Question

The equivalent conductance of \[B{a^{2 + }}\] and \[C{l^ - }\] are respectively 127 and \[76{\text{ }}oh{m^{ - 1}}c{m^2}e{q^{ - 1}}\] at infinite dilution. What will be the equivalent conductance of \[BaC{l_2}\] at infinite dilution?
a.) \[139.5\;oh{m^{ - 1}}c{m^2}e{q^{ - 1}}\]
b.) \[203\;oh{m^{ - 1}}c{m^2}e{q^{ - 1}}\]
c.) \[279\;oh{m^{ - 1}}c{m^2}e{q^{ - 1}}\]
d.) \[101.5\;oh{m^{ - 1}}c{m^2}e{q^{ - 1}}\]

Answer 1

Hint: Barium Chloride is an inorganic salt composed of cations of barium (\[B{a^{2 + }}\]) and anions of chloride (\[C{l^ - }\]). It is also called Barium Muriate, or Dichloride Barium. This is a white solid that is water-soluble, hygroscopic and that gives a flame a faint yellow-green hue. Barium Chloride chemical formula is \[BaC{l_2}\]. Barium salts are used widely in industry. The sulfate is used especially for outdoor use in white paints. The barium chloride is naturally poisonous.

Complete step-by-step answer:
As per Kohlrausch law at infinite dilution, once dissociation is complete, each ion makes a definite contribution to the equivalent conductance of the electrolyte regardless of the existence of the ion it is associated with and the value of equivalent conductance at infinite dilution for any electrolyte is the amount of the contribution of its constituent ions, i.e., anions and cations.
The chemical equation includes,
\[\begin{gathered}
  BaC{l_2} \to B{a^{2 + }} + 2C{l^ - } \\
  \Lambda _{BaC{l_2}}^0 = \Lambda _{B{a^{2 + }}}^0 + 2C{l^ - } \\
\end{gathered} \]
Electrical Conductivity = \[\dfrac{{279}}{2} = \]\[139.5\;oh{m^{ - 1}}c{m^2}e{q^{ - 1}}\]
Therefore, the equivalent conductance of \[BaC{l_2}\] at infinite dilution is \[139.5\;oh{m^{ - 1}}c{m^2}e{q^{ - 1}}\]
Hence option A is the right answer.

Note: Kohlrausch's law states that at infinite dilution the relative conductivity of an electrolyte is equal to the sum of the anions and cations' conductance. A solution's molar conductivity at a given concentration is the conductance of the volume of solution containing one mole of electrolyte held between two electrodes with cross-section unit area and unit length size. A solution's molar conductivity decreases with reduced concentration. This increase in molar conductivity is due to the increase in the total volume of the electrolyte which contains one mole. Once the electrolyte concentration reaches zero, the molar conductivity is called molar conductivity limiting.