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The electrical resistance of a column of...

The electrical resistance of a column of 0.05 M NaOH solution of diameter 1 cm and length 50 cm is 5.55 `xx 10^(3) Omega`. Calculate its resistivity, conductivity and molar conductivity.

Text Solution

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Area, `A = pi r^(2) = 3.14 xx (( 1)/( 2))^(2) cm^(2) = 0.785 cm^(2)`
Resistivity, `rho = ( RA)/( l )`
` = ( 5.55 xx 10^(3) xx 0.785 cm^(2))/( 50 cm ) = 87. 135cm`
Conductivity, `k = ( 1)/( r ) = ( 1)/( 87.135) Omega^(-1) cm^(-1) = 0.01148 `
`= 1.148 xx 10^(-2) S cm^(-1) Omega^(-1) cm^(-1)`
Molar conductivity,
`Lambda_(m) = ( k xx 1000)/( M ) = ( 1.1 48xx 10^(-2) xx 1000)/( 0.05)`
`= 229.6 S cm^(2) " mol"^(-1)`
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