State and exlain Kohlarausch.s law of independent migration of ions .
The equivalent conductance of infinite dilution `(A_(0))` for sodium acetate , sodium chloride and hydrochloric acid are 78, 109 and 384 `ohm^(-1)cm^(2)` g.
Calculate the `A_(0)` of acetic acid .

Explanation

Kohlrausch.s law of independent migration of ions states that "at infinite dilution , each ion makes a definite contribution towards equivalent conductance of the electrolyte irrespective of the nature of the other ion with which it is associated .The value of equivalent conductance at infinite dilution for any electrolyte is given by the sum of the contributions of the two ions "
So `Delta_(0) =lambda_(a)^(0)+lambda_(C )^(0)`
Kohlarusch examine `A_(0)` values for a number of strong electrolytes and found that for a pair of electrolytes with teh same negative ion but differing only in the positive ion , the difference between the `Delta_(0)` values is constant .
e.g `wedge_(0(KCl))-wedge_(0(Nacl))=wedge_(0(KBr))-wedge_(0(NaBr))`
`= wedge_(0(KI)) -wedge_(0(Nal))`
`= 23.4 Omega^(-1) cm^(-2)g eq^(-1) (S cm^(2) g eq^(-1))`
Similarly , with a common cation , the difference between `wedge_(0)` values is also found to be constant .
`wedge_(0(KBr))-wedge_(0(KCl)) =wedge_(0(NaBr))-wedge_(0(NaCl))`
` = 1.8 Omega^(-1)cm^(2) " g eq"^(-1) (S cm^(2) " g eq"^(-1))`
According to Kohlrausch.s law ,
`wedge_(0)(CH_(3)COOH)`
`=wedge_(0)(H^(+))+wedge_(0)(CH_(3)OO^(-))`
`=wedge_(0(.^(+)))+wedge_(0(CH_(3)OO^(-)))`
`=wedge_(0(.^(+)))+wedge_(0(.^(-)))+wedge_(0(.^(+)))-wedge_(0(.^(-)))-wedge_(0(.^(+)))-wedge_(0(.^(+)))-wedge_(0(.^(-)))-wedge_(0(.^(+)))`
`=wedge_(0( ))+wedge_(0(._(3)^(-+)))-wedge_(0( ))`
`=(384 +78 - 109)"ohm"^(-1)`
` = 353^(-1)`.