Chemistry • Year 11 • Module 1 • Lesson 17
Periodic Trends: Atomic Radius
Build HSC Band 5–6 extended-response technique by evaluating data, designing investigations, and constructing multi-criteria arguments about atomic size trends.
1. Data + scenario: isoelectronic species in industrial chemistry (Band 5–6)
8 marks Band 5–6
Scenario. In some Australian industrial electrolysis processes, solutions containing isoelectronic species — ions with the same number of electrons — are compared. The table below shows four isoelectronic species all with 18 electrons (the neon configuration). Despite having the same electron count, their ionic radii are different.
| Species | Symbol | Nuclear charge (protons) | Electrons | Ionic radius (pm) |
|---|---|---|---|---|
| Sulfide ion | S2− | 16 | 18 | 184 |
| Chloride ion | Cl− | 17 | 18 | 181 |
| Argon atom | Ar | 18 | 18 | 188 (van der Waals) |
| Potassium ion | K+ | 19 | 18 | 138 |
| Calcium ion | Ca2+ | 20 | 18 | 100 |
Ionic radius data adapted from Shannon (1976), Acta Crystallographica A32: 751–767. Illustrative values.
Q1. Analyse and evaluate the data above to explain why isoelectronic species with 18 electrons have different radii. In your response you must:
- Identify the trend in ionic radius as nuclear charge increases among these 18-electron species and describe it quantitatively using data from the table.
- Explain the trend in terms of effective nuclear charge: refer to what changes and what stays the same across these species.
- Distinguish between the radii of the anions (S2−, Cl−) compared to their parent neutral atoms (S: 104 pm, Cl: 99 pm), explaining what this tells us about the effect of electron gain on size.
- Evaluate the claim: “K+ is smaller than Cl− because it has fewer electrons.” Assess whether this is a complete or incomplete explanation.
- State one limitation of using ionic radius alone to predict reactivity in solution.
2. Experimental design — testing whether atomic radius predicts reactivity in Group 1 (Band 5–6)
7 marks Band 5–6
Background. The lesson states that smaller atoms generally hold outer electrons more tightly, which should mean they are less reactive in reactions that involve losing electrons (e.g. reaction of Group 1 metals with water). This suggests the reactivity of Group 1 metals should increase down the group as atomic radius increases: Li < Na < K.
Research question. Design a scientific investigation to test whether the reactivity of Group 1 metals with water increases in order Li < Na < K, using observable evidence to rank reactivity.
Constraints: You have access to standard senior laboratory equipment (beakers, water, spatulas, tongs, pH indicator, gas collection, a video camera, a balance). Safety: Group 1 metals must be handled in small amounts under teacher supervision. Limit each sample to 0.05 g.
Q2. Design the investigation and present it in the format below.
- State a testable hypothesis that links atomic radius to reactivity (include a predicted ranking).
- Identify the independent variable, dependent variable, and at least two controlled variables.
- Describe the procedure in at least four numbered steps, including how you will measure or rank reactivity quantitatively or semi-quantitatively.
- Explain what result would falsify your hypothesis.
- State two limitations of your design and one way to improve reliability.
