Question

The specific conductance of a \[{{2M}}\] solution of electrolyte is \[{{0}}{{.3 oh}}{{{m}}^{{{ - 1}}}}{{c}}{{{m}}^{{{ - 1}}}}\] at \[{{2}}{{{5}}^{{0}}}{{C}}\]. Its equivalent conductance is:
A. ${{14 oh}}{{{m}}^{{{ - 1}}}}{{c}}{{{m}}^{{2}}}{{e}}{{{q}}^{{{ - 1}}}} $
B. ${{}}{{15 oh}}{{{m}}^{{{ - 1}}}}{{c}}{{{m}}^{{2}}}{{e}}{{{q}}^{{{ - 1}}}} $
C. ${{}}{{140 oh}}{{{m}}^{{{ - 1}}}}{{c}}{{{m}}^{{2}}}{{e}}{{{q}}^{{{ - 1}}}} $
D. ${{}}{{150 oh}}{{{m}}^{{{ - 1}}}}{{c}}{{{m}}^{{2}}}{{e}}{{{q}}^{{{ - 1}}}}$

Answer 1

Hint: We can easily calculate the value of equivalent conductance by knowing the value of specific conductance by using the relation between them. Both these quantities are connected with the normality of the solution.

Complete step by step answer:
Specific conductivity is commonly denoted by the letter K. It is calculated by taking the product of observed conductivity and cell constant. Conductance will always be the inverse of resistance. After knowing the value of specific conductance, we can use its value and the normality of the solution to find out the equivalent conductance.
The value of conductance is always related with the distance between the electrodes, the area of the cross- section of the electrode and the specific resistance or resistivity of the material. The specific resistance is characteristic to each material and may have varying values according to the material used for the electrode.
Here we can consider the normality equal to molarity and therefore, \[{{N = 2N}}\]
Specific conductance, \[{{K = 0}}{{.3 oh}}{{{m}}^{{{ - 1}}}}{{c}}{{{m}}^{{{ - 1}}}}\].
Now we have the relation
\[{{{\lambda }}_{{{eq}}}}\;{{ = K \times }}\dfrac{{{{1000}}}}{{{N}}}\], where ${\lambda _{{{eq}}}}$ is the equivalent conductance, ${{K}}$ is the specific conductance and ${{N}}$ is the normality.
On substituting the values and solving, we get
\[{\lambda _{{{eq}}}}{{ = 0}}{{.3 \times }}\dfrac{{{{1000}}}}{{{2}}}{{ = 150 oh}}{{{m}}^{{{ - 1}}}}{{c}}{{{m}}^{{{2}}\;}}{{e}}{{{q}}^{{{ - 1}}}}\]
So we got the value as \[{{ 150 oh}}{{{m}}^{{{ - 1}}}}{{c}}{{{m}}^{{{2}}\;}}{{e}}{{{q}}^{{{ - 1}}}}\]

So, the correct answer is Option D.

Additional Information:
Electrochemistry deals with the study of electrical properties of solutions of electrolytes and with the inter-relation of chemical phenomenon and electrical energies. It mainly analyses the chemical changes happening during electrolysis.

Note: On passing electric current through an electrolyte, chemical changes take place in it and this process is called electrolysis. Conductance of a solution always depends upon its concentration calculated in terms of molarity or normality.