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The ionisation constant of overset(oplus)NH_(4)ion in water5.6xx10^(-10)" at "25^(@)CThe rate constant for the reaction of overset(oplus)NH_(4) and oversetThetaOHion to formNH_(3) and H_(2)O " at " 25^(@)C" is " 3.4xx10^(10)"L.mol"^(-1).s^(-1) Calculate the rate constant for proton transfer from water toNH_(3)

Answer»

Solution :Given `NH_(4)^(+)+H_(2)OhArrNH_(3)+H_(3)O^(+)`
`K_(a) = ([NH_(3)][H_(3)O^(+)])/([NH_(4)^(+)][H_(2)O]) (K_(a)= 5.6xx10^(-10))""...[1]`
`NH_(4)^(+)+BAR(O)Hunderset(k_(b))OVERSET(k_(f))hArrNH_(3)+H_(2)O`
`""(k_(f)=3.4xx10^(10)"L.mol"^(-1).s^(-1))""...[2]`
`K_(eq)=(k_(f))/(k_(b))=([NH_(3)][H_(2)O])/([NH_(4)^(+)][OH^(-)])`
`=([NH_(3)][H_(3)O^(+)])/([NH_(4)^(+)][H_(2)O])xx([H_(2)O]^(2))/([H_(3)O^(+)][OH^(-)])=(K_(a))/(K_(W))`
`thereforek_(b)=(K_(w))/(K_(a))xxk_(f)=(1.0xx10^(-14))/(5.6xx10^(-10))xx3.4xx10^(10)=6.07xx10^(5)`


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