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The resistance of a solution A is 50 ohm...

The resistance of a solution `A` is `50 ohm` and that of solution `B` is `100ohm,` both solutions are taken in the same conductivity cell. If equal volumes of solution`A` and `B` are mixed, what is the resistance of the mixture using the same cell ? `(` Assume there is no change or increase in the `prop` of `A` and `B` on mixing `)`.

Text Solution

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Let us suppose `kappa_(1)` and `kappa_(2)` are the specific conductances of solutions 'A' and 'B' respectively and cell constant is 'y'. We know that,
Specific conductance= Conductance `xx` Cell constant
For (A), `kappa_(1)=1/50xxy`
For (B), `kappa_(2)=1/100xxy`
When equal volumes of (A) and (B) are mixed, the volume becomes double. Then,
Specific conductance of mixtiure `=(kappa_(1)+kappa_(2))/(2)`
`:. (kappa_(1)+kappa_(2))/(2)=1/Rxxy`
`1/2 [y/50+y/100]=1/Rxxy`
`1/100+1/200=1/R`
`R=200//3=66.66` ohm
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