Mr. Eliot Overgatch owns a platinum tea kettle that has been valued at $100,000.

Question

Mr. Eliot Overgatch owns a platinum tea kettle that has been valued at $100,000. Because of heavy usage over the last 20 years, the kettle has accumulated so much "scale" that it is virtually impossible to boil water in it. One of his many minions informs "The Big E" that the scale is actually Calcium Carbonate, CaCO_3, which could be dissolved out by filling the kettle with water and emptying it out a certain number of times. Overgatch tells his servant Igor (that's EYE-gor) to start this task immediately. The "Gor-ster" is to figure out how many times he needs to fill the kettle up and empty it out and to use Evian springwater, costing $2.15 per liter, to do it. If the kettle has a volume of 1.0 Liter and contains 155.0 grams of scale, how many times must Igor fill the kettle up and empty it out to dissolve all of the CaCO_3. How much will it cost Overgatch to have the kettle reconditioned in this manner? (The K_sp for CaCO_3 = 3.8 times 10^-9)

Explanation / Answer

CaCO3 ----------> Ca+2 + CO32-
Ksp = [Ca+2] [CO32-] = 3.8*10-9
one of these 2 speices will have concentration as sqrt(3.8*10-9) = 6.1644*10-5 M
Therefore 6.1644*10-5*2 = 1.2328*10-4 moles of CaCO3 will dissolve in 1L
Molar mass of CaCO3 = 100 gm/mol
So 1 liter of water can dissolve 100*1.2328*10-4 = 0.012328 gm of CaCO3
0.012328 gm ------------- 1L
155 gm ----------- ? (cross multiply)
It would take 12573 L of spring water to dissolve all the CaCO3
If the kettle has 1 L volume then he has to fill 12573 times
To have the kettle reconditioned it will cost = 12573*2.15 = 27031.959 $

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