# Purity and Density of metals

Determination of density has many practical applications. Is a piece of jewelry pure gold or is it an alloy perhaps of gold and silver? Give that the densities of gold and silver at 25 degrees C are 19.3 and 10.5g/mL respectively and that the volume of the alloy is the sum of the volumes of the metals used, calculate the density of an alloy that is 75% by mass gold and 25% silver. (Hint: Assume you have 1.00g of the alloy).

Also, determine the density of an alloy that is 50% by mass gold and 50% silver. If the volume of the jewelry is about 1 mL, could you use your lab balance and graduated cylinder to distinguish between pure gold and the above alloys? Explain your answer.

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Determination of density has many practical applications. Is a piece of jewelry pure gold or is it an alloy perhaps of gold and silver? Give that the densities of gold and silver at 25 degrees C are 19.3 and 10.5g/mL respectively and that the volume of the alloy is the sum of the volumes of the metals used, calculate the density of an alloy that is 75% by mass gold and 25% silver. (Hint: Assume you have 1.00g of the alloy).

If we have one gram of the alloy, it will contain 0.75g gold and 0.25g silver.

Because gold has a density 19.3g/ml, the volume of 0.75 g gold is

Volume of gold = mass/density = 0.75/19.3 = 0.0389 ml

Similarly volume of silver = 0.25 /10.5 = 0.024 ml

Total volume of the material = 0.0389 + 0.024 = 0.0629 ml

But its weight is only 1 gram ïƒ¨ density = mass/volume = 1/0.0629 = 15.898 g/ml

Also, determine the density of an alloy that is 50% by mass gold and 50% silver. If the volume of the jewelry is about 1 mL, could you use your lab balance and graduated cylinder to distinguish between pure gold and the above alloys? Explain your answer.

Total volume of metals used = 0.5/19.3 + 0.5/10.5 = 0.0735 ml and mass = 1gram

Therefore, Density = mass/volume = 1/0.0735 = 13.6 g/ml

Because gold has a density of 19.3g/ml, 1 gm of gold will have a volume v = 1/19.3 = 0.052 ml

If you immerse this much amount of gold in your water filled graduated cylinder, it will increase the water level by an amount equal to 0.052/cross sectional area of the cylinder in cm. Note this rise in level.

Now take the 50 - 50 sample.

Its volume = 0.735 ml and will raise the water level by an amount 0.0735/cross sectional area of the cylinder in cm. The level will go well above the earlier value

Now to the 75 - 25 sample

It will raise the level by 0.0629/cross sectional area of the cylinder in cm. This will be in between the above two values.

Since the cross sectional area of the cylinder is a constant for all the measurements, you can easily distinguish between the three samples just by noting the water level.

The following web page will give you a clear and detailed view of the original work by Archimedes http://www.mcs.drexel.edu/~crorres/Archimedes/Crown/CrownIntro.html

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