Daniel D. answered • 06/01/20

College sophomore studying computer science and prehealth

The first step would be to write out equation for the K_{sp} of this substance, which would be...

K_{sp} = [Ca^{2+}][CO_{3}^{2-}]

(CaCO_{3} is not included in the K_{sp} since it is a solid)

We know from the chemical equation that however many moles of CaCO_{3} dissolve, we will get the same number of moles of each of the ions. Therefore...

K_{sp} = x * x = x^{2}

Here, x represents the molar solubility of the compound, which is related to the solubility of the compound. Once you find x, you can determine the K_{sp}. You are given that 0.0067g of CaCO_{3} dissolve in 1L of water, so the solubility is 0.0067g/L, but to get molar solubility, we must divide by the molar mass of CaCO_{3}. After finding that the molar mass is around 100.0868g/mol, we divide 0.0067g/L by this to get...

(0.0067g/L)/(100.0868g/mol) = 6.69E-5mol/L = x

Now we just square this to get k_{sp}...

K_{sp} = x^{2} = (6.69E-5)^{2} = __4.48E-9 __

When we round for sig figs, we get __4.5E-9__