Answer : The remaining concentration of the first ion to precipitate when the second ion begins to precipitate is, 
Explanation :
The dissociation of barium fluoride is written as:

The expression for solubility constant for this reaction will be,
![K_{sp}=[Ba^{2+}][F^-]^2](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D%5BBa%5E%7B2%2B%7D%5D%5BF%5E-%5D%5E2)
As we know that at room temperature
the
of barium fluoride is,
.
Now put all the given values in this expression, we get:
![1\times 10^{-6}=(2.75\times 10^{-2})\times [F^-]^2](https://tex.z-dn.net/?f=1%5Ctimes%2010%5E%7B-6%7D%3D%282.75%5Ctimes%2010%5E%7B-2%7D%29%5Ctimes%20%5BF%5E-%5D%5E2)
![[F^-]=6.03\times 10^{-3}M=0.00603M](https://tex.z-dn.net/?f=%5BF%5E-%5D%3D6.03%5Ctimes%2010%5E%7B-3%7DM%3D0.00603M)
The barium fluoride precipitate when fluoride ion is equal to 0.00603 M.
The dissociation of calcium fluoride is written as:

The expression for solubility constant for this reaction will be,
![K_{sp}=[Ca^{2+}][F^-]^2](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D%5BCa%5E%7B2%2B%7D%5D%5BF%5E-%5D%5E2)
As we know that at room temperature
the
of calcium fluoride is,
.
Now put all the given values in this expression, we get:
![3.90\times 10^{-11}=(6.70\times 10^{-2})\times [F^-]^2](https://tex.z-dn.net/?f=3.90%5Ctimes%2010%5E%7B-11%7D%3D%286.70%5Ctimes%2010%5E%7B-2%7D%29%5Ctimes%20%5BF%5E-%5D%5E2)
![[F^-]=2.41\times 10^{-5}M=0.0000241M](https://tex.z-dn.net/?f=%5BF%5E-%5D%3D2.41%5Ctimes%2010%5E%7B-5%7DM%3D0.0000241M)
The calcium fluoride precipitate when fluoride ion is equal to 0.0000241 M.
Since, the fluoride ion concentration in calcium fluoride is less then the fluoride ion concentration in barium fluoride. That means, calcium fluoride will precipitate first.
Thus, the concentration
ion remaining at
concentration (0.00603 M) is calculated as:
![K_{sp}=[Ca^{2+}][F^-]^2](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D%5BCa%5E%7B2%2B%7D%5D%5BF%5E-%5D%5E2)
Now put all the given values in this expression, we get:
![3.90\times 10^{-11}=[Ca^{2+}]\times (0.00603)^2](https://tex.z-dn.net/?f=3.90%5Ctimes%2010%5E%7B-11%7D%3D%5BCa%5E%7B2%2B%7D%5D%5Ctimes%20%280.00603%29%5E2)
![[Ca^{2+}]=1.07\times 10^{-6}M](https://tex.z-dn.net/?f=%5BCa%5E%7B2%2B%7D%5D%3D1.07%5Ctimes%2010%5E%7B-6%7DM)
Therefore, the remaining concentration of the first ion to precipitate when the second ion begins to precipitate is, 