VKC ScienceChemistry for written exams Telegram

UPSC Combined Geo-Scientist

Chemist

  • 3 descriptive papers
  • 200 marks each
  • 3 h per paper

Mains Paper III covers analytical and organic chemistry.

UPSC Combined Geo-Scientist, Mains · 2023 · Mains Paper III

Q1(a). Relative standard deviation of replicate results

Question

The following results were obtained in the replicate determinations of Fe content in a mineral ore (in mg): 10.5, 10.6, 10.3, 10.6, 10.2 and 10.4. Calculate the relative standard deviation (RSD) of this data.

Answer in brief

x̄ = 10.43 mg, s = 0.163 mg, RSD = 100 s/x̄ = 1.57 % (15.7 parts per thousand).

Key points

  • Mean: x̄ = Σx/n = 62.6/6 = 10.433 mg.
  • Sum of squared deviations Σ(x − x̄)² = 0.1333 mg²; s = √(0.1333/5) = 0.1633 mg (n − 1 = 5 degrees of freedom).
  • RSD = (s/x̄) × 100 = (0.1633/10.433) × 100 = 1.57 % = 15.7 parts per thousand.
  • The RSD in per cent is the coefficient of variation: a measure of precision, not of accuracy.
  • Result to report: 10.4 ± 0.2 mg Fe (n = 6); division by n instead of n − 1 would give 1.43 %.

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

Model answer to Q1(a), 2023 Mains Paper III: solution pages 1 and 2
Solution pages 1 and 2 of 40
Read the whole 2023 solution2023 question paper

Topic notes: errors in chemical analysis, standard deviation, confidence limits and the Q-, t- and F-tests, with every Civil Services, IFoS and Geo-Scientist PYQ →

Coversrelative standard deviationstandard deviationcoefficient of variationprecisionreplicate analysis

All parts of Question 1