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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 · 2017 · Paper I

Q1(e). Debye–Hückel limiting law; γ_± of 0.1 M NaCl

  • 10 marks
  • Answered
Question

Write down the Debye-Hückel limiting equation with symbolic significances and their units. Calculate mean ionic activity co-efficient of 0.1 M NaCl (aq) solution at 25°C. The value of Debye-Hückel constant (A) is 0.51 mol^(-1/2) L^(1/2).

Answer in brief

γ_±=-A|z₊z₋|√I; for 0.1 M NaCl, I=0.1 mol L⁻¹, γ_±=-0.161, γ_±=0.690.

Key points

  • Debye–Hückel limiting law: γ_±=-A |z₊z₋| √I
  • Symbols and units: itemize
  • γ_±: mean ionic activity coefficient, γ_±=(γ₊^ν₊γ₋^ν₋)^(1/ν); dimensionless.
  • z₊, z₋: charge numbers of cation and anion; dimensionless.

The full model answer

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

  1. Debye–Hückel limiting law: γ_±=-A |z₊z₋| √I
  2. Symbols and units: itemize
  3. γ_±: mean ionic activity coefficient, γ_±=(γ₊^ν₊γ₋^ν₋)^(1/ν); dimensionless.
  4. z₊, z₋: charge numbers of cation and anion; dimensionless.
  5. I: ionic strength, I=12Σᵢ cᵢzᵢ²; mol L⁻¹.
  6. A: constant for the solvent and temperature, A∝(εᵣT)^(-3/2); 0.509 for water at 25°C; unit mol^(-1/2) L^(1/2) (so that A√I is a number). itemize
  7. Ionic strength of 0.1 M NaCl: I=12[(0.1)(+1)²+(0.1)(-1)²]=0.1 mol L⁻¹; √I=0.316.
  8. γ_±=-(0.51)(1×1)(0.316)=-0.161; γ_±=10⁻⁰˙¹⁶¹=0.690
  9. Limits: the law treats ions as point charges in an ionic atmosphere; it holds well only below about 0.01 M. At 0.1 M it already overestimates the lowering of γ_±; the extended law γ_±=-A|z₊z₋|√I/(1+B√I) is used there.

Application. activity coefficients correct solubility products and electrode potentials; the salt effect (AgCl more soluble in KNO₃ solution) follows from the fall of γ_±.

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Model answer to Q1(e), 2017 Paper I: solution page 6
Solution page 6 of 38
Read the whole 2017 solution2017 question paper

All parts of Question 1