Answer:
% gold = 92.83 %
% copper = 7.17 %
Explanation:
<u>Step 1</u>: 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
<u>Step 2:</u> 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 %
