Chemistry entrance exam, 2013 E.C. (2021)

A measured value can never be perfectly exact. Significant figures are all the digits you are sure about, plus one final digit that is estimated. That last digit carries the uncertainty of the measurement.

For example, if a burette reads 24.35 mL, the digits 2, 4 and 3 are certain and the 5 is the estimated one. All four are significant figures.

Options A, B and C talk about precision, accuracy and uncertainty. Those words describe the quality of a measurement, not what significant figures are.

Textbook: Chemistry Grade 9, Unit 2 Measurements and Scientific Methods, section 2.1 Measurements and Units in Chemistry (page 20).

The question describes a branch of chemistry that separates a sample into its parts, identifies each part, and measures how much of each is present. That is exactly what analytical chemistry does. An analytical chemist may use instruments to find out what an unknown material contains and in what amounts.

Physical chemistry is a tempting wrong choice, but it studies energy changes, reaction rates and the theories behind chemical behaviour. It does not focus on separating and measuring the components of samples.

Textbook: Chemistry Grade 9, Unit 1 Chemistry and its Importance, section 1.1 Definition and Scope of Chemistry (page 2).

Divide mass by volume:

\[ d = \frac{m}{V} = \frac{3.8056\ \text{g}}{2.5\ \text{mL}} = 1.52224\ \text{g/mL} \]

Now apply the rule for significant figures. In multiplication and division, the answer keeps as many significant figures as the least precise measurement. The mass (3.8056 g) has 5 significant figures, but the volume (2.5 mL) has only 2. So the reported density must have 2 significant figures.

Rounding 1.52224 to 2 significant figures gives 1.5 g/mL.

Options A and C keep digits that the rough volume reading cannot support, so they overstate the precision of the result.

Textbook: Chemistry Grade 9, Unit 2 Measurements and Scientific Methods, section 2.1 Measurements and Units in Chemistry (page 20).

The scientific method is the organized way scientists build reliable knowledge. It moves from observation and questions to a hypothesis, then to experiments that test the hypothesis, and finally to analysis and conclusions. The key idea is that the experiments must be reproducible: anyone who repeats them should get the same result.

Option A stops at guessing, option C describes rules rather than a method, and option D describes lucky accidents. None of these is the method itself.

Textbook: Chemistry Grade 9, Unit 2 Measurements and Scientific Methods, section 2.2 Chemistry as Experimental Science (page 37).

Uncertainty enters a measurement through three main doors: the measuring device (a worn ruler or a badly calibrated balance), the person doing the measuring (reading errors, reaction time, parallax), and the environment (temperature changes, vibration, air currents).

The type of material being measured is not one of these causes. A given balance reads gold with the same uncertainty as it reads salt; what matters is the instrument, the person and the surroundings, not what the sample is made of.

Textbook: Chemistry Grade 9, Unit 2 Measurements and Scientific Methods, section 2.1.4 Uncertainty in Measurements (page 28).

Isotopes are atoms of the same element. They must have the same number of protons, because the proton number is what defines the element. What differs is the number of neutrons, so their mass numbers differ.

For example, carbon-12 and carbon-14 both have 6 protons, but they have 6 and 8 neutrons.

Option D reverses the facts: isotopes have the same atomic number but different masses. Option C is wrong because isotopes share the same chemical properties; only some physical properties (like mass) differ slightly.

Textbook: Chemistry Grade 9, Unit 3 Structure of the Atom, section 3.5 Composition of an Atom and the Isotopes (page 87).