gold (by mass) = (Mass of Gold / Total Mass) * 100

To find the total mass of the jewelry, we can use the given weight of the jewelry:

Total Mass = Weight of Jewelry

Now plug in the known values and calculate the percentage of gold (by mass) in the jewelry.

Answer 2

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

Answer 3

Let x = mass Au,

then 9.50-x = mass Ag.
---------------------
(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
---------------------------------

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 = ?

Answer 4

To calculate the percentage of gold (by mass) in the jewelry, we need to determine the mass of gold and the mass of silver in the jewelry.

let G equal volume of gold , and S equal volume of silver

Let x = mass Au,

You have the system. Work it to find the answer. You should be thankful you have been given the equations to solve the problem.