Question

Gold in its pure form is too soft to be used for most jewelry. Therefore, the gold is mixed with other metals to produce an alloy. The composition of gold alloys are always calculated by mass, using the karat (kt) as a unit of measure. A karat represents a proportion by mass of one part in twenty-four. The higher the karat value, the higher the proportion of gold in relation to the total metal content. Pure gold is therefore 24 karat, while an 18-karat gold alloy contains (at least) 18 parts (by mass) of gold out of 24 parts total.
In a sample of 18-karat gold, 75 percent of the total mass is pure gold, while the rest is typically 16 percent silver and 9 percent copper. If the density of pure gold is rhogold = 19.3 g/cm^3, while the densitites of silver and copper are respectively rhosilver = 10.5 g/cm^3 and rhocopper = 8.90 g/cm^3.
a) What is the overall density rho18kt of this alloy of 18-karat gold?
Express your answer in grams per cubic centimeter to three significant figures.

Answer 1

Answer:

Explanation:18kt alloy contains

i) 75% of gold

rhogold=19.3g/cm^3

=75/100×19.3

=14.475g/cm^3

ii) 16% of silver

rhosilver=10.5g/cm^3

=16/100×10.5

=1.68g/cm^3

iii) 9% of copper

rhocopper =8.90g/cm^3

=9/100×8.9

=0.801g/cm^3

Overall density of 18kt gold

=(0.801+1.68+14.475)g/cm^3

=16.956g/cm^3

=17g/cm^3 to 3s.f