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Electrochemistry question

2024 · 5 Apr · Shift 1 · Q15
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  5. /2024 · 5 Apr · Shift 1 · Q15

Electrochemistry question

2024 · 5 Apr · Shift 1 · Q15

JEE MainChemistryElectrochemistryMCQ+4 / −1
Molar ionic conductivities of divalent cation and anion are 57 S cm2 mol−157 \mathrm{~S~cm}^2 \mathrm{~mol}^{-1}57 S cm2 mol−1 and 73 S cm2 mol−173 \mathrm{~S~cm}^2 \mathrm{~mol}^{-1}73 S cm2 mol−1 respectively. The molar conductivity of solution of an electrolyte with the above cation and anion will be:
  1. A
    187 S cm2 mol−1187 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}187 S cm2 mol−1
  2. B
    260 S cm2 mol−1260 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}260 S cm2 mol−1
  3. C
    65 S cm2 mol−165 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}65 S cm2 mol−1
  4. D
    130 S cm2 mol−1130 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}130 S cm2 mol−1
View written solutionFree

Correct answer: D

  1. Use Kohlrausch’s law of independent migration of ions

For an electrolyte, the molar conductivity at infinite dilution is the sum of the molar ionic conductivities of the ions, each multiplied by its stoichiometric coefficient:

Λm∘=ν+λ+∘+ν−λ−∘\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circΛm∘​=ν+​λ+∘​+ν−​λ−∘​

  1. Identify the electrolyte type

The cation is divalent and the anion is also divalent.

So the electrolyte formed is of type:

M2++X2−→MX\text{M}^{2+} + \text{X}^{2-} \rightarrow \text{MX}M2++X2−→MX

Thus, the stoichiometric coefficients are:

ν+=1,ν−=1\nu_+ = 1, \qquad \nu_- = 1ν+​=1,ν−​=1

  1. Substitute the given ionic conductivities

Given:

λ+∘=57 S cm2 mol−1\lambda_+^\circ = 57\ \mathrm{S\,cm^2\,mol^{-1}}λ+∘​=57 Scm2mol−1 λ−∘=73 S cm2 mol−1\lambda_-^\circ = 73\ \mathrm{S\,cm^2\,mol^{-1}}λ−∘​=73 Scm2mol−1

Hence,

Λm∘=57+73=130 S cm2 mol−1\Lambda_m^\circ = 57 + 73 = 130\ \mathrm{S\,cm^2\,mol^{-1}}Λm∘​=57+73=130 Scm2mol−1

  1. Match with the options

130 S cm2 mol−1130\ \mathrm{S\,cm^2\,mol^{-1}}130 Scm2mol−1

So the correct option is D.

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