a. A solution of `caF_(2)` is found to contain `10^(-4)M F^(Θ)` ions. What is the `K_(sp)` of `caF_(2)`?
b. A solution of calcium phoshate contains `2 xx 10^(-5)M PO_(4)^(3-)` ions. What is `K_(sp)`of `ca_(3)(PO_(4))_(2)`?
c. A solution of `Ca_(3)(PO_(4))_(2)` contains `6 xx 10^(-5)M ca^(2+)` ions. What is the `K_(sp)` of `Ca_(3) (PO_(4))_(2)`?
d. A solution of `Zr_(3)(PO_(4))_(4)` constains `8 x 10^(-5) M PO_(4)^(3-)`ions. what is the `K_(sp)` of `Zr_(3) (PO_(4))_(4)`?
e. A solution of `Zr_(3)(PO_(4))_(4)` contain `3 xx 10^(-5) M Zr^(4+)` ions. What is the `K_(sp)` of `Zr_(3)(PO_(4))_(4)`?

Explanation

`CaF_(2)hArr underset(S)(Ca^(2+))+underset(2S)(2F^(Theta))`
Total `[F^(Θ)] = 2S = 10^(-4), S = ((10^(-4))/(2))M`
`K_(sp) = 4S^(3) = 4 xx ((10^(-4))/(2))^(-3) = 0.5 xx 10^(-12)M^(3)`
b. `Ca_(3)(PO_(4))_(2) hArr underset(3S)(3Ca^(2+))+underset(2S)(2PO_(4)^(3-))`
Total `[PO_(4)^(3-)] = 2S = 2xx10^(-5)M, S = 10^(-5)M`
`K_(sp) = 3^(2).2^(2)s^(5) = 108S^(5) = 108 xx (10^(-5))^(5)`
`= 108 xx 10^(-25) M^(5)`
`= 1.08 xx 10^(-23)`
c. `Ca_(3)(PO_(4))_(2)hArr underset(3S)(3Ca^(2+))+ underset(2S)(2PO_(4)^(3-))`
Total `[Ca^(2+)] = 3S = 6 xx 10^(-5)M,S = 2 xx 10^(-5)M`
`K_(sp) = 108S^(5) = 108 xx (2xx10^(-5))^(5) = 108 xx 32 xx 10^(-25)`
`= 3435 xx 10^(-25)`
`= 34.25 xx 10^(-23)M^(5)`
d. `Zr_(3)(PO_(4))_(4) hArr underset(3S)(3Zr^(4+))+ underset(4S)(4PO_(4)^(3-))`
Total `[PO_(4)^(3-)] = 4S = 8 xx 10^(-5) M,S = 2 xx 10^(-5)M`
`K_(sp) = 3^(3).4^(4).S^(7) = 6912S^(7) = 6912 (2 xx 10^(-5))^(7)`
`= 6912 xx 128 xx 10^(-35)`
`= 884736 xx 10^(-35)`
`= 884.736 xx 10^(-32)M^(7)`
e. `Zr_(3)(PO_4)_(4)hArr underset(3S)(3Zr^(4+))+ underset(4S)(4PO_(4)^(3-))`
Total `[Zr^(4+)] = 3S = 3 xx 10^(-5) M,S = 10^(-5)M`
`K_(sp) = 6912S^(7) = 6912 (10^(-5))^(7) = 6921 xx 10^(-35)M^(7)`
`= 69.12 xx 10^(-33) M^(7)`