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Equilibrium

Question
CBSEENCH11006616

The solubility of Sr(OH)2 at 298K is 19·23g/L of the solution. Calculate the concentration of strontium and hydroxyl ions and pH of the solution. 

Solution
Molar mass of Sr(OH)2 = 87·6 + 32 + 2 = 121·6
  Solubility space of space Sr left parenthesis OH right parenthesis subscript 2 space equals space 19.23 space gL to the power of negative 1 end exponent
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 19.23 over denominator 121.6 end fraction space equals space 0.1581 space mol space straight L to the power of negative 1 end exponent
The solubility equilibrium is
  Sr left parenthesis OH right parenthesis subscript 2 space space space rightwards harpoon over leftwards harpoon space space space space Sr to the power of 2 plus end exponent space space plus space space 2 OH to the power of minus
i.e. 1 mole of Sr left parenthesis OH right parenthesis subscript 2 in the solution gives 1 mole of Sr to the power of 2 plus end exponent space ion space and space 2 space moles space of space OH to the power of minus space ions.
Hence in the solution, 
     open square brackets Sr to the power of 2 plus end exponent close square brackets space equals space 0.581 space mol space straight L to the power of negative 1 end exponent
open square brackets OH to the power of minus close square brackets space equals space 2 space cross times space 0.1581 space space equals space 0.3162 space mol space straight L to the power of negative 1 end exponent
We space know comma
space space space space space space open square brackets straight H to the power of minus close square brackets space open square brackets OH to the power of minus close square brackets space equals space 1 space cross times space 10 to the power of negative 14 end exponent
or space space space space space space space space open square brackets straight H to the power of plus close square brackets space equals space fraction numerator 1 space cross times space 10 to the power of negative 14 end exponent over denominator open square brackets OH to the power of minus close square brackets end fraction space equals fraction numerator 1 space cross times space 10 to the power of negative 14 end exponent over denominator 0.3162 end fraction
space space space space space space space space space space space space space space space space space space space equals space 3.162 space cross times space 10 to the power of negative 4 end exponent space mol space straight L to the power of negative 1 end exponent space
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