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Question: Molar conductivities of AgCl, BaSO4, AlPO4 and Ba3(PO4)2 are 200, 300, 500 and 700 S cm² mol⁻¹. Whic...

Molar conductivities of AgCl, BaSO4, AlPO4 and Ba3(PO4)2 are 200, 300, 500 and 700 S cm² mol⁻¹. Which of the following solution has greater conducting ability?

A

Ba3(PO4)2

B

AlPO4

C

BaSO4

D

AgCl

Answer

BaSO4

Explanation

Solution

To determine which solution has greater conducting ability, we need to consider both the solubility product (KspK_{sp}) and the molar conductivity (Λm\Lambda_m) of each salt.

  1. Solubility and Dissociation: For a sparingly soluble salt ABAB that dissociates into A+A^+ and B−B^-, the solubility ss is related to KspK_{sp} by:

    s=Ksps = \sqrt{K_{sp}}

  2. Conductivity Measure: The electrical conductivity is roughly proportional to the product of the solubility ss and the molar conductivity Λm\Lambda_m.

  3. Given Values:

    • AgCl: Ksp≈1.8×10−10K_{sp} \approx 1.8 \times 10^{-10}, Λm=200\Lambda_m = 200 S cm² mol⁻¹
    • BaSO₄: Ksp≈1.1×10−10K_{sp} \approx 1.1 \times 10^{-10}, Λm=300\Lambda_m = 300 S cm² mol⁻¹

  4. Calculations:

    • AgCl: s≈1.8×10−10≈1.34×10−5 Ms \approx \sqrt{1.8 \times 10^{-10}} \approx 1.34 \times 10^{-5} \text{ M} Conductivity measure: 200×1.34×10−5≈2.68×10−3200 \times 1.34 \times 10^{-5} \approx 2.68 \times 10^{-3}
    • BaSO₄: s≈1.1×10−10≈1.05×10−5 Ms \approx \sqrt{1.1 \times 10^{-10}} \approx 1.05 \times 10^{-5} \text{ M} Conductivity measure: 300×1.05×10−5≈3.15×10−3300 \times 1.05 \times 10^{-5} \approx 3.15 \times 10^{-3}

  5. Comparison: Since 3.15×10−3>2.68×10−33.15 \times 10^{-3} > 2.68 \times 10^{-3}, BaSO₄ has a greater conducting ability.

Therefore, the BaSO₄ solution has greater conducting ability.