Question

Gold is alloyed(mixed) with other metals to increase its hardness in making jewelry. (A) 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, repectively. 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. (B) The relative amount of gold in an alloy is commonly expressed in units of karats.

Answer 1

Continuation in letter (B): Pure gold is 24-karat, and the percentage of gold in an alloy is given as a percentage of this value. For example, an alloy that is 50% gold is 12-karat. State the purity of the gold jewelry in karats.

Answer 2

@theEric this will be the last question eric, i need your help in this problem.

Answer 3

Did you convert 9.85 grams to cubic cm?

Answer 4

So you have this "gold" ring of \(.675\ [cm^3]\).
Part of the volume is gold, and part is silver.

Now, \(\rho_{gold}=19.3\ [g/cm^3]\), and \(\rho_{silver}=10.5\ [g/cm^3]\).

Their volumes add up to the ring's volume, right?

Now, I don't want you to think past that yet. Do you really understand that much?

Answer 5

Ohh okay. then?

Answer 6

Well!
\(\rho=m\div V\qquad\)by definition. So
\(V=m\div \rho\qquad\)by multiplying both sides by \(\large\frac{V}{\rho}\)

We'd say \(V_{gold}=m_{gold}\div\rho_{gold}\), right?

Answer 7

Yeaah. Right :)

Answer 8

eric. I'll be out now. Just send me how to answer

Answer 9

And, likewise, \(V_{silver}=m_{silver}\div\rho_{silver}\)

And, like I said earlier, those two volumes add up to the ring's total volume.
\(V_{gold}+V_{silver}=V_{ring}\)

I'll send you hints!

Answer 10

Take care!

Answer 11

We want the percentage of gold. How much mass is gold of the total mass (it says, "by mass")?
We want\[\frac{m_{gold}}{m_{total}}\times\frac{ 100\%}{1}\]


\(m_{gold}+m_{silver}=m_{ring}=9.85\ [g]\qquad\)(1)

\(V_{gold}+V_{silver}=V_{ring}=0.675\ [cm^3]\)
\(\qquad\qquad\qquad\Downarrow\)
\( m_{gold}\div\rho_{gold}+m_{silver}\div\rho_{silver}=V_{ring}\qquad\)(2)

We have a "system of equations" to solve.

You can solve for the \(m_{silver}\) in the first equation and substitute that in for \(m_{silver}\) in the second. Then you'll be able to solve \(m_{gold}\)

Once you've solved for \(m_{gold}\), you'll be able to calculate \(\Large \frac{m_{gold}}{m_{total}}\times\frac{ 100\%}{1}\)

For part b, you want to multiply that percentage by 24 karats.