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Electrochemistry question

2021 · 27 Aug · Shift 2 · Q18
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Electrochemistry question

2021 · 27 Aug · Shift 2 · Q18

JEE MainChemistryElectrochemistryNumerical+4 / −1
The resistance of a conductivity cell with cell constant 1.14 cm −-− 1, containing 0.001 M KCl at 298 K is 1500 Ω\OmegaΩ. The molar conductivity of 0.001 M KCl solution at 298 K in S cm2 mol −-− 1 is ‾\underline{\hspace{2cm}}​. (Integer answer)
Numerical answer
View written solutionFree

Correct answer: 760

  1. Given data

    • Cell constant: lA=1.14 cm−1\dfrac{l}{A} = 1.14\ \text{cm}^{-1}Al​=1.14 cm−1
    • Resistance: R=1500 ΩR = 1500\ \OmegaR=1500 Ω
    • Concentration: C=0.001 MC = 0.001\ \text{M}C=0.001 M
  2. Find conductivity κ\kappaκ

    We use κ=cell constantR\kappa = \frac{\text{cell constant}}{R}κ=Rcell constant​

    So, κ=1.141500 S cm−1\kappa = \frac{1.14}{1500}\ \text{S cm}^{-1}κ=15001.14​ S cm−1

    κ=0.00076 S cm−1=7.6×10−4 S cm−1\kappa = 0.00076\ \text{S cm}^{-1} = 7.6 \times 10^{-4}\ \text{S cm}^{-1}κ=0.00076 S cm−1=7.6×10−4 S cm−1

  3. Use relation between molar conductivity and conductivity

    Molar conductivity is Λm=κ×1000C\Lambda_m = \kappa \times \frac{1000}{C}Λm​=κ×C1000​ where CCC is in mol L−1^{-1}−1.

    Substituting: Λm=7.6×10−4×10000.001\Lambda_m = 7.6\times 10^{-4} \times \frac{1000}{0.001}Λm​=7.6×10−4×0.0011000​

    Λm=7.6×10−4×106\Lambda_m = 7.6\times 10^{-4} \times 10^6Λm​=7.6×10−4×106

    Λm=760 S cm2 mol−1\Lambda_m = 760\ \text{S cm}^2\text{ mol}^{-1}Λm​=760 S cm2 mol−1

  4. Final integer answer

    760\boxed{760}760​

  5. Comparison with stored correct answer

    Stored correct answer = 760760760

    This matches the derived answer.

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