Question

Red gold is a gold‑copper alloy used to make jewelry. A piece of jewelry made of red gold weighs 7.67 g and has a volume of 0.430 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: carats

Answer 1

Answer:

% gold = 92.83 %

% copper = 7.17 %

Explanation:

Step 1: Data given

Mass of the piece = 7.67 grams

Volume of the piece = 0.430 cm³

Density of gold = 19.3 g/cm³

Denisty of copper = 8.96 g/cm³

Step 2: define volumes

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

Vgold + Vcopper = 0.430 cm³

with Vgold = Mass of gold / Density of gold

with Vcopper = Mass of copper / Density of copper

Step 3: rearrange formules

19.3 g/cm³ = m1/V1 → 19.3*V1 = m1    (mass of the gold in terms of it's density and volume )

8.96 g/cm³ = m2/V2 --> 8.96g * V2 = m2   (mass of the silver in terms of it's density and volume)

m1 + m2 = 7.67grams  

19.3*V1 + 8.96g * V2 = 7.67 grams    

 

Step 4: Calculate volumes

Total volume = 0.430 cm³

V1 + V2 = 0.430 cm³ --> V1 = 0.430 - V2

 

19.3*(0.430 - V2) + 8.96*V2 = 7.67

8.299 - 19.3V2 + 8.96V2 = 7.67

8.299 - 7.67 = 19.3 V2 - 8.96V2

0.629 =10.34V2

V2 =0.061 cm³

V1  *= 0.430 cm³ - 0.061cm³ = 0.369 cm³

Volume of gold = 0.369 cm³

Volume copper = 0.061

Total volume = 0.369 + 0.061 = 0.430  cm³

Step 5: Calculate mass

Mass gold = volume gold * density

Mass gold = 0.369 cm³ * 19.3 g/cm³

Mass gold = 7.1217 grams

Mass copper = volume copper * density copper

Mass copper = 0.061 cm³ * 8.96 g/cm³

Mass copper = 0.54656 grams

Total mass = 7.12+0.55 = 7.67 grams

Step 6: Calculate % godl and copper

% gold = (7.12/7.67) * 100% = 92.83 %

% copper = (0.55 / 7.67) *100% = 7.17 %