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Chapter 7: Problem 34

Arrange each of the following sets of atoms and ions, in order of increasing size: (a) \(\mathrm{Pb}, \mathrm{Pb}^{2+}, \mathrm{Pb}^{4+}\) (b) \(\mathrm{V}^{3+}, \mathrm{Co}^{2+}, \mathrm{Co}^{3+}\) (c) \(\mathrm{Se}^{2-}, \mathrm{S}^{2-}, \mathrm{Sn}^{2+}\) (d) \(\mathrm{K}^{+}, \mathrm{Rb}^{+}, \mathrm{Br}^{-}\)

Short Answer

Expert verified
(a) \(\mathrm{Pb}^{4+} < \mathrm{Pb}^{2+} < \mathrm{Pb}\) (b) \(\mathrm{Co}^{3+} < \mathrm{V}^{3+} < \mathrm{Co}^{2+}\) (c) \(\mathrm{Sn}^{2+} < \mathrm{Se}^{2-} < \mathrm{S}^{2-}\) (d) \(\mathrm{Rb}^{+} < \mathrm{K}^{+} < \mathrm{Br}^{-}\)

Step by step solution

01

Ionic Radius Comparison

Comparing the atomic and ionic radii of the same element, we simply need to consider the different number of electrons that an ion has. As the charge of an ion increases, there will be fewer electrons, and as a result, the electrons are pulled closer to the nucleus. This leads to a decrease in size. So, \(\mathrm{Pb}^{4+}\) is smaller than \(\mathrm{Pb}^{2+}\), which is smaller than \(\mathrm{Pb}\).
02

Arrange the Sizes

Based on the above analysis, we can arrange the atoms and ions in order of increasing size: \[\mathrm{Pb}^{4+} < \mathrm{Pb}^{2+} < \mathrm{Pb}\] (b) For \(\mathrm{V}^{3+}, \mathrm{Co}^{2+}, \mathrm{Co}^{3+}\):
03

Effect of Charge on Size

Considering the different charges, we can determine that \(\mathrm{Co}^{3+}\) will be smaller than \(\mathrm{Co}^{2+}\) because it has one less electron.
04

Effect of Atomic Number on Size

Given that \(\mathrm{V}^{3+}\) and \(\mathrm{Co}^{3+}\) have the same charge, we can compare their radii based on position in the periodic table. Vanadium (Z=23) has fewer protons than Cobalt (Z=27), therefore \(\mathrm{V}^{3+}\) will have a larger size compared to \(\mathrm{Co}^{3+}\) as the electrons are pulled less towards the nucleus.
05

Arrange the Sizes

Based on the above analysis, we can arrange the atoms and ions in order of increasing size: \[\mathrm{Co}^{3+} < \mathrm{V}^{3+} < \mathrm{Co}^{2+}\] (c) For \(\mathrm{Se}^{2-}, \mathrm{S}^{2-}, \mathrm{Sn}^{2+}\):
06

Effect of Charge on Size

Since the negative ions have equal charges, we must compare their sizes based on their positions in the periodic table.
07

Effect of Atomic Number on Size

Selenium (Z=34) has more protons than Sulfur (Z=16), so \(\mathrm{Se}^{2-}\) will be smaller than \(\mathrm{S}^{2-}\) due to the greater pull of its nucleus. Tin (Z=50) has more protons than Selenium, so \(\mathrm{Sn}^{2+}\) will be smaller than \(\mathrm{Se}^{2-}\).
08

Arrange the Sizes

Based on the above analysis, we can arrange the atoms and ions in order of increasing size: \[\mathrm{Sn}^{2+} < \mathrm{Se}^{2-} < \mathrm{S}^{2-}\] (d) For \(\mathrm{K}^{+}, \mathrm{Rb}^{+}, \mathrm{Br}^{-}\):
09

Effect of Charge on Size

Since we have both positive and negative ions, we should first consider the negative ion to be larger than the positive ions due to their extra electrons.
10

Effect of Atomic Number on Size

Potassium (Z=19) has fewer protons than Rubidium (Z=37), so \(\mathrm{K}^{+}\) will have a larger size compared to \(\mathrm{Rb}^{+}\).
11

Arrange the Sizes

Based on the above analysis, we can arrange the atoms and ions in order of increasing size: \[\mathrm{Rb}^{+} < \mathrm{K}^{+} < \mathrm{Br}^{-}\]

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Most popular questions from this chapter

As we move across a period of the periodic table, why do the sizes of the transition elements change more gradually than those of the representative elements?

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Lithium is added to water. (b) Calcium is added to water. (c) Potassium reacts with chlorine gas. (d) Rubidium reacts with oxygen.

Tungsten has the highest melting point of any metal in the periodic table: \(3422^{\circ} \mathrm{C}\). The distance between \(\mathrm{W}\) atoms in tungsten metal is 274 pm. (a) What is the atomic radius of a tungsten atom in this environment? (This radius is called the metallic radius.) (b) If you put tungsten metal under high pressure, predict what would happen to the distance between W atoms.

Consider the first ionization energy of neon and the electron affinity of fluorine. (a) Write equations, including electron configurations, for each process. (b) These two quantities have opposite signs. Which will be positive, and which will be negative? (c) Would you expect the magnitudes of these two quantities to be equal? If not, which one would you expect to be larger?

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, \(\mathrm{F}\) ?
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