Question

Gold is alloyed with other metals to increase its hardness in making jewelry.

Consider a piece of gold jewelry that weighs 9.30 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.

Answer 1

The percentage of gold is 52.5 %

Step-by-step explanation:

Step 1: Data given

Piece of gold jewelry that weighs 9.30 g and has a volume of 0.675 cm³

Density of gold = 19.3 g/cm³

Density of silver = 10.5 g/cm³

Step 2: Calculate the volume of gold

Density = mass/ volume

Mass = density (gold) * volume (gold) + density silver * volume silver

9.30 g= 19.3 * V(gold) + 10.5* (0.675 - V(gold))

9.30g = 19.3V(gold) + 7.0875 - 10.5V(gold)

2.2125 = 8.8(Vgold)

V(gold) = 0.2514 cm³

Step 3: Calculate the mass of gold

Mass gold = density * volume

Mass gold = 19.3 g/cm³ * 0.2514 cm³

Mass gold = 4.85 grams

Step 4: Calculate the percentage of gold

% gold = (mass gold / total mass) * 100%

% gold = (4.85 grams / 9.30 grams )*100%

% gold = 52.2 %

The percentage of gold is 52.5 %