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Question

# What is dissociation constant of water at 25oC from the following data:Conductivity of H2O=5.8×10−8Scm−1, λ∞H+=350.0 and λ∞OH−=198.0Scm2mol−1

A
3.8×1016mol/litre
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B
2×1016mol/litre
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C
1.8×1016mol/litre
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D
None of these
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Solution

## The correct option is C 1.8×10−16mol/litreSuppose water contains X mol/litre or X eq/litre of H+ ions or OH− ions.∵ Equivalent of H+= Eq. of H2∴ Volume of H2O in mL having 1 Eq. H+=1000X∴ Equivalent conductivity of water, A∞eq.H2O=k×1000N=5.8×10−8×1000XSince, water dissociated feebly, i.e., water may be considered to be a dilute solution of H+ and OH− ions.∴A∞eq.H2O=λ∞H++λ∞OH−∴5.8×10−8×1000X=350+198=548∴X=1.0×10−7∴[H+]=[OH−]=1×10−7For the equilibriumH2O⇌H++OH−Equilibrium constant (K)=[H+][OH−][H2O]Kw=K×[H2O]=[H+][OH−]=1.0×10−7×1.0×10−7=1×10−14∴K=Kw[H2O]=1×10−1455.5 [[H2O]=100018=55.5mol/litre]=1.8×10−16mol/litre

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