JEE Main | 2018Ionic EquilibriumHard

Question

A aqueous solution contains an unknown concentration of Ba2+. When 50 mL of a 1 M solution of Na2SO4 is added, BaSO4 just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO4 is 1 × 10-10. What is the original concentration of Ba2+ ?

Options

A.

2 × 10-9 M

B.

1.1 × 10-9 M

C.

1.0 × 10-10 M

D.

5 × 10-9 M

Solution


Concentration of SO4-2 in Ba+2 solution
M1V1 = M2V2
1 ×50 = M2 × 500
M2 = 110
for just precipitation
I.P = Ksp
[Ba+2] [SO4-2] = Ksp (BaSO4)
[Ba+2] ×110=10-10
[Ba+2] = 10-9 Min 500ml solution
For calculation of [Ba+2] in original solution (450 ml)
M1 × 450 = 10-9 × 500
M1 = 500450×10-9 = 1.11 × 10-9 M
[M1= molarity of Ba+2 in original solution  (450ml)]

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