[srya2000]

Please help

A very large single crystal of gypsum, CaSO₄·2H₂O measuring 12 x 1 x 1m has been found in the Naica mine in Chihuahu, Mexico. Imagine we took this crystal and placed it in the reflecting pool (assume a teperature of 20°C and a pool depth of 1m). What would be the concentration of calcium ions at equilibrium?

I know gypsum is moderately water soluble so i assume i will need to calculate solubility constant. But other then that i am totally lost

[Borek]

Direct application of solubility product.

[srya2000]

ok here is what i have.

density is 2.3808 g/cm^3 and the volume of the gypsum is 1200 cm^3 so the mass is 2769.6g giving 14.1595 mols using a molar mass of 195.6g/mol. Ksp=10^-4.6 and Ksp ~ [ca²⁺][SO4^2-] 

Since there is a 1mol/1mol ratio between the ions and the original solid does that mean that the concentration would be 14.15mol/1000L (does 1m mean 1000L?) But then i haven't used the solubility constant.. and does the 2H₂O come into effect at all?

I know i probably just need to find the [SO4^2-] and use solubility product  but if i can just find that concentration why would i need to use the constant to find Ca?

[AWK]

density is 2.3808 g/cm^3 and the volume of the gypsum is 1200 cm^3 so the mass is 2769.6g giving 14.1595 mols using a molar mass of 195.6g/mol. Ksp=10^-4.6 and Ksp ~ [ca2+][SO42-] 

Other dimensions of pool are other than 1 cm. Calculate volume correctly.

In the first post you gave only a depth of pool - other dimensions are missing.

[Borek]

the volume of the gypsum is 1200 cm^3

No, it is many, many times larger. At least starting from the 12x1x1m size that you posted initially (and which fits sizes reported in Wikipedia for the Naica mine).

My bet is that because of the huge quantity of the calcium solution in the reflecting pool will be saturated (and the volume of the reflecting pool doesn't matter). But you can always try to estimate the volume of the typical reflecting pool knowing its depth and assuming it is - say - 20 meters wide and 200 meters long.

[AWK]

Lincoln Memorial Reflection Pool (probably the most known in USA)  is 681 meters long and 51 meters wide.

[Borek]

Lincoln Memorial Reflection Pool (probably the most known in USA)  is 681 meters long and 51 meters wide.

That would mean solution is not saturated.