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Equilibrium

Question
CBSEENCH11006524

What do you understand by ionic product of water?

Solution
Water is a weak electrolyte. It dissociates to small extent to give H3O+ (aq) and OH (aq) ions as represented below:
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Applying the law of chemical equilibrium,
       straight K space equals space fraction numerator open square brackets straight H subscript 3 straight O to the power of plus close square brackets space open square brackets OH to the power of minus close square brackets over denominator open square brackets straight H subscript 2 straight O close square brackets squared end fraction
Since the degree of dissociation of water is low, so its concentration remains practically unchanged. Thus [H2O] may be taken as constant.
K × [H2O]2 = [H3O+][OH]
or Kw = [H3O+][OH]
where KM,is constant and is known as an ionic product of water. It may be defined as the product of the hydronium ion concentration and hydroxyl ion concentration at a given temperature. The value of Kw at 298K is 1·008 × 10–14 mol2 L–2.
For space pure space water space left square bracket straight H subscript 3 straight O to the power of plus right square bracket space equals left square bracket OH to the power of minus right square bracket
we space know comma
left square bracket straight H subscript 3 straight O to the power of plus right square bracket left square bracket OH to the power of minus right square bracket space equals space straight K subscript straight H equals space 1 space straight x space 10 to the power of negative 14 end exponent
or space
left square bracket straight H subscript 3 straight O to the power of plus right square bracket squared equals space 1 space straight x 10 to the power of negative 14 end exponent
or
left square bracket straight H subscript 3 straight O to the power of plus right square bracket space equals square root of 1 space straight x 10 to the power of negative 14 end exponent space end root space
space equals 1 space straight x space 10 to the power of negative 7 end exponent space mol space straight L to the power of negative 1 end exponent
Hence space for space pure space water space left square bracket straight H subscript 3 straight O to the power of plus right square bracket
equals space left square bracket OH to the power of minus right square bracket space equals 1 space straight x space 10 to the power of negative 7 end exponent space mol space straight L to the power of negative 1 end exponent