Question

Limiting molar conductivity of $NH_4OH $ $[i.e. \,\wedge^\circ {m (NH_4OH)}]$ is equal to

• A. ${ \wedge^{\circ}_{m(NH_4OH)} + \wedge^{\circ}_{m(Nacl)} - \wedge^{\circ}_{m(NaOH)} } $
• B. ${ \wedge^{\circ}_{m(NH4Cl)} + \wedge^{\circ}_{m(NHOH)} + \wedge^{\circ}_{m(NaCl)} } $
• C. ${ \wedge^{\circ}_{m(NH4Cl)} + \wedge^{\circ}_{m(NaCl)} - \wedge^{\circ}_{m(NaOH)} } $
• D. $\Lambda^\circ_{m}\left(N H_{4} C l\right)+\Lambda_{m}^{\circ}(N a O H)-\Lambda_{m}^{\circ}(N a C l)$

Answer 1

The Correct Option is D

 The  limiting molar conductivity that is denoted by Λ°. It is the measure of the conductivity of the solution that contains one mole of an electrolyte that is dissolved in the solution. 

For the question, the limiting molar conductivity of NH4OH is given by:
Λ°(NH4Cl) +Λ°( NaOH) - Λ° (NaCl) 

According to Kohlrausch law of independent migration of ions: 

\(\Lambda_{m}\left(N H_{4} O H\right)=\Lambda_{m}\left(N H_{4}^{+}\right)+\Lambda_{m}^{*}\left(O H^{-}\right)\)
\(=\Lambda_{m}\left(N H_{4}^{+}\right)+\Lambda_{m}\left(C l^{-}\right)+\Lambda_{m}^{\circ}\left(O H^{-}\right)\)
\(=\Lambda_{m}^{*}\left(N H_{4}^{+}\right)-\Lambda_{m}^{-}\left(C l^{-}\right)-\Lambda_{m}^{n}\left(N a^{+}\right)\)
\(=\Lambda_{m}^{*}\left(N H_{4} C l\right)+\Lambda_{m}^{-}(N a O H)-\Lambda_{m}^{\circ}(N a C l)\)

Answer 2

Ans. The limiting molar conductivity of an electrolyte to its component ions is described by Kohlrausch Law. The sum of the limiting molar conductivities of an electrolyte's cations and anions determines its limiting molar conductivity. A different name for this statute is the Kohlrausch Statute of Independent Migration. The Kohlrausch rule and its applications are essential to the study of diluted liquids and electrochemical cells. Among other important uses, this rule is used to determine the limiting conductivity of a weak electrolyte.

The equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations, according to Kohlrausch's law.

The molar conductivity of a solution is determined by the volume of the solution containing one mole of electrolyte retained between two electrodes with unit cross-sections and unit distances. The molar conductivity of a solution increases with a drop in concentration. This rise in molar conductivity is due to an increase in the volume holding one mole of electrolyte. The molar conductivity is referred to as the limiting molar conductivity as the electrolyte concentration approaches zero.

𝛌^∞_eq = 𝛌^∞_C + 𝛌^∞_a  

𝛌^∞_eq refers to the molar conductivity at an infinite dilution.

𝛌^∞_C refers to the conductivity of cation at an infinite dilution

𝛌^∞_a refers to the conductivity of anion at an infinite dilution

While comparing the limiting molar conductivity values of a few strong electrolytes, Kohlrausch noticed several patterns. On the basis of the observations he made, Kohlrausch proposed that “limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anions and cations of the electrolyte”. The Kohlrausch law of independent ion movement is the name given to this law.