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Equilibrium

Question
CBSEENCH11006606

The solubility of CaF2 in water at 298K is 1·7×10–3 gram per 100 cm3. Calculate the solubility product of CaF2 at 298K.

Solution
The molecular mass of CaF2
                           equals space 40 plus space 2 space cross times 19 space equals space 78
Solubility of CaF2 = 1.7 x 10-3 g/100 cm3
                          = 1.7 x 10-2 g L-1

                          equals space fraction numerator 1.7 space cross times 10 to the power of negative 2 end exponent over denominator 78 end fraction mol space straight L to the power of negative 1 end exponent
equals space 2.18 space cross times space 10 to the power of 4 space mol space straight L to the power of negative 1 end exponent
The solubility equilibrium is
           
 CaF subscript 2 space rightwards harpoon over leftwards harpoon space space space space Ca to the power of 2 plus end exponent space plus space 2 straight F to the power of minus
i.e. 1 mole of CaF2 in the solution gives 1 mole of Ca2+ ions and 2 moles of F- ions. Hence in the solution.
   open square brackets Ca to the power of 2 plus end exponent close square brackets space equals space 2.18 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
open square brackets straight F to the power of minus close square brackets space equals space 2 space cross times space left parenthesis 2.18 space cross times space 10 to the power of negative 4 end exponent right parenthesis
space space space space space space space space space equals space 4.36 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
 Applying the law of solubility product
       straight K subscript sp space equals space open square brackets Ca to the power of 2 plus end exponent close square brackets space space open square brackets straight F to the power of negative 1 end exponent close square brackets squared
space space space space space space space equals space left parenthesis 2.18 space cross times space 10 to the power of negative 4 end exponent right parenthesis thin space left parenthesis 4.36 space cross times space 10 to the power of negative 4 end exponent right parenthesis squared
space space space space space space space equals 4.14 space cross times space 10 to the power of negative 11 end exponent