Question

You have a piece of gold jewelry weighing 9.35g. Its volume is 0.654cm 3 . Assume the metal is an alloy of gold and silver, which have densities of 19.3g/cm 3 and 10.5g/cm 3 , respectively. Also assume that there is no change in volume when the pure metals are mixed. Calculate the percentage of gold (by mass) in the alloy.

Answer 1

57.54% is the percentage of gold by mass in the alloy.

Step-by-step explanation:

The mass of the mixture is 9.35g. That is:

9.35g = Mass Gold + Mass Silver

Mass silver = 9.35g - Mass gold (1)

Now, the volume of the jewelry is the sum of volumes of gold and silver:

0.654cm³ = Mass Gold / 19.5g/cm³ + Mass silver / 10.5g/cm³ (2)

Volume = Mass / Density.

Replacing (1) in (2):

0.654cm³ = Mass Gold / 19.5g/cm³ + (9.35g - Mass gold) / 10.5g/cm³

0.654 = 0.051282 Mass Gold + 0.890476 - 0.095238 Mass gold

-0.236476 = -0.043956 Mass gold

Mass gold = 5.38g

And mass percent of gold in the alloy is:

5.38g / 9.35g * 100 =

57.54%