Question

The specific conductance in \[oh{m^{--1}}c{m^{ - 1}}\] of four electrolytes P, Q, R, and S are given in brackets: P \[(5.0 \times {10^{ - 5}})\] Q \[(7.0 \times {10^{ - 8}})\] R \[(1.0 \times {10^{ - 10}})\] S \[(9.2 \times {10^3})\] The one that offers the highest resistance to the passage of electric current is:
A. P
B. Q
C. S
D. R

Answer 1

Hint: Conductance is a reciprocal of resistance to the system. It is also a ratio of the current to the potential difference. The unit of conductance is siemens or \[oh{m^{ - 1}}\] .

Complete step by step answer:
According to ohm’s law of resistance, resistance is directly proportional to the length and inversely proportional to the cross-sectional area. which can be written as, \[R\alpha \dfrac{l}{A}\] . Where length is \[{\text{l}}\] and the cross sectional area is A. it can also be written with a proportional constant \[{\text{\rho }}\] which is called resistivity. Therefore, the formula of resistance is \[R = \rho \dfrac{l}{A}\] .
 Conductance is a reciprocal of resistance of the system, \[G = \dfrac{1}{R}\] where G is conductance. Therefore, the formula of conductance can be written as, \[G = \dfrac{1}{R} = \dfrac{1}{\rho } \times \dfrac{A}{l}\] . Where \[\dfrac{1}{\rho }\] can be written with a new term specific conductance or conductivity. Therefore, the formula of conductance is,
  \[
  G = \kappa \times \dfrac{A}{l} \\
  or,G \times \dfrac{l}{A} = \kappa \\
 \]
Now, this \[\dfrac{l}{A}\] is known as a cell constant. as it is a constant value, \[\kappa \] is the specific constant, and G is the conductance.
Now as Conductance is a reciprocal of resistance of the system, \[G = \dfrac{1}{R}\] , it means the specific conductance is also inversely proportional to resistance,
 \[
  G = \kappa \times \dfrac{A}{l} \\
  or,\dfrac{1}{R} \times \dfrac{l}{A} = \kappa \\
  or,\dfrac{1}{R}\infty \kappa \\
 \]
So, with increasing the resistance the specific conductance decreases, therefore the values of the specific conductance of four electrolytes P, Q, R, and S are given in brackets: P \[(5.0 \times {10^{ - 5}})\] Q \[(7.0 \times {10^{ - 8}})\] R \[(1.0 \times {10^{ - 10}})\] S \[(9.2 \times {10^3})\] in \[oh{m^{--1}}c{m^{ - 1}}\] .
Considering these values, the order of resistance of these electrolytes is \[R > Q > P > S\]
So, the one that offers the highest resistance to the passage of electric current is R

The correct option is D.

Note:
With the dilution of the electrolyte the equivalent conductance and molar conductance value increases. This is because on dilution the degree of dissociation of electrolyte increases as well as the number of ions increases. Remember the definitions of resistance, conductance. Remember the formula of conductance and resistance. The ratio of length to the cross-sectional area is called cell constant. Remember the formula of molar conductivity \[{\Lambda _m} = \dfrac{{1000 \times \kappa }}{c}\] .