Answer: c. [tex]6.2\times 10^{-5}moles/L[/tex]
Explanation:
Solubility product is defined as the equilibrium constant in which a solid ionic compound is dissolved to produce its ions in solution. It is represented as [tex]K_{sp}[/tex]
The equation for the ionization of the calcium carbonate is given as:
[tex]CaCO_3\leftrightharpoons Ca^{2+}+CO_3^{2-}[/tex]
We are given:
[tex]K_{sp}=3.8\times 10^{-9}[/tex]
By stoichiometry of the reaction:
1 mole of [tex]CaCO_3[/tex] gives 1 mole of [tex]Ca^{2+}[/tex] and 1 mole of [tex]CO_3^{2-}[/tex].
Expression for the equilibrium constant of [tex]CaCO_3[/tex] will be:
[tex]K_{sp}=[Ca^{2+}][CO_3^{2-}][/tex]
[tex]3.8\times 10^{-9}=[s][s][/tex]
[tex]3.8\times 10^{-9}=s^2[/tex]
[tex]s=6.2\times 10^{-5}moles/L[/tex]
Hence, the concentration in moles/liter of calcium ion in a saturated solution of calcium carbonate is [tex]6.2\times 10^{-5}moles/L[/tex]
