An aqueous solution contains an unknown concentration of Ba 2+ . When 50 mL of a 1M solution of Na 2 SO 4 is added, BaSO 4 just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO 4 is 1 × 10 –10 . What is the original concentration of Ba 2+ .
Text Solution
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Ba +2 +SO 4 2– 
BaSO 4(s)
ppt
final conc. of [SO 4 2– ] = 
Final conc. of [Ba +2 ] when BaSO 4 start precipitating
K SP =Q SP = [Ba +2 ] [SO 4 2– ]
10 –10 = [Ba +2 ] (0.1M)
[Ba +2 ] = 10 –9 M
initial conc. 
;initial volume was = 500 –50 =450ml
M 1 V 1 = M 2 V 2
M 1 = 
M 1 = 1.1×10 –9 M
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