An electrolyte of a polymer -salt complex of poly (ethylene oxide ) `LiCF_3 SO_3 ` is shaped into a free standing circular film of 20 mm diameter and a thickness of `20 mu m`. When it is sandwiched between 2 stainless steel circular electrodes of the same diameter , this
cell exhibits a conductance of `(314)/5` S. What is
the specific conductivity of the electrolyte ?

Options

A. `4 m S cm^(-1)`
B. `0.4 S cm ^(-1)`
C. `40 m S cm^(-1)`
D. `0.004 S cm^(-1)`

Answer

C

Explanation

Gven,
`"Conductance"=413/5S=62.8S`
Diameter (2r) = 20mm = 2 cm
Thickness = `20mum=2xx10^(-3)` cm
Thus, specific conductivity
`(62.8xx2xx2)/(2xx3.14)=(62.8xx4)/6.28=40mScm^(-1)`
Hence, option © is the correct answer.