# percent composition in alloys and karats.

Submitted by alisonaesthetic on Sun, 07/12/2009 - 19:30

Gold is alloyed with other materials to increase hardness for jewelry.
A) Consider a piece of gold that weight 9.85g and has a volume of 0.675 g/cm3. The jewelry contains gold and silver only with densities of 19.3g/cm3 and 10.5g/cm3. If the total volume is the sum of the gold and silver, calculate the percentage of gold (in mass) in the jewelry.

B) The relative amount of gold in an alloy is expressed in units of karats. Pure gold is 24-karats and percent of gold in an alloy is given as percentage of value. An alloy is 50% and is 12-karats. State the purity of the alloy karats.

You have a typo in the problem:  volume of 0.675 g/cm3
Volume is measure in cm3 not g/cm3.  Is the volume 0.675 cm3?

If it is, then you need to find the density of the gold alloy (density = mass / volume)

Let the percent of gold in the alloy = y
Then the percent of Silver in the alloy must be (100 - y)

The density of the sample must be less than gold and more than silver.  The value of the density of the alloy depends on the amount of gold (x) and silver (100-x).  This suggests an equation:

density of alloy (calculated above)  =  y  x 19.3 g/cm3    +    (100 - y) x 10.5 g/cm3
Since all values (except y) are known, you can solve the equation for y.

B)  An alloy is 50% and is 12-karats.  State the purity of the alloy (in?) karats ?  50 % ?!?!?!

spock wrote:

You have a typo in the problem:  volume of 0.675 g/cm3
Volume is measure in cm3 not g/cm3.  Is the volume 0.675 cm3?

If it is, then you need to find the density of the gold alloy (density = mass / volume)

Let the percent of gold in the alloy = y
Then the percent of Silver in the alloy must be (100 - y)

The density of the sample must be less than gold and more than silver.  The value of the density of the alloy depends on the amount of gold (x) and silver (100-x).  This suggests an equation:

density of alloy (calculated above)  =  y  x 19.3 g/cm3     +     (100 - y) x 10.5 g/cm3
Since all values (except y) are known, you can solve the equation for y.

B)  An alloy is 50% and is 12-karats.  State the purity of the alloy (in?) karats ?   50 % ?!?!?!

okay, yeah, thank you. I didn't see the typo.

and I thought that's what the second problem was, but I thought that was too obvious, so I thought I didn't understand the concept entirely. Thank youuuu. :)