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Equilibrium

Question
CBSEENCH11008349

If pH ofa saturated solution of Ba(OH)2 is 12, the value of its Ksp is 

  • 4.00 x 10-6 M3

  • 4.00 x 10-7 M3

  • 5.00 x 10-6 M3

  • 5.00 x 10-7 M3

Solution

C.

5.00 x 10-6 M3

Given pH of Ba(OH)2 = 12
therefore, [H+] = [1 x 10-12]
and [OH-] = 1 x 10-14 / 1 x 10-12   {[H+][OH-] = 1 x 10-14}
Ba left parenthesis OH right parenthesis subscript 2 space equals space stack Ba to the power of 2 plus end exponent space with straight s below plus space stack 2 OH to the power of minus with 2 straight s below
Ksp space equals space left square bracket Ba to the power of 2 plus end exponent right square bracket left square bracket OH to the power of minus right square bracket squared
space equals space left square bracket straight s right square bracket left square bracket 2 straight s squared right square bracket

equals space open square brackets fraction numerator 1 space straight x space 10 to the power of negative 2 end exponent over denominator 2 end fraction close square brackets left parenthesis 1 space straight x space 10 to the power of negative 2 end exponent right parenthesis squared

equals space 0.5 space straight x space 10 to the power of negative 6 end exponent space equals space 5.0 space straight x space 10 to the power of negative 7 end exponent space straight M cubed