Question

Red gold is a gold‑copper alloy used to make jewelry. A piece of jewelry made of red gold weighs 8.00 g

and has a volume of 0.536 cm3
. Gold has a density of 19.3 g/cm3
and copper has a density of 8.96 g/cm3
. 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.
gold:
%
copper:
%
Pure gold is defined as having 24 carats. When mixed in an alloy, the carats of gold are given as a percentage of this value. For example, a piece of jewelry made with 50% gold has 12 carats. State the purity of this piece of red gold jewelry in carats.
purity:
TOOLS
x10y
carats

Answer 1

I don’t know the answer sorry

Answer 2

Explanation:

To calculate the percentage by mass of each metal in the jewelry, we need to first calculate the mass of each metal in the piece of jewelry.

Let's assume that x is the mass of gold in the jewelry, then the mass of copper in the jewelry would be (8.00 - x) g.

Using the densities of gold and copper, we can calculate the volumes of each metal in the jewelry:

Volume of gold = x / 19.3 g/cm³

Volume of copper = (8.00 - x) / 8.96 g/cm³

Since the total volume of the jewelry is the sum of the volumes of the two metals it contains, we have:

x / 19.3 g/cm³ + (8.00 - x) / 8.96 g/cm³ = 0.536 cm³

Solving for x, we get:

x = 3.321 g

Therefore, the mass of copper in the jewelry is:

8.00 g - 3.321 g = 4.679 g

To calculate the percentage by mass of each metal, we use the following formulas:

% gold = (mass of gold / total mass of jewelry) x 100%

% copper = (mass of copper / total mass of jewelry) x 100%

Substituting the values we just calculated, we get:

% gold = (3.321 g / 8.00 g) x 100% = 41.51%

% copper = (4.679 g / 8.00 g) x 100% = 58.49%

Therefore, the percentage by mass of gold and copper in the jewelry are approximately 41.51% and 58.49%, respectively.

To find the purity of the piece of red gold jewelry in carats, we need to divide the mass of gold in the jewelry by the total mass of the jewelry and multiply by 24 (the number of carats in pure gold). Substituting the values we just calculated, we get:

purity = (3.321 g / 8.00 g) x 24 carats = 9.96 carats

Therefore, the purity of the red gold jewelry is approximately 9.96 carats.