Question

Consider a piece of gold jewelry that weighs 9.85 g and has a volume of 0.675 cm3 . 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.

a. 57.2% Au
b. 42.8% Au
c. 35.6% Au
d. 64.4% Au

Answer 1

To determine the percentage of gold (by mass) in the jewelry, you can calculate the mass of the gold and divide it by the total mass of the jewelry. Using the densities of gold and silver, you can find the mass of each metal and then calculate the percentage.

Step-by-step explanation:

The percentage of gold (by mass) in the jewelry can be determined by finding the mass of the gold and dividing it by the total mass of the jewelry, then multiplying by 100 to get the percentage.

First, calculate the mass of the gold in the jewelry. Since the density of gold is 19.3 g/cm³ and the volume of the gold is 0.675 cm³, the mass of the gold is 19.3 g/cm³ x 0.675 cm³ = 13.0525 g.

Next, find the total mass of the jewelry by adding the mass of the gold and the mass of the silver. The mass of the silver can be calculated using the same method: density of silver (10.5 g/cm³) x volume of silver (total volume - volume of gold).

Finally, calculate the percentage of gold by dividing the mass of the gold by the total mass of the jewelry and multiplying by 100: (13.0525 g / (13.0525 g + mass of silver)) x 100.