Red gold is a gold‑copper alloy used to make jewelry. a piece of jewelry made of red gold weighs 7.24 g and has a volume of 0.436 cm3 . gold has a density of 19.3 g/cm^3 and copper has a density of 8.96 g/cm^3 . calculate the percentage by mass of each metal in the jewelry. assume the total volume of the jewelry is the sum of the volumes of the two metals it contains.

%cu = 13.95%

%au=86.05%

Explanation:

Since the total volume is the sum of both volumes (gold, copper) we can say:

We know that  and . Replacing these values into our volume equation:

We also know that:

Solving this equation system:

Percentage by mass of Gold is about 86%

Percentage by mass of Copper is about 14%

Let's recall Density formula as follows:

where:

ρ = density of object ( kg/m³ )

m = mass of object ( kg )

V = volume of object ( m³ )

Let us now tackle the problem!

Given:

total mass of jewelry = m = 7.24 g

total volume of jewelry = V = 0.436 cm³

density of gold = ρ_g = 19.3 g/cm³

density of copper = ρ_c = 8.96 g/cm³

Asked:

percentage by mass of gold = m_g = ?

percentage by mass of copper = m_c = ?

Solution:

Grade: High School

Subject: Physics

Chapter: Physical Quantities

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