Calculating solubilities from solubility products
Reversing the sums we have been doing isn't difficult as long as you know how to start. We will take the magnesium hydroxide example as above, but this time start from the solubility product and work back to the solubility.
If the solubility product of magnesium hydroxide is 2.00 x 10-11mol3 dm-9 at 298 K, calculate its solubility in mol dm-3 at that temperature.
The trick this time is to give the unknown solubility a symbol like x or s. I'm going to choose s, because an x looks too much like a multiplication sign.
If the concentration of dissolved magnesium hydroxide is s mol dm-3, then:
[Mg2+] = s mol dm-3[OH-] = 2s mol dm-3
Put these values into the solubility product expression, and do the sum.
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