Q1 — Sample Band 6 response (8 marks), annotated
Trend identification and quantitative description: Among the five 18-electron species, ionic radius decreases as nuclear charge increases: S2− (184 pm) → Cl− (181 pm) → Ar (188 pm, anomalous noble gas) → K+ (138 pm) → Ca2+ (100 pm). Excluding the van der Waals radius of Ar (not directly comparable to ionic radii), the clear trend is that ionic radius decreases from S2− (184 pm) to Ca2+ (100 pm) as nuclear charge rises from 16 to 20 — a decrease of 84 pm for 4 additional protons. [1 — trend with quantitative reference to data]
Explanation via effective nuclear charge: All five species contain 18 electrons in identical shell configurations. What differs is the nuclear charge (number of protons). A higher nuclear charge exerts a stronger attractive force on the same 18 electrons, pulling them closer to the nucleus and reducing the ionic radius. Shielding is essentially constant across these species because the electron count and arrangement are fixed. Therefore, as nuclear charge increases from 16 (S2−) to 20 (Ca2+), effective nuclear charge increases, and each successive species is smaller. [1 — Zeff explanation; 1 — shielding constant / electron count fixed]
Anions compared to parent atoms: S2− (184 pm) is much larger than neutral S (104 pm), and Cl− (181 pm) is larger than neutral Cl (99 pm). In both cases, gaining electrons adds to electron–electron repulsion in the outer shell without adding protons. The same nuclear charge must now attract more electrons; the effective nuclear charge per electron decreases, so the electron cloud expands. This confirms that electron gain always increases atomic/ionic radius. [1 — anion vs atom comparison with data; 1 — mechanism (repulsion, no extra protons)]
Evaluation of the K+ vs Cl− claim: The claim that “K+ is smaller than Cl− because it has fewer electrons” is incomplete and partly incorrect. K+ and Cl− have the same number of electrons (18). The reason K+ is smaller (138 pm vs 181 pm) is that K+ has more protons (19 vs 17): a higher nuclear charge pulling the same electron count more strongly. Saying K+ “has fewer electrons” is factually wrong for this comparison; the correct explanation is higher effective nuclear charge in K+. [1 — identification that electron count is equal; 1 — correct explanation referencing higher Z/Zeff in K+]
Limitation: Ionic radius alone does not predict reactivity in solution because charge density (charge÷size), hydration energy, and the nature of the chemical interaction all play important roles. For example, a smaller, highly charged ion may actually be less reactive toward certain ligands because it is too strongly hydrated. [1 — valid limitation beyond simple size]
Marking criteria summary (8 marks): 1 = identifies decreasing trend with quantitative data reference; 1 = explains via effective nuclear charge increasing with proton number; 1 = notes shielding/electron count constant; 1 = compares anion to parent atom with data; 1 = explains mechanism of anion expansion (repulsion, no new protons); 1 = identifies claim as incorrect/incomplete (same electron count); 1 = provides correct Zeff explanation for K+ vs Cl−; 1 = states a valid limitation of using ionic radius alone.
Q2 — Sample Band 6 response (7 marks), annotated
Hypothesis: If atomic radius increases down Group 1 (Li < Na < K), then K will react most vigorously with water because its outer electron is held least tightly by the nucleus, followed by Na, then Li. Independent variable: identity of the Group 1 metal (Li, Na, K). Dependent variable: rate/vigour of hydrogen gas production (measured as volume of H2 collected per minute, or subjective rating: slow/moderate/vigorous based on bubble count and movement). Controlled variables: mass of metal (0.05 g each), water volume (200 mL), water temperature (room temperature, ~20 °C). [1 — testable hypothesis with IV and DV]
Procedure: (1) Fill three 250 mL beakers with 200 mL of distilled water each; add 3 drops of universal indicator to each. (2) Using tongs and teacher supervision, place a 0.05 g piece of Li into beaker 1, Na into beaker 2, and K into beaker 3. Start a timer for each. (3) Observe and record: (a) speed of bubbling (count bubbles per 10 s using video replay), (b) colour change of indicator (monitors H2/OH− production), (c) movement of metal across the surface, (d) whether the reaction is self-sustaining or stops. (4) After 60 s (or when metal is consumed), record the maximum temperature change using a thermometer placed in each beaker, and the final colour of the indicator. [1 — four steps including semi-quantitative reactivity measure]
Falsification: If Li reacts more vigorously than Na or K (or if there is no clear ranking Li < Na < K), the hypothesis would be falsified — atomic radius alone would not explain the reactivity trend. [1]
Limitations: (1) Sample mass of 0.05 g is very small and may not give clearly distinguishable gas volumes for comparison, especially for the less reactive Li. [1] (2) Subjectivity in rating “vigour” of bubbling introduces observer bias; two different students may rank the same reaction differently without video evidence. [1]
Improvement: Repeat each trial three times with the same mass and water volume to calculate an average bubble count or temperature rise, improving reliability. Use an inverted measuring cylinder filled with water to collect and quantify H2 gas volume. [1]
Expected outcome: K should react most vigorously (may ignite spontaneously), Na moderately, and Li most slowly — consistent with increasing atomic radius and decreasing hold on the outer electron down Group 1. [1 — prediction linked to atomic radius reasoning]
Marking criteria summary (7 marks): 1 = hypothesis linking atomic radius to reactivity with predicted ranking; 1 = four procedural steps including a semi-quantitative reactivity measure; 1 = falsification condition stated; 1 = first limitation; 1 = second limitation; 1 = improvement to reliability; 1 = precise chemical terminology (effective nuclear charge, outer electron, independent/dependent/controlled variable, Group 1 reactivity trend).