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Question: The resistance of a N/10 \(KCl\) solution is 245 ohms. The specific conductance and the equivalent c...

The resistance of a N/10 KClKCl solution is 245 ohms. The specific conductance and the equivalent conductance of the solution if the electrodes in the cell are 4 cm apart and each having an area of 7.0 sq. cm. are:
A) 2.332×10−3mho cm−12.332 \times {10^{ - 3}}mho\,c{m^{ - 1}} , 23.32mho cm2 eq−123.32mho\,c{m^2}\,e{q^{ - 1}}
B) 2.302×10−3mho cm−12.302 \times {10^{ - 3}}mho\,c{m^{ - 1}} , 21.22mho cm2 eq−121.22mho\,c{m^2}\,e{q^{ - 1}}
C) 2.312×10−3mho cm−12.312 \times {10^{ - 3}}mho\,c{m^{ - 1}} , 22.12mho cm2 eq−122.12mho\,c{m^2}\,e{q^{ - 1}}
D) None of the above

Explanation

Solution

To solve this question, you must calculate Specific Conductance(K) first and then calculate equivalent conductance by using its formula. Then you will get your desired answer. But the most important point to keep in mind while solving these types of questions is that, handle the unit conversion carefully and make the units in the same format.

Complete step-by-step solution:
Step 1: In this step we will calculate the specific conductance:
Specific Conductance is, inverse of resistance multiplied by length per unit area, and we will use this formula for calculation.
Specific Conductance (K)(K) = lR×a\dfrac{l}{{R \times a}} = 4245×7\dfrac{4}{{245 \times 7}} = 2.332×10−3mho cm−12.332 \times {10^{ - 3}}mho\,c{m^{ - 1}}
So, here we got our Specific Conductance (K)(K) = 2.332×10−3mho cm−12.332 \times {10^{ - 3}}mho\,c{m^{ - 1}}
By calculating this we can say that options B and C are the wrong one. But we will calculate the second part also to find the correct option between option A and option D.
Step 2: In this step we will calculate Equivalent Conductance (∧)( \wedge )
Equivalent Conductance is, (K)(K) multiplied by 1000 and divided by the concentration, and we will use this formula for calculation.
Equivalent Conductance (∧)( \wedge ) = K×1000CK \times \dfrac{{1000}}{C} = 2.332×10−3×10001102.332 \times {10^{ - 3}} \times \dfrac{{1000}}{{\dfrac{1}{{10}}}} = 23.32mho cm2 eq−123.32mho\,c{m^2}\,e{q^{ - 1}}

So, here we got our Equivalent Conductance (∧)( \wedge ) = 23.32mho cm2 eq−123.32mho\,c{m^2}\,e{q^{ - 1}}
After calculating this, clearly the value matches with the value given in option A, and hence the option D ruled out.

Hence, the correct answer is option ‘A’.

Note: Specific conductance is defined as the conducting capacity of a solution of the dissolved electrolyte and the whole solution is being placed between two electrodes 1 sq. cm and length 1 cm.
Equivalent Conductivity is defined as the conducting power of all the ions produced by dissolving one gram equivalent of an electrolyte in solution.