Respuesta :
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 %
% gold = 92.83 %
% copper = 7.17 %
Given:
Mass of the piece = 7.67 grams
Volume of the piece = 0.430 cm³
Density of gold = 19.3 g/cm³
Density of copper = 8.96 g/cm³
To find:
% gold and % copper=?
Since the total volume is the sum of both volumes (gold, copper) we can say:
Vgold + Vcopper = 0.430 cm³
Density:
For Vgold = Mass of gold / Density of gold
For Vcopper = Mass of copper / Density of copper
On substituting the values in the above formula we will get:
- For gold:
[tex]19.3 g/cm^3 = \frac{m_1}{V_1 } \\\\19.3*V_1 = m_1[/tex]
- For copper:
[tex]8.96 g/cm^3 = \frac{m_2}{V_2}\\\\8.96g * V_2 = m_2[/tex]
On rearranging both the equations:
[tex]m_1 + m_2 = 7.67grams\\\\ 19.3*V_1 + 8.96g * V_2 = 7.67 grams[/tex]
- Calculation for volume:
Total volume = 0.430 cm³
[tex]V_1 + V_2 = 0.430 cm^3 \\\\V_1 = 0.430 - V_2\\\\19.3*(0.430 - V_2) + 8.96*V_2 = 7.67\\\\8.299 - 19.3V_2 + 8.96V_2 = 7.67\\\\8.299 - 7.67 = 19.3 V_2 - 8.96V_2\\\\0.629 =10.34V_2\\\\V_2 =0.061 cm^3[/tex]
[tex]V_1-V_2= 0.430 cm^3 - 0.061cm^3 = 0.369 cm^3[/tex]
Volume of gold = 0.369 cm³
Volume of copper = 0.061 cm³
Total volume = 0.369 + 0.061 = 0.430 cm³
- Calculation of 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
- Calculation of %gold and % copper
% gold = (7.12/7.67) * 100% = 92.83 %
% copper = (0.55 / 7.67) *100% = 7.17 %
Find more information about "Mass percentage" here:
brainly.com/question/26150306
