Find the stability constant of the complex `[ Zn ( NH_(3))_(4)]^(2+)` formed in the reaction,
`Zn^(2+) + 4NH_(3) hArr [ Zn ( NH_(3))_(4)]^(2+)`
Given that , `E_(Zn^(2+) //Zn)^(@) = - 0.76 V` and `E_([Zn(NH_(3))_(4)]^(2+)//Zn,4NH_(3))^(@) = - 1.03 V`

Explanation

Given that,
`Zn^(2+) ( aq) + 2e^(-) hArr Zn(s), E^(@) = - 0.76 ` …..(i)
`[Zn(NH_(3))_(4)]^(2+)+ 2e^(-) hArr Zn (s) + 4NH_(3), E^(@)= - 1.03 V`
or `Zn(s) + 4NH_(3) hArr [Zn(NH_(3))_(4)]^(2+) + 2e^(-), E^(@) = 1.03V` ....(ii)
Adding Eq. (i) and (ii), we get the overall reaction,
`Zn^(2+) + 4NH_(3) hArr[Zn(NH_(3))_(4)]^(2+)` and `E_("cell")^(@) =1.03 - 0.76 V = 0.27 V`
`E_("cell")^(@) = ( 0.0491)/( n) logK, n = 2`
or `log K = ( 0.27 xx 2)/(0.0591)= 9.1371`
or K = antilog 9.1371 = `1.371 xx 10^(9)`