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Resistance of a conductivity cell filled with 0.1 mol L^(-1) KCl solution is 100Omega. If the resistance of the same cell when filled with 0.02 mol L^(-1) KCl solution is 520 Omega, calculate the conductivity and molar conductivity of 0.02 mol L^(-1) KCl solution. the conductivity of 0.1 mol L^(-1) KCl solution is 1.29 S/m. |
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Answer» Solution :Calculation for cell constant `G^(**)`: Cell constant `G^(**)`=conductivity `xx`resistance Where, resistivity of resistance cell `R=100Omega` Resistivity of solution `K=1.29"S "m^(-1)` `therefore G^(**)=(1.29"S "m^(-1))xx100Omega` `=129" S "OMEGA" "m^(-1)""["but "1S=1Omega^(-1)]` `=129m^(-1)""["but "1m^(-1)=0.01cm^(-1)]` `therefore G^(**)=1.29cm^(-1)` Calculation for conductivity (k) of KCl solution 0.02 mol `L^(-1)`: conductivity of 0.02 mol `L^(-1)` KCl solution=cell constant/resistance Resistivity of cell `(k)=("Cell constant "(G^(**)))/("Resistance of solution (R)")` Where, `G^(**)=129m^(-1),R=520Omega` `therefore k=(129m^(-1))/(520Omega)` `=0.248Omega^(-1)m^(-1)` `=0.248S" "m^(-1)` `=0.248xx10^(-2)" S "CM^(-1)""(because 1m^(-1)=10^(-2)cm^(-1))` Calculation for molar conductivity `Lamda_(m)` of solution: `Lamda_(m)=(k)/(c)=("Resistivity of solution")/("Molarity of solution")` Molarity of solution `c=0.02" mol "L^(-1)` [But `L^(-1)=1000m^(-1)`] `=1000xx0.02" mol "m^(-3)` =20 mol `m^(-3)` Resistivity of solution `k=0.248"S "m^(-1)` `=0.248xx1000xx10^(-3)" S "m^(-1)` `=248xx10^(-3)S " "m^(-1)` `therefore Lamda_(m)=(248xx10^(-3)S" "m^(-1))/(20" mol "m^(-3))` `=1.24xx10^(-2)" S "m^(2)" "mol^(-1)` `=124xx10^(4)" S "m^(2)" "mol^(-1)`. . . (i) OR Resistivity of 0.02 M KCl `k=("Cell constant "(G^(**)))/("Resistance of solution (R)")` `=(1.29cm^(-1))/(520Omega)` `=0.248xx10^(-2)" S "cm^(-1)` Where, `k=0.248xx10^(-2)" S "cm^(-1)` `Lamda_(m)=(k)/(c)` `c=0.02" mol "L^(-1)` `Lamda_(m)=(0.248xx10^(-2)" S "cm^(-1)xx1000cm^(3)L^(-1))/(0.02" mol "L^(-1))` `Lamda_(m)=124" S "cm^(2)mol^(-1)`. . . (ii) According to And `Lamda_(m)=124xx10^(4)S" "m^(2)mol^(-1)`. . (i) According to Hence, `1.0cm^(2)=1xx10^(-4)m^(2)` |
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