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Equilibrium

Question
CBSEENCH11006617

The solubility product of BaSO4 is 1·5 × 10–9. Find solubility in:
(i) pure water    
(ii) 0·10 M BaCl
2.

Solution
Let the solubility of BaSO4 be S mole per litre.
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Applying the law of solubility product, 
      straight K subscript sp space equals space open square brackets Ba to the power of 2 plus end exponent close square brackets space open square brackets SO subscript 4 superscript 2 minus end superscript close square brackets space equals space straight S space cross times space space straight S
or space space straight S squared space equals space straight K subscript sp
or space space space straight S space equals space square root of straight K subscript sp end root space equals space square root of 1.5 space cross times space 10 to the power of negative 9 end exponent end root
space space space space space space space space space space space equals space 3.78 space cross times space 10 to the power of negative 5 end exponent space mol space straight L to the power of negative 1 end exponent

left parenthesis ii right parenthesis space Solubility space in space 0.10 straight M space BaCl subscript 2 colon
open square brackets Ba to the power of 2 plus end exponent close square brackets space equals space 0.1 space plus space straight S semicolon space open square brackets SO subscript 4 superscript 2 minus end superscript close square brackets space equals space straight S
space space space straight K subscript sp space equals space open square brackets Ba to the power of 2 plus end exponent close square brackets space open square brackets SO subscript 4 superscript 2 minus end superscript close square brackets
space space space space space space space space equals space space left parenthesis 0.1 plus straight S right parenthesis space left parenthesis straight S right parenthesis space equals space 0.1 space straight S space plus space straight S squared
straight S squared space being space the space product space of space two space small space quanitities space is space neglected.
therefore space space space straight K subscript sp space equals space 0.15 space
therefore space space space 0.1 space straight S space equals space 1.5 space cross times space 10 to the power of negative 9 end exponent
or space space space space space straight S space equals space fraction numerator 1.5 space cross times space 10 to the power of negative 9 end exponent over denominator 0.1 end fraction space equals space 1.5 space cross times space 10 to the power of negative 8 end exponent space mol space straight L to the power of negative 1 end exponent