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Calculate the dissociation constant of w...

Calculate the dissociation constant of water at `25^(@)C` from the following data. Specific conductance of `H_(2)O = 5.8 xx 10^(-8) mho cm^(-1), lambda_(H^(+))^(oo) = 350.0` and `lambda_(OH^(-))^(oo) = 198.0 mho cm^(2)`

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Verified by Experts

The correct Answer is:
`2xx10^(-16)"mole"//"litre"`
`K=5.8xx10^(-8)Scm^(-1)`,`^^_(H^(+))^(@)=350Scm^(2)`,^^_(OH^(-))^(@)=198Scm^(2)`
`^^_(H_(2)O)=(1000xx5.8xx10^(-8))/(55.5),alpha=(^^H_(2)O)/(^^H_(2)O)=((1000xx5.8xx10^(-8)))/(55.5xx(350+198))=0.1907xx10^(-8)=1.907xx10^(-9)`
`K_(a)=Calpha^(2)=55.55xx(1.907)^(2)xx10^(-18)=2.02xx10^(-16)`
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