Periodic Relationships Between the Elements: Describe Ionic Radii of Isoelectronic Series
Question
The ionic radii of the ions S2–, Cl–, and K+ are 184, 181, and 138 pm, respectively. Explain why these ions have different sizes even though they contain the same number of electrons.
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Even though S2-, Cl–, and K+ have the same number of electrons, the number of protons they have differs. This causes a difference in their effective nuclear charge and a variation in their size.
Refer to Section 3.2: Periodic Variations in Elemental Properties (1)
Strategy Map
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1. Identify the difference between a parent atom and an ion.
Show/Hide HintParent atoms are the elements in their neutral state, with an equal number of protons and electrons. Ions are charged atoms that have either gained or lost electrons. |
2. Identify the change occurring when each element becomes a cation or anion.
Show/Hide HintAnions have gained electrons (more electrons than protons, i.e., negative) and cations have lost electrons (more protons than electrons, i.e., positive). |
Note the characteristic differences between each of the elements being considered.
Show/Hide HintThe number of electrons is the same for each ion; what about the number of protons or position in the periodic table? |
Solution
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Sulfur (S; Z = 16), chlorine (Cl; Z = 17), and potassium (K; Z = 19) are characteristically unique elements with different numbers of protons located in their nucleus.
Protons are positively charged; electrons are negatively charged. Each element’s parent atom has an equal number of electrons and protons (Z = atomic number) and is neutrally charged. Each ion has the same number of electrons, but they are held around the nucleus with differing strengths.
An atom with more protons has a more positive nuclear charge and can hold onto the electrons more tightly, reducing the ionic radius. Additionally, anions with more electrons have additional electrostatic repulsion, leading to an increased ionic radius.
Guided Solution
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This is question a theory question that requires an understanding of the relationship between the number of electrons and ionic radii.
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Reread the question and pull out the important information. What are you being asked?
Think Think About This!We are told the ions are varied sizes, so we can use our knowledge to determine what the other differences are between them that can explain their sizes. |
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Consider the characteristics of cations and anions.
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Summarize the similarities and differences between each of the ions.
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| Species | Sulfur | Chlorine | Potassium |
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| Atomic Number (Z) | 16 | 17 | 19 |
| Number of Protons | 16 | 17 | 19 |
| Ion | S2- | Cl1- | K+ |
| Number of Electrons | 18 | 18 | 18 |
| Size | Biggest | Middle | Smallest |
Think Think About This!
This is an ‘isoelectric series’; all three ions have the same number of negatively charged electrons around the nucleus. However, they each have a different number of positively charged protons in their core. Electrons are held by electrostatic attractive forces between positive and negative charges. The ion with the least number of protons (i.e., the most negatively charged) will be largest in size because it has the least nuclear charge to hold onto the electrons.
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| A cation always has fewer electrons and the same number of protons as the parent atom; as a result, they will be smaller than the parent atom.
An anion always has more electrons and the same number of protons as the parent atom; as a result, they will be larger than the parent atom. In general, for an isoelectric series, the more negatively charged an atom, the larger it will be, and the more positively charged an atom, the smaller it will be. Even though S2-, Cl–, and K+ have the same number of electrons, the number of protons they have differs. This causes a difference in their effective nuclear charge and a variation in their size. |
Check Your Work
Summary of what we would expect based on the related chemistry theory.
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You can have multiple atoms with the same number of electrons, but they will all vary in size. This size variation is because they have a different number of protons.
Does your answer make chemical sense?
Show/Hide Answer
A cation is an atom that has lost at least 1 electron and is left with an unequal number of protons and electrons. Because there is a greater number of protons, the valence electron(s) will feel a greater effective nuclear charge and, as a result, be pulled closer to the nucleus in the centre. This causes the cation to be smaller than its parent atom.
The opposite is true for an anion; it has gained at least 1 electron and, therefore, has more electrons than it does protons. Because there are fewer protons then electrons, the valence electrons will feel a weaker effective nuclear charge.
Additionally, the ionic radii will be affected by greater repulsions between the valence electrons, and they will be pushed further from the nucleus. This causes the anion to be larger than its parent atom.
PASS Attribution
- LibreTexts PASS Chemistry Book CHEM 1500 (2).
- Question 3.E.18 from LibreTexts PASS Chemistry Book CHEM 1500 (3) is used under a CC BY-NC-SA 4.0 license.
- Question 3.E.18 was adapted from question 6.5.18 from LibreTexts Chemistry 1e (OpenSTAX) (4), which is under a CC BY 4.0 license.
- Question 6.5.18 is question 84 from OpenStax Chemistry 2e (5), which is under a CC BY 4.0 license. Access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction.
References
1. OpenStax. 3.2: Periodic Variations in Element Properties. In CHEM 1500: Chemical Bonding and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/03%3A_Periodic_Relationships_Among_the_Elements/3.02%3A_Periodic_Variations_in_Element_Properties.
2. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1500; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500.
3. Blackstock, L.; Brewer, S.; Jensen, A. 3.3: Question 3.E.18 PASS – Describe Ionic Radii of Isoelectronic Series. In PASS Chemistry Book CHEM 1500. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/03%3A_Periodic_Relationships_Among_the_Elements/3.03%3A_Question_3.E.18_PASS_-_describe_ionic_radii_of_isoelectronic_series.
4. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/06%3A_Electronic_Structure_and_Periodic_Properties/6.E%3A_Electronic_Structure_and_Periodic_Properties_(Exercises).
5. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises.
