Consider a piece of gold jewelry that weighs 9.30 g and has a volume of 0.650 cm^3 . The jewelry contains only gold and silver, which have densities of 19.3 g/cm3 and 10.5 g/cm3, 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.
let Ms be mass silver, and Vs the volume.
let Mg, Vg be the mass and volume for gold
a. Ms+Mg=9.30
b. Vs+Vg=.650
given Mg/Vg=19.3 and Ms/Vs=10.5
so we can change equation b to read
c. Ms/10.5 + Mg/19.3=.650
so with equation a, and c, you have two equations, two unknowns, I assume you can solve it. Here is the change of c to solve for ms
c'. Ms+ Mg*10.5/19.3=.650*10.5
subtract c' from a, solve for Mg.
final percentage of gold is Mg/(Ms+Mg) * 100
To calculate the percentage of gold (by mass) in the jewelry, we first need to determine the masses of gold and silver present in the jewelry.
Given:
Weight of jewelry = 9.30 g
Volume of jewelry = 0.650 cm³
Density of gold (ρgold) = 19.3 g/cm³
Density of silver (ρsilver) = 10.5 g/cm³
To find the mass of gold in the jewelry, we can use the formula:
Mass of gold = Volume of gold × Density of gold
Since the total volume of the jewelry is the sum of the volumes of gold and silver, we can write:
Volume of jewelry = Volume of gold + Volume of silver
Given that the volume of the jewelry is 0.650 cm³ and the volume of gold is unknown, let's solve for the volume of gold:
Volume of gold = Volume of jewelry - Volume of silver
With the volumes of gold and silver, we can now calculate their respective masses using their densities:
Mass of gold = Volume of gold × Density of gold
Mass of silver = Volume of silver × Density of silver
Finally, to determine the percentage of gold (by mass) in the jewelry, we use the equation:
Percentage of gold = (Mass of gold / Total mass of jewelry) × 100
Now we have all the necessary equations and values to calculate the percentage of gold (by mass) in the jewelry.