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Class 11 Chemistry Chapter 1: Some Basic Concepts of Chemistry case study question with answers

One case-based question of the kind CBSE-pattern school exams ask: a passage and a table, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks

Riya is asked to find the density of a small brass cylinder. On the analytical balance its mass reads 21.4613 g. She then fills a graduated cylinder with water to the 20.0 mL mark and lowers the brass piece in; the level rises to 22.6 mL. Her calculator shows 21.4613 ÷ 2.6 = 8.254346... Her teacher reminds the class that every measurement carries some uncertainty, and that a result is reported only to the digits the measurements justify.

Measurement	Instrument	Reading
mass	analytical balance	21.4613 g
water level before	graduated cylinder	20.0 mL
water level after	graduated cylinder	22.6 mL

Part 1 · 1 mark

The number of significant figures in the mass reading is

(a) 4(b) 6(c) 2(d) 5

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Answer: (b) 6

All non-zero digits are significant: 2, 1, 4, 6, 1, 3 give six significant figures, the last digit being the uncertain one.

Part 2 · 1 mark

Riya should report the density of the brass as

(a) 8.254 g mL⁻¹(b) 8.25 g mL⁻¹(c) 8 g mL⁻¹(d) 8.3 g mL⁻¹

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Answer: (d) 8.3 g mL⁻¹

Volume = 22.6 − 20.0 = 2.6 mL (two significant figures). In division the result keeps the fewest significant figures, two: 8.254 rounds to 8.3 g mL⁻¹.

Part 3 · 2 marks

Explain why the six-figure mass does not make the density more certain, and express the reported density in kg m⁻³ in scientific notation.

Answer and marking scheme

The volume, 2.6 mL, is known to only two significant figures; the uncertainty of the least precise measurement limits the result, however precise the balance. 8.3 g mL⁻¹ = 8.3 g cm⁻³ × (1 kg/1000 g) × (10⁶ cm³/1 m³) = 8.3 × 10³ kg m⁻³.

the two-figure volume limits the result (1)
8.3 × 10³ kg m⁻³ by unit factors (1)

Riya repeats the experiment twice more and gets 8.2, 8.3 and 8.3 g mL⁻¹ in all. The accepted density of this brass is 8.5 g mL⁻¹. Comment on the precision and accuracy of her results, and suggest one change of apparatus that would improve them.

Answer and marking scheme

The three results lie within 0.1 g mL⁻¹ of each other, so they are precise; their average, about 8.27 g mL⁻¹, is well away from 8.5 g mL⁻¹, so they are not accurate. The volume reading limits the result: measuring the volume with a burette (readable to 0.1 mL over a smaller range) or using a larger piece of brass would give a volume with more significant figures.

precise (close together) but not accurate (far from 8.5) (1)
a more precise volume measurement or larger sample (1)

Chapter 2: Structure of Atom →