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Chapter 7: Problem 36

For each of the following sets of atoms and ions, arrange the members in order of increasing size: \((a) \mathrm{Se}^{2-}, \mathrm{Te}^{2-}\), Se; (b) \(\mathrm{Co}^{3+}, \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}\) (d) \(\mathrm{Be}^{2+}, \mathrm{Na}^{+}, \mathrm{Ne}\) (c) \(\mathrm{Ca}, \mathrm{Ti}^{4+}, \mathrm{Sc}^{3+}\)

Short Answer

Expert verified
The order of increasing size for the given sets of atoms and ions are: (a) Se < \(\mathrm{Se}^{2-}\) < \(\mathrm{Te}^{2-}\) (b) \(\mathrm{Fe}^{3+}\) < \(\mathrm{Co}^{3+}\) < \(\mathrm{Fe}^{2+}\) (c) \(\mathrm{Ti}^{4+}\) < \(\mathrm{Sc}^{3+}\) < Ca (d) \(\mathrm{Be}^{2+}\) < Ne < \(\mathrm{Na}^{+}\)

Step by step solution

01

(a) Ordering Se^2-, Te^2-, and Se by increasing size

First, note the atomic numbers of Se and Te: Se=34 and Te=52. Selenium, Se, and tellurium, Te, are in the same group in the periodic table, with Se above Te. In the case of \(\mathrm{Se}^{2-}\) and Se, Se has lost two electrons, causing it to be smaller in size due to the increased effective nuclear charge. In comparison to \(\mathrm{Se}^{2-}\), \(\mathrm{Te}^{2-}\) has a larger atomic number and more electron shells, making it larger in size. Hence the order is: Se < \(\mathrm{Se}^{2-}\) < \(\mathrm{Te}^{2-}\).
02

(b) Ordering Co^3+, Fe^2+, and Fe^3+ by increasing size

We compare these ions based on their respective atomic numbers: Cobalt (Co = 27) and Iron (Fe=26). \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) have the same number of electron shells but different effective nuclear charges. \(\mathrm{Fe}^{3+}\) has a higher effective nuclear charge due to losing one more electron compared to \(\mathrm{Fe}^{2+}\), making it smaller in size. Both \(\mathrm{Co}^{3+}\) and \(\mathrm{Fe}^{3+}\) have the same effective nuclear charge, but \(\mathrm{Co}^{3+}\) has one more proton than \(\mathrm{Fe}^{3+}\), making it slightly smaller in size. Hence, the order is: \(\mathrm{Fe}^{3+}\) < \(\mathrm{Co}^{3+}\) < \(\mathrm{Fe}^{2+}\).
03

(c) Ordering Ca, Ti^4+, and Sc^3+ by increasing size

Arrange these atoms based on their atomic numbers: Calcium (Ca=20), Titanium (Ti=22), and Scandium (Sc=21). Since \(\mathrm{Ti}^{4+}\) lost 4 electrons, it has a higher effective nuclear charge, making it smaller in size compared to the other ions. In comparison, \(\mathrm{Sc}^{3+}\) lost 3 electrons and has an atomic number in between Ca and Ti, implying that it is of intermediate size. Calcium has the least effective nuclear charge due to no loss of electrons, making it the largest in size. Hence, the order is: \(\mathrm{Ti}^{4+}\) < \(\mathrm{Sc}^{3+}\) < Ca.
04

