Question:

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

Updated On: Jun 27, 2024
  • ${ \wedge^{\circ}_{m(NH_4OH)} + \wedge^{\circ}_{m(Nacl)} - \wedge^{\circ}_{m(NaOH)} } $
  • ${ \wedge^{\circ}_{m(NH4Cl)} + \wedge^{\circ}_{m(NHOH)} + \wedge^{\circ}_{m(NaCl)} } $
  • ${ \wedge^{\circ}_{m(NH4Cl)} + \wedge^{\circ}_{m(NaCl)} - \wedge^{\circ}_{m(NaOH)} } $
  • $\Lambda^\circ_{m}\left(N H_{4} C l\right)+\Lambda_{m}^{\circ}(N a O H)-\Lambda_{m}^{\circ}(N a C l)$
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The Correct Option is D

Approach Solution - 1

 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: 

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

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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.

𝛌eq = 𝛌C + 𝛌a  

𝛌eq refers to the molar conductivity at an infinite dilution.

𝛌C refers to the conductivity of cation at an infinite dilution

𝛌a 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.

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Concepts Used:

Electrochemical Cells

An electrochemical cell is a device that is used to create electrical energy through the chemical reactions which are involved in it. The electrical energy supplied to electrochemical cells is used to smooth the chemical reactions. In the electrochemical cell, the involved devices have the ability to convert the chemical energy to electrical energy or vice-versa.

Classification of Electrochemical Cell:

Cathode

  • Denoted by a positive sign since electrons are consumed here
  • A reduction reaction occurs in the cathode of an electrochemical cell
  • Electrons move into the cathode

Anode

  • Denoted by a negative sign since electrons are liberated here
  • An oxidation reaction occurs here
  • Electrons move out of the anode

Types of Electrochemical Cells:

Galvanic cells (also known as Voltaic cells)

  • Chemical energy is transformed into electrical energy.
  • The redox reactions are spontaneous in nature.
  • The anode is negatively charged and the cathode is positively charged.
  • The electrons originate from the species that undergo oxidation.

Electrolytic cells

  • Electrical energy is transformed into chemical energy.
  • The redox reactions are non-spontaneous.
  • These cells are positively charged anode and negatively charged cathode.
  • Electrons originate from an external source.