(i) State the relationship amongst cell constant of a cell, resistance of the solution in the cell and conductivity of the solution. How is molar conductivity of a solution related to conductivity of its solution ?
(ii) A voltaic cell is set up at 25 °C with the following half cell,
`Al//Al^(3+) (0.001 M)` and `Ni//Ni^(2+) (0.50 M)`
Calcualte the cell voltage: `[E_(ni^(2+)//Ni)^(@) =-0.25 V, E_(Al^(+)//Al)^(@) = -1.66 V]`

Explanation

(i) Relation between cell constant of a cell, resistance of the solution in the cell and conductivity of the solution is given by:
`k =G/R`
where K - Conductivity of the solution
G* = Cell constant
R = Resistance of the solution Relation between molar conductivity and conductivity is given by `Lambda_(m) = (1000 K)/C`
where `Lambda_(m)` = Molar conductivity
C = No. of moles
(ii) Electrode potentials for `Al^(3+)//Al` and `Ni^(2+)//Ni` electrodes are first calculated using Nernst equation :
`E_(Ni^(2+)//Ni) =E_(Ni^(2+)//Ni)^(@) -0.0591/n log 1/0.50`
`=-0.25 -0.0591/2 log 2`
`=-0.25 -0.0089 =-0.2589` V
`E_(Al^(3+)//Al)^(@) =E_(Al^(3+)//A)^(@) -0.0591/3 log 1/0.001`
`=-1.66 V - 0.0591/3 log 1/0.001`
`=-1.66 V - 0.0591/3 xx 3 = -1.7191`
`E_("cell") =E_(Ni^(2+)//Ni) - E_(Al^(3+)//Al)`
`=-0.2589 V -(-1.7191 V) = 1.4602 V`