Question

Consider a piece of gold jewelry that weighs 9.85 g and has a volume of 0.675 cm3 . The jewelry contains only gold and silver, which have densities of 19.3 g/cm3 and 10.5 g/cm3, respectively. If the total volume of the jewelry is the sum of the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry.

Answer 1

Answer:

61.5096 %

Explanation:

Let the amount of gold in the jewelry = x g

Let the amount of silver in the jewelry = y g

Total mass of jewelry = 9.85 g

So,

x + y = 9.85 g    .................................1

Density = Mass / Volume

Given that:

Density of gold = 19.3 g/cm³

Thus, volume is:

Volume = Mass / Density = x / 19..3 cm³

Given that:

Density of silver = 10.5 g/cm³

Thus, volume is:

Volume = Mass / Density = y / 10.5 cm³

The total volume of the jewelry = 0.675 cm³

So,

$\frac {x}{19.3}+\frac {y}{10.5}=0.675$

Or,

10.5 x + 19.3 y = 136.78875  ................2

Solving 1 and 2, we get that:

x = 6.0587 g

y = 3.7913 g

So, mass % of gold:

Mass % = (6.0587 / 9.85)×100 = 61.5096 %