Question

In a conductivity cell the two platinum electrodes, each of area 10 sq.cm. are fixed 1.5 cm apart. The cell contained 0.05 N solution of a salt. If the two electrodes are just half dipped into the solution which has a resistance of 50 ohms, the equivalent conductance of the salt solution will be:
A. 120 mho $c{m^2}e{q^{ - 1}}$
B. 100 mho $c{m^2}e{q^{ - 1}}$
C. 220 mho $c{m^2}e{q^{ - 1}}$
D. none of these

Answer 1

Hint: For solving this question, we need to understand the concept of specific conductivity of a solution. We can define conductivity or specific conductivity of an electrolytic solution at any given concentration is the conductance of one unit volume of a solution kept between two platinum electrodes with the unit area of cross-section and at a distance of unit length.

Complete step by step answer:
As mentioned in the question, the two platinum electrodes of the cell are just half dipped and the effective area will be 5 sq cm.
So, we will derive the value of a cell constant $ = \dfrac{1}{a} = \dfrac{{1.5}}{5} = 0.3c{m^2}$
As we know that the 0.05N solution contains 0.05g equivalent in 1000mL.
For,$V = \dfrac{{1000}}{{0.05}} = 20000mL$
Now, we know that the formula of Specific conductance is
Specific conductance=$ = \dfrac{1}{{{\text{resistance}}}} \times {\text{cell constant}}$
Substituting the values we get,
Specific conductance$ = \dfrac{1}{{50}} \times 3 = \dfrac{3}{{500}}mhoc{m^2}e{q^{ - 1}}$
Then, based on the question we have to derive equivalent conductance. The formula for equivalent conductance is:
Equivalent conductance = Specific conductance $ \times $ volume
Substituting the values of specific conductance and volume we get,
$ \Rightarrow $ Equivalent conductance = $\dfrac{3}{{500}} \times 20000 = 120mhoc{m^2}e{q^{ - 1}}$
$\therefore$ the equivalent conductance of the salt solution will be 120 mho$c{m^2}e{q^{ - 1}}$.

So, the correct answer is Option A.

Note:
After solving this question, we need to understand the difference between conductivity and specific conductivity. Specific conductivity takes the area of the electrodes into account to make sure that the measurement of the current conducted is as accurate as possible. While specific conductance is the measure of how well water can conduct an electrical current. Whereas conductivity increases with increasing amount and mobility of ions.