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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

Q8(c). Surface area of silica gel from the nitrogen monolayer

  • 10 marks
  • Answered
Question

Volume of nitrogen gas at 1 atm and 273 K required to cover 1 g of silica gel is 0.129 dm³. Calculate the surface area of the gel if each nitrogen molecule occupies an area of 16.2×10⁻¹⁰ m².

Answer in brief

Surface area =562 m² g⁻¹ (taking the area of one N₂ molecule as 16.2×10⁻²⁰ m²).

Key points

  • in a monolayer each adsorbed molecule lies on the surface and covers its own cross-section σ, so area = number of molecules × σ.
  • Amount of N₂ (ideal gas, 1 atm, 273 K, Vₘ=22.414 dm³ mol⁻¹): n=(0.129)/(22.414)=5.755×10⁻³ mol
  • N=nN_A=(5.755×10⁻³)(6.022×10²³)=3.466×10²¹
  • A=Nσ=(3.466×10²¹)(16.2×10⁻²⁰m²)=561.5m²≈562m² g⁻¹

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 cross-section of N₂ is 16.2 ²=0.162 nm²=16.2×10⁻²⁰ m²; “10⁻¹⁰” is a misprint for 10⁻²⁰. (With the printed value the area would be 5.6×10¹² m² for one gram, which is impossible.)

  1. Method: in a monolayer each adsorbed molecule lies on the surface and covers its own cross-section σ, so area = number of molecules × σ.
  2. Amount of N₂ (ideal gas, 1 atm, 273 K, Vₘ=22.414 dm³ mol⁻¹): n=(0.129)/(22.414)=5.755×10⁻³ mol
  3. Number of molecules: N=nN_A=(5.755×10⁻³)(6.022×10²³)=3.466×10²¹
  4. A=Nσ=(3.466×10²¹)(16.2×10⁻²⁰m²)=561.5m²≈562m² g⁻¹

Check: 1 cm³ of N₂ at STP spread as a monolayer covers N_Aσ/22 414=4.35 m²; 129×4.35=561 m².

Reading the answer: more than 500 m² for one gram is possible only for a highly porous solid; nearly all of it is the inner surface of the pores of the gel. The monolayer volume itself comes from N₂ adsorption at 77 K analysed by the BET equation.

Application. the BET surface area is the standard measure of adsorbents and catalyst supports (silica gel, alumina, activated charcoal), since adsorption capacity and the rate of a surface reaction are proportional to the area available.

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Model answer to Q8(c), 2016 Paper I: solution page 45
Solution page 45 of 46
Read the whole 2016 solution2016 question paper

All parts of Question 8