3.3: Question 3.E.18 PASS - describe ionic radii of isoelectronic series
- Page ID
- 452278
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The ionic radii of the ions S2-, Cl- and K+ are 184, 181, 138 pm respectively. Explain why these ions have different sizes even though they contain the same number of electrons.
- Answer
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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 (Zeff) and a variation in their size. The most negatively charged atom in an isoelectric series will have the greatest ionic radii due to the weakest Zeff and greatest electron repulsions.
See LibreText 3.2 Periodic Variations in Elemental Properties
- Strategy Map
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Step Hint 1. Identify the difference between a parent atom and an ion See LibreText 3.2.3 Variation in Ionic Radii
Parent atom: atoms in their original state before any electrons are added or removed
Ions: charged atoms that have either gained or lost electrons
2. Identify the change occurring when an element becomes a cation or anion Anion: atom has gained electrons, is negatively charged
- Ionization energy is related to the amount of energy required to remove an electron from an atom
Cation: atom has lost electrons, is positively charged
- Electron affinity is related to the amount of energy required to add an electron to an atom
3. Summarize the total number of protons and electrons for the ion To find the number of protons and electrons for the neutral (uncharged) parent atom, refer to the periodic table atomic number (z).
Note: a neutral atom has the same number of electrons and protons
4. Recall the relationship between protons and electrons, and consider the factors that influence their attraction Protons are positively charged, electrons are negatively charged; they are attracted to each other by electrostatic 'Coloumbic' forces (just like oppositely charged magnets).
- protons are contained within the nucleus, the centre of the atom
- if there are more protons then electrons (positively charged), the electrons will be held more tightly (i.e., closer) to the nucleus, the ionic radii will be smaller
- if there are more electrons than protons (negatively charged), the electrons will be held less tightly (i.e., further) from the nucleus, the ionic radii will be larger
- Solution
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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.
The charge on an atom or ion is the sum of all electrons (-1) and protons (+1)
The parent atom has no charge, it has the same number of protons and electrons
- A cation (positively charged) always has fewer electrons and the same number of protons as the parent atom
- will be smaller than the parent atom.
- An anion (negatively charged) always has more electrons and the same number of protons as the parent atom
- 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.
- A cation (positively charged) always has fewer electrons and the same number of protons as the parent atom
- Guided Solution
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Download Guided Solution as a pdf
Guided Solution Hint This is a theory question requiring an explanation on why K+, Cl- and S2- are not the same size even though they are an isoelectric series Recall 'isoelectric series' is a group of elements (atoms and or/ions) that have the same number of electrons (i.e., the same electronic configuration)
See LibreText 3.2 Periodic Variations in Elemental Properties
Question
The ionic radii of the ions S2–, Cl–, and K+ are 184, 181, 138 pm respectively. Explain why these ions have different sizes even though they contain the same number of electrons.
We are told the ions are varied sizes, we can use our knowledge to determine what an ion is and what the differences are between them
Recall: when an ion is formed, the number of electrons changes, the number of protons remains the same.
Consider the characteristics anions. Recall:
anions have gained electrons; electrons are negatively charged
- There are more electrons (-1) than protons (+1)
- the anion will be negatively charged
this means two things:
- The relative effective nuclear charge (Zeff) from the nucleus is less
- the valence electrons will be held less tightly (i.e., further away from the nucleus)
- The negative-negative repulsions between valence electrons is increased
- when electrons are repelled by each other they move further apart
Therefore: the ionic radii of anions is greater than the atomic radii of the parent atom
See LibreText 3.2.1 Effective Nuclear Charge: Penetration and ShieldingConsider the characteristics of cations Recall:
cations have lost electrons; electrons are negatively charged
- There are less electrons (-1) than protons (+1)
- the cation will be positively charged
this means two things:
- The relative effective nuclear charge (Zeff) from the nucleus is greater
- the valence electrons will be held more tightly (i.e., closer to the nucleus)
- The negative-negative repulsions between valence electrons is decreased
Therefore: the ionic radii of cations is less than the atomic radii of the parent atom
See LibreText 3.2.3 Variation in Ionic RadiiSummarize the total number of protons and electrons for the ion Species Atomic Number (Z) = Number of protons Number of Electrons Ion Charge S2– +16 -18 -2 Cl– +17 -18 -1 K+ +19 -18 +1 The most negatively charged atom in an isoelectric series will have the greatest ionic radii due to the weakest Zeff and greatest electron repulsions.
Answer
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.
- K+ is the smallest because it has the most positive ionic charge
- S2- is the largest because it has the most negative ionic charge
Check your work!
Why does this answer make chemical sense?
A cation is an atom that has lost at least one electron therefore 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 center. This causes the cation to be smaller than its parent atom.
The opposite is true for an anion, it has gained at least one 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.
(question source adapted from 6.5.18 from 6.E: Electronic Structure and Periodic Properties (Exercises): https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/06%3A_Electronic_Structure_and_Periodic_Properties_of_Elements/6.E%3A_Electronic_Structure_and_Periodic_Properties_(Exercises), shared under a CC BY 4.0 license, authored, remixed, and/or curated by OpenStax, original source question 84 https://openstax.org/books/chemistry-2e/pages/6-exercises, Access for free at https://openstax.org/books/chemistry/pages/1-introduction)
- There are more electrons (-1) than protons (+1)