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(a) State the relationship amongst cell ...

(a) 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 solute related to conductivity of its solution ?
(b) A voltanic cell is set up at `25^(@)C` with the following half-cells :
`Al|Al^(3+) (0.001M)` and `Ni|Ni^(2+) (0.50M)`
Calculate the cell voltage [`E_(Ni^(2+)|Ni)^(@) = -0.25V , E_(Al^(3+) |Al)^(@) = -1.66 V`]

Text Solution

Verified by Experts

(a) The relationship between cell constant of a cell `(G^(**))` , resistance of the solution in the cell (R) and conductivity (K) is given by
`K = ("Cell constant")/(R) = (G^(**))/(R)`
The relationship between molar conductivity (`Delta_(m)`) and conductivity of the solution (K) is given by
`Delta_(m) = (K)/(C)`
where C is the concentration of the solution .
(b) The cell may be represented as
`Al|Al^(3+)| |Ni^(2+)| Ni to Al+ 3Ni^(2+) to Al^(3+) + Ni`
`E_("cell")^(@) = E_("right")^(@) - E_("left")^(@)`
= `(-0.25) - (-1.66)`
`-0.25 + 1.66 = 1.41 V`
`E_("cell")^(@) = E_("cell")^(@)- (0.0591)/(n)"log" ([Al^(3+)]^(2+))/([Ni^(2+)]^(3))`
=`1.41 - (0.0591)/(6) "log" ((0.001)^(2))/((0.50)^(2)) = Al to Al^(3+) + 3e`
`=1.41 + (0.0591)/(6) xx 5.3969`
`=1.41 + 0.0531 = 1.463 V`
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