Question

: The specific conductivity of \[0.02M\]\[KCl\] solution at \[{25^O}C\] is \[2.768 \times {10^{^{ - 3}}}oh{m^{ - 1}}/cm\]. The resistance of this solution at\[{25^O}C\] when measured with a particular cell was \[250.2ohm\]. The resistance of \[0.01M\] copper sulphate solution at \[{25^O}C\] measured with the same cell was\[8331ohm\]Calculate the molar conductivity of the copper sulphate solution?

Answer 1

Hint: Specific conductivity term related to thermodynamics. In thermodynamics deals with the forms of heat and heat is the form of energy. And how one energy is converted into other forms of energy.

Complete step by step answer:
According to Ohm’s law voltage applied in a circuit is directly proportional to the current circulated in the circuit.
So \[V \propto I \Rightarrow V = IR\]
Here R is the resistance that slows up the speed of the current.
Conductance may be defined as it is the inverse to the resistance that fastens the speed of the current. It is denoted by G.
So \[G \propto 1/R\]
And the cell constant may be defined as the ratio of specific conductance of\[KCl\]to the conductance of\[KCl\].
Cell constant = specific conductance of\[KCl\]/conductance of \[KCl\]
Cell constant = \[2.768 \times {10^{^{ - 3}}}oh{m^{ - 1}}/cm\]/ \[\dfrac{1}{{250.2}}\]
Cell constant = \[2.768 \times {10^{ - 3}} \times 250.2\]
The specific conductivity of \[0.01M\] solution of copper sulphate\[(CuS{O_4})\]is = cell constant\[ \times \] conductance
= \[2.768 \times {10^{ - 3}} \times 250.2\]\[ \times \] \[\dfrac{1}{{8331}}\]
= \[0.0831 \times {10^{ - 3}}\]
Molar conductance= Specific conductivity\[ \times \]\[1000/concentration\]
Molar conductance=\[0.0831 \times {10^{ - 3}}\]\[ \times \]\[1000/100\]
Molar conductance=\[8.312oh{m^{ - 1}}c{m^2}m\]

So, the molar conductivity of copper sulphate solution is \[8.312oh{m^{ - 1}}c{m^2}m\].

Note:
Two types of conductivity occur in electrochemistry-\[\left( 1 \right)\] Molar conductivity- it is the conductivity occurs by total ions given by one mole of an electrolyte on V dilution when distance between two electrodes is \[1cm\] and area is so much that whole solution is contained between them. This conductivity is known as molar conductivity.
\[\left( 2 \right)\]Equivalent conductivity: it is the conductivity occurs by total ions given by one gram equivalent of an electrolyte on V dilution when distance between two electrodes is \[1cm\]and area is so much that whole solution is contained between them. This conductivity is known as Equivalent conductivity.