Question

The equivalent conductance of $NaCl$ at concentration $C$ and at infinite dilution are ${{\lambda }_{C}}$ and ${{\lambda }_{\infty }}$ respectively. The correct relationship between ${{\lambda }_{C}}$ and ${{\lambda }_{\infty }}$ is given as:
A) ${{\lambda }_{C}}={{\lambda }_{\infty }}-(B)\sqrt{C}$
B) ${{\lambda }_{C}}={{\lambda }_{\infty }}+(B)\sqrt{C}$
C) ${{\lambda }_{C}}={{\lambda }_{\infty }}+(B)C$
D) ${{\lambda }_{C}}={{\lambda }_{\infty }}-(B)C$

Answer 1

We know that conductance, Molar Conductance, Molar conductivity, increases with dilution as, on dilution a greater number of ions are produced, also they are much free to move or to conduct. For a weak electrolyte the variation of molar conductivity with dilution can be found by plotting the concentration against molar conductivity.

Complete answer:
Conductivity of an electrolyte is also called as specific conductance. It is the measure of ability of an electrolyte to conduct electricity. Conductivity is expressed in Siemens per meter in SI units. As we are aware, molar conductivity of a solution at a given concentration is the conductance of volume V of a solution containing one mole of electrolyte kept between two electrodes with an area of cross section A and distance of unit length.

Since conductivity is the conductance per centimeter cube of the solution, on dilution the concentration of ions per centimeter cube decreases and as a result conductivity also decreases. We have seen that dilution conductivity would decrease. But that is not the case with molar conductance. The dilution volume containing one mole of an electron increases and from the above equation, we could see that molar conductivity will increase with volume. Hence, molar conductivity increases with dilution. The Debye Huckel Onsager equation gives us ideas about variation of molar conductivity of a weak electrolyte with dilution.

The Debye-Huckel Onsager equation can be written as: ${{\lambda }_{C}}={{\lambda }_{\infty }}-(B)\sqrt{C}$ where,
${{\lambda }_{C}}=$ Molar conductivity of the solution at certain concentration,
${{\lambda }_{\infty }}=$ Limiting molar conductivity and $C=$ Concentration;
$B=$ Constant that depends on temperature charges on the ions and dielectric constant as well as viscosity of the solution.

Therefore, the correct answer is option A.

Note: Remember that the terminologies must be used cautiously. Conductance is the reverse of electrical resistance; conductivity is the inverse of resistivity. Molar conductance is conductance of all the ions produced by ionization of one g mole of an electrolyte which is present in $V\text{ }mL$ of solution. Molar conductivity is conductivity of one mole of electrolyte.