(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]

(i) State the relationship amongst cell constant of a cell, resistance

1.	(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]
Answer» Solution : (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`