An aqueous solution contains an unk...
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An aqueous solution contains an unknown concentration of Ba2+. When 50mL of a 1M solution of Na SO is added, BaSO just begins to precipitate. The final volume is 500mL. The solubility product of Baso, is 1 x 10-10. What is the original concentration of Ba2+? [JEE-MAINS.2018] (1) 5 y 10-9M 10

JEE/Engineering Exams
Chemistry
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( 1 mathrm{M} mathrm{Na}_{2} mathrm{SO}_{4}+mathrm{Ba}^{2+} rightarrow ) Final precipitate ( 40 mathrm{mL} quad 400 mathrm{ml} ) Concenteation of ( mathrm{SO}_{4}^{2-} ) in Bat solution is [ begin{array}{l} M, V_{1}=M_{2} V_{2} 1 times 50=11_{2} times 500 therefore quad r 1=frac{1 times 50}{50 %}=frac{1}{10} end{array} ] for preeipitation we Know, Ron'sation product ( =K_{text {sp }} ) (solubility [ begin{array}{c} sqrt{B a^{2}+}left[delta 0_{4}^{2-}right]=operatorname{Ksp}_{10} 0 f B a S_{4} {left[B a^{2+2 times frac{1}{10}}=10^{-10}right.} B a^{2+}=10^{-9} M end{array} ] Sos Coneri of ( frac{91}{4} ) Ba in oniginal seln. fies in ( 450 mathrm{ml} ) is [ begin{array}{l} M_{1} V_{1}=M_{2} V_{2} M_{1} times 450=100^{-9} times 500 M_{1}=frac{50 phi}{4 Omega} times 10^{-9}=1,11 times 10^{-9} mathrm{M} end{array} ]
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