[Sca-cooks] A 210 carat pearl (should) dissolve in a glass of wine - long

[Andrea Scott]

Greetings to the list!

I usually lurk, as I have much to learn, but someone else usually asks my
questions before I can.  However, I mentioned the discussion on dissolving
pearls to my husband, who like a good engineer, decided to figure out if one
could dissolve a pearl in a drinkable glass of wine.  Below are his
findings.

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I think that a 210 carat pearl (30 mm in diameter) could be dissolved in
wine. Cleopatra might have been able to do it.

The long explanation, sources at the end:

Natural pearls are made up of aragonite crystals (86%) and conchiolin
protein (10%) arranged in radial and concentric layers, with 2 to 4 % water.
[1][2]

Aragonite is chemically calcium carbonate (CaCO3), which has a molecular
weight of 100.9 g/mol   [3]

The pH of wine is about 3 to 3.6.  pH is (generally) how acidic things are.
[4]

This website shows the solubility of CaCO3 as a function of pH.  In a liquid
having a pH of 4,
molar solubility of CaCO3 is 1.7 mol/liter.  That means that an acid having
a pH of 4 could dissolve 1.7 moles of CaCO3 per liter of the acid.  (a pH of
4 is less acidic than pH of wine at 3, so a liquid of pH 3 could dissolve
_more_).  [5]

A mole is a given number (Avogadro's number) of something.  We can convert
from moles to mass by multiplying by the molecular weight of something. To
convert 1.7 mol/liter to grams per liter we multiply by the molecular weight
of CaCO3:

   1.7 mol/L * 100.9 g/mol = 171.53 g/L

So this one liter of acid (wine) at pH of 4 could dissolve 171.53 grams of
CaCO3. But one liter is a lot...250mL is maybe more realistic.  250mL is 25%
of 1L, and 25% of 171.53 grams is about 42 grams.  So we can dissolve a 42
gram pearl in 250mL of this pH 4 wine.

How big is a 42 gram pearl? 1 gram = 5 carats, so this pearl is 42 * 5 =

  210 carats!

Knowing the density of pearls is about 2.6 to 2.8 g/cm^3, we can figure out
its volume:  [6]

  (42 g) / (2.7 g/cm^3) = 15.5 cm^3

The volume of sphere is 4/3 * pi * radius^3. [7]
Solving for radius with a volume of 15.5 cm^3 gives us
radius = 1.54 cm -- or a

  30 mm diameter pearl!

This account [8] asserts that it was wine vinegar, and not wine that was
used.  They also believe it was possible to dissolve the pearl.

This explanation assumes simple chemistry, and does not take into account
temperature, speed of dissolution, or many other things.  Perhaps the best
way to do this is to try dissolving a pearl in some wine!

--Diego


[1] http://www.voguegioiello.net/06per/perle/10ana/eindex.asp
[2] http://ist-socrates.berkeley.edu/~eps2/wisc/Lect17.html
[3] http://webmineral.com/data/Aragonite.shtml
[4] http://eat.epicurious.com/dictionary/wine/index.ssf?DEF_ID=2294&ISWINE=T
[5] http://www.chem.usu.edu/faculty/sbialkow/Classes/3600/Alpha/alpha3.html
[6] http://www.voguegioiello.net/06per/perle/10ana/eindex.asp
[7] http://mathworld.wolfram.com/Sphere.html
[8]
http://itsa.ucsf.edu/~snlrc/encyclopaedia_romana/miscellanea/cleopatra/caban
el.html

Disclaimers: I am not a chemist. Don't try this at home.  Don't drink acid.

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-I promise to do some cooking trials so I'll have cooking questions to ask
soon.  Maybe in preparation for Steppes Artisan in August.

Abigail Pinel
(Andi Scott)
Shire of the Shadowlands
Ansteorra (College Station, Texas)