The resistance of the solution 'A' is 40 ohm and that of solution 'B' is 70 ohm, both solutions being taken in the same conductivity cell. If equal volumnsof solutions '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.)

Explanation

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.