From the solubility product constants for CaF2 (fluorite) and CaSO4 (anhydrite) determine the equilibrium constant for the reaction
CaF2 + SO4 2- --> CaSO4 + 2F-
eqn 1 CaF2 ==> Ca^2+ + 2F^-
eqn 2 Ca^2+ + SO4^2- ==> CaSO4
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sum 1+2 CaF2 + SO4^2- ==> (F^-)^2 + CaSO4
since CaF2 and CaSO4 are solids we can cancel them since they are not involved in the Keq. You note that eqn 1 is Ksp for CaF2 and eqn 2 is 1/Ksp for CaSO4; therefore, Keq for the reaction is
KspCaF2/KspCaSO4 = ?
To determine the equilibrium constant for the reaction, we can use the solubility product constants of the compounds involved. The solubility product constant (Ksp) is an equilibrium constant that is related to the dissociation of a solid compound into its ions in a solution.
The solubility product constant for CaF2, also known as the fluorite, can be denoted as Ksp1. It is defined as the product of the concentrations of the calcium ions (Ca2+) and fluoride ions (F-) when CaF2 is dissolved in water:
CaF2 (s) ⇌ Ca2+ (aq) + 2F- (aq)
Ksp1 = [Ca2+][F-]^2
Similarly, the solubility product constant for CaSO4, also known as anhydrite, can be denoted as Ksp2. It is defined as the product of the concentrations of the calcium ions (Ca2+) and sulfate ions (SO4 2-) when CaSO4 is dissolved in water:
CaSO4 (s) ⇌ Ca2+ (aq) + SO4 2- (aq)
Ksp2 = [Ca2+][SO4 2-]
Now, let's write the balanced equation for the reaction we are interested in:
CaF2 (s) + SO4 2- (aq) ⇌ CaSO4 (s) + 2F- (aq)
To determine the equilibrium constant for this reaction (K), we need to express it as the product of the concentrations of the products divided by the product of the concentrations of the reactants, each raised to their respective stoichiometric coefficients:
K = [CaSO4][F-]^2 / ([CaF2][SO4 2-])
Using the solubility product constants (Ksp1 and Ksp2) from above, we can substitute them into the equation as follows:
K = (Ksp2)([F-]^2) / (Ksp1)([SO4 2-])
Note that the concentrations of ions are related to the solubility product constants as follows:
[Ca2+] = [F-] (from dissociation of CaF2)
[Ca2+] = [SO4 2-] (from dissociation of CaSO4)
Substituting the concentrations of the ions:
K = (Ksp2)([Ca2+]^2) / (Ksp1)([SO4 2-])
Thus, the equilibrium constant for the given reaction can be determined using the relationship between the solubility product constants and the concentrations of the ions in each compound.