(d) Ordering Be^2+, Na^+, and Ne by increasing size

Arrange these atoms based on their atomic numbers: Beryllium (Be=4), Sodium (Na=11), and Neon (Ne=10). These ions belong to different groups in the periodic table, with \(\mathrm{Be}^{2+}\) and Ne in the same period. Since \(\mathrm{Be}^{2+}\) has a higher effective nuclear charge due to losing 2 electrons compared to Ne, which has not lost any electrons, \(\mathrm{Be}^{2+}\) is smaller in size. \(\mathrm{Na}^{+}\) has lost one electron, making it smaller than Ne and has more electron shells than \(\mathrm{Be}^{2+}\), making it larger in size. Hence, the order is: \(\mathrm{Be}^{2+}\) < Ne < \(\mathrm{Na}^{+}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Periodic Table Concept
The periodic table is a systematic arrangement of elements in order of increasing atomic number. Elements in the same column, known as a group, typically have similar chemical properties. Moving from left to right across a period, the atomic number - which represents the number of protons in an atom - increases sequentially.
This organization helps predict trends in atomic size across a period and down a group.
  • Across a period: Atomic size generally decreases as electrons are added to the same energy level but the nuclear charge increases, pulling electrons closer.
  • Down a group: Atomic size increases as additional electron shells are added, outweighing the increasing nuclear charge.
Understanding these trends is pivotal in predicting and explaining atomic behavior, as seen in the ordering of elements or ions by size in various chemical reactions and compounds.
Ionic Size
Ionic size refers to the size of an ion compared to its atom. When an atom loses or gains electrons, it forms an ion, which can be smaller or larger than its neutral atom.
  • Cations (positively charged ions) form when an atom loses electrons, leading to a decrease in size due to reduced electron repulsion and a greater effective nuclear charge.
  • Anions (negatively charged ions) form when an atom gains electrons, increasing in size as added electron repulsions outweigh the nuclear charge.

For instance, \[\text{Se}^2-\text{, which is an anion, is larger than Se due to electron gain. On the other hand, } \text{Ti}^{4+}\] is a cation, resulting in a much smaller size compared to the neutral titanium atom. Ionic size is crucial in understanding the properties of metals and nonmetals and their behavior in forming compounds.
Effective Nuclear Charge
Effective nuclear charge (Z_eff) is the net positive charge experienced by valence electrons. It is essentially the actual nuclear charge (number of protons) minus the shielding effect of inner-shell electrons.Effective nuclear charge helps explain why outer electrons are more tightly bound or less shielded. When an electron is added, the additional shielding, in effect, reduces the overall pull of the nucleus on outer electrons.
  • Higher Z_eff results in smaller atomic or ionic size because the outer electrons are pulled more strongly towards the nucleus.
  • Conversely, lower Z_eff leads to a larger atomic size as the outer electron hold is weaker.
An understanding of Z_eff is key in predicting changes in atomic size when comparing ions like \( \text{Fe}^{3+} \) - where a higher Z_eff due to more protons relative to electrons results in a smaller radius than \( \text{Fe}^{2+} \).
Atomic Number
The atomic number is a fundamental property of an element, defined as the number of protons in the nucleus of an atom. It not only determines the identity of the element but also its position on the periodic table.
  • An increase in atomic number signifies an additional proton, inherently increasing the atomic mass.
  • Higher atomic numbers typically correlate with heavier elements and more electron shells, affecting atomic and ionic sizes.
The atomic number's importance is evident when comparing elements or ions, such as Se (atomic number 34) with Te (atomic number 52), where Te, having more protons, typically has larger ionic and atomic sizes due to additional electron shells. Understanding atomic number helps in distinguishing elements and predicting their chemical properties and reactions.

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Most popular questions from this chapter

Make a simple sketch of the shape of the main part of the periodic table, as shown. (a) Ignoring \(\mathrm{H}\) and \(\mathrm{He}\), write a single straight arrow from the element with the smallest bonding atomic radius to the element with the largest. (b) Ignoring \(\mathrm{H}\) and He, write a single straight arrow from the element with the smallest first ionization energy to the element with the largest. (c) What significant observation can you make from the arrows you drew in parts (a) and (b)? [Sections \(7.3\) and 7.4]

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Potassium metal burns in an atmosphere of chlorine gas. (b) Strontium oxide is added to water. (c) A fresh surface of lithium metal is exposed to oxygen gas. (d) Sodium metal is reacted with molten sulfur.

What is the relationship between the ionization energy of an anion with a 1 - charge such as \(\mathrm{F}\) and the electron affinity of the neutral atom, F?

(a) Which will have the lower energy, a \(4 s\) or a \(4 p\) electron in an As atom? (b) How can we use the concept of effective nuclear charge to explain your answer to part (a)?

Until the early 1960 s the group 8 A elements were called the inert gases; before that they were called the rare gases. The term rare gases was dropped after it was discovered that argon accounts for roughly \(1 \%\) of Earth's atmosphere. (a) Why was the term inert gases dropped? (b) What discovery triggered this change in name? (c) What name is applied to the group now?
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