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UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2016 · Paper I

Q1(e). Specific conductance of saturated BaSO₄

  • 10 marks
  • Answered
Question

The solubility product of BaSO₄ is 1×10⁻¹⁰ md² dm⁻⁶. If the ionic conductance at infinite dilution at 25°C of Ba⁺² =127.28×10⁻⁴ m² mho mol⁻¹ and SO₄⁻² =160.0×10⁻⁴ m² mho mol⁻¹, calculate the specific conductance of BaSO₄.

Answer in brief

κ=2.87×10⁻⁴ S m⁻¹ (=2.87×10⁻⁶ S cm⁻¹).

Key points

  • Solubility. BaSO₄(s) ⇌ Ba²⁺ + SO₄²⁻, so Kₛₚ=s²: 3pt] s=1×10⁻¹⁰=1.0×10⁻⁵ mol dm⁻³ =1.0×10⁻⁵×10³ mol m⁻³ =1.0×10⁻² mol m⁻³
  • Molar conductivity. The saturated solution is so dilute that Λₘ≈Λ°. By Kohlrausch's law of independent migration: 3pt] Λ°(BaSO₄)=λ°(Ba²⁺)+λ°(SO₄²⁻)=(127.28+160.0)×10⁻⁴=287.28×10⁻⁴ S m² mol⁻¹
  • Specific conductance. Λₘ=κ/c, so κ=Λ° c with c in mol m⁻³: 3pt] κ=287.28×10⁻⁴×1.0×10⁻², κ=2.87×10⁻⁴S m⁻¹=2.87×10⁻⁶S cm⁻¹
  • S m² mol⁻¹ × mol m⁻³ = S m⁻¹. The common slip is to use c in mol dm⁻³, which gives an answer 10³ times too small.

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

Reading: the unit “md² dm⁻⁶” is mol² dm⁻⁶; mho = S.

  1. Solubility. BaSO₄(s) ⇌ Ba²⁺ + SO₄²⁻, so Kₛₚ=s²: 3pt] s=1×10⁻¹⁰=1.0×10⁻⁵ mol dm⁻³ =1.0×10⁻⁵×10³ mol m⁻³ =1.0×10⁻² mol m⁻³
  2. Molar conductivity. The saturated solution is so dilute that Λₘ≈Λ°. By Kohlrausch's law of independent migration: 3pt] Λ°(BaSO₄)=λ°(Ba²⁺)+λ°(SO₄²⁻)=(127.28+160.0)×10⁻⁴=287.28×10⁻⁴ S m² mol⁻¹
  3. Specific conductance. Λₘ=κ/c, so κ=Λ° c with c in mol m⁻³: 3pt] κ=287.28×10⁻⁴×1.0×10⁻², κ=2.87×10⁻⁴S m⁻¹=2.87×10⁻⁶S cm⁻¹
  4. Units check: S m² mol⁻¹ × mol m⁻³ = S m⁻¹. The common slip is to use c in mol dm⁻³, which gives an answer 10³ times too small.
  5. In practice the conductance of the water itself is subtracted: even good conductivity water conducts about as well as this saturated solution.

Application. run backwards, s=κ/Λ° gives the solubility and Kₛₚ of a sparingly soluble salt (BaSO₄, AgCl, PbSO₄) from one conductance measurement.

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Model answer to Q1(e), 2016 Paper I: solution page 8
Solution page 8 of 46
Read the whole 2016 solution2016 question paper

All parts of Question 1