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The resistance of a solution 'A' is 50 o...

The resistance of a solution 'A' is 50 ohm and that of solution 'B' is 100 ohm, both solution being taken in the same conductivity cell. If equal volumes of solution A and B are mixed, what will be the resistance of the mixture using the same cell. (Assume that there is no increase in the degree of dissociation of A and B on mixing)

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Let us suppose `k_1 and k_2` are the specific conductances of solutions .A and B. respectively and cell constant Is .y.. We know that,
Specific conductance -`"Conduclance "xx " Cell.constant"`
For (A), `k_(1)=1/(50)xx y`
For (B), `k_(2)=1/(100) xx y`
When equal volumes of (A) and (B) are mixed, the volume becomes double. Then,
Specific conductance of mixture `=(k_(1)+k_(2))/(2)`
`therefore (k_(1)+k_(2))/(2)=1/R xx y`
`1/2 [(y)/(50)+(y)/(100)]=1/R xx y`
`(1)/(100)+1/(200)=1/R`
R=200/3=66.66 ohm.
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