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Chapter 7: Problem 43

Based on their positions in the periodic table, predict which atom of the following pairs will have the smaller first ionization energy: (a) \(\mathrm{Br}, \mathrm{Kr} ; \mathbf{( b )} \mathrm{C}, \mathrm{Ca} ;(\mathbf{c}) \mathrm{Li}, \mathrm{Rb} ;\); (d) \(\mathrm{Pb}, \mathrm{Si} ;\) (e) \(\mathrm{Al}, \mathrm{B}\).

Short Answer

Expert verified
The elements with smaller first ionization energies in each pair are: (a) Br, (b) Ca, (c) Rb, (d) Pb, and (e) Al.

Step by step solution

01

(a) Comparing Br and Kr

Br (Bromine) is in Group 17 (7A) and Period 4, while Kr (Krypton) is in Group 18 (8A) and also Period 4. Since they are in the same period and ionization energy generally increases from left to right within a period, Br will have the smaller first ionization energy compared to Kr.
02

(b) Comparing C and Ca

C (Carbon) is in Group 14 (4A) and Period 2, while Ca (Calcium) is in Group 2 (2A) and Period 4. The ionization energy decreases from top to bottom within a group, so Ca (being lower in the periodic table) will have the smaller first ionization energy compared to C.
03

(c) Comparing Li and Rb

Li (Lithium) is in Group 1 (1A) and Period 2, while Rb (Rubidium) is in Group 1 (1A) and Period 5. Since they are in the same group, we will apply the trend that ionization energy decreases from top to bottom and determine that Rb will have the smaller first ionization energy compared to Li.
04

(d) Comparing Pb and Si

Pb (Lead) is in Group 14 (4A) and Period 6, while Si (Silicon) is in Group 14 (4A) and Period 3. As they are in the same group, ionization energy decreases from top to bottom within a group, so Pb will have the smaller first ionization energy compared to Si.
05

(e) Comparing Al and B

Al (Aluminum) is in Group 13 (3A) and Period 3, while B (Boron) is in Group 13 (3A) and Period 2. Since they are in the same group, we will apply the trend that ionization energy decreases from top to bottom within a group, thereby concluding that Al will have the smaller first ionization energy compared to B.

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Key Concepts

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

Periodic Table
The periodic table is a powerful tool in chemistry, organizing all known elements in a tabular format that reveals various trends and relationships. Elements are arranged by increasing atomic number, meaning each element has one more proton in its nucleus than the previous element. This organization allows for the prediction of chemical properties and reactivity patterns.

Key elements of the periodic table include:
  • Groups: These are the vertical columns that run from top to bottom. Elements in the same group have similar electron configurations and chemical properties.
  • Periods: These are the horizontal rows. As you move across a period, properties of elements change predictably.
Understanding the layout of the periodic table and the group and period information can help us predict various properties of elements such as ionization energy.
Ionization Energy Trends
Ionization energy is the amount of energy required to remove an electron from an atom in its gaseous state. Understanding ionization energy trends helps in predicting the reactivity of elements. The general trend is that ionization energy increases across a period from left to right and decreases down a group.

Several factors influence these trends:
  • Nuclear Charge: As the positive charge of the nucleus (from protons) increases, it holds electrons more tightly, requiring more energy for removal.
  • Electron Shielding: Inner electrons can block the attraction between the nucleus and the outermost electrons, which can lower ionization energy.
  • Atomic Radius: Larger atoms tend to have lower ionization energies because the valence electrons are farther from the nucleus and are less strongly attracted.
These factors work together to create the observable trends in ionization energy across the periodic table.
Group and Period Trends
Trends within groups and periods in the periodic table critically affect elements' chemical and physical properties, including ionization energy. In a group, as you go from top to bottom, the principal quantum number increases, meaning that there are more electron shells, and hence, the atomic size increases.

When discussing period trends:
  • Within Groups: Ionization energy usually decreases down a group because the increase in electron shells outweighs other factors, causing the electrons to be further from the nucleus.
  • Across Periods: Ionization energy tends to increase across a period since electrons are added to the same energy level, and the increased nuclear charge increases the attraction between the nucleus and electron.
Having a firm grasp on these trends allows for better predictions about the properties and behaviors of different elements in various chemical contexts.

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Most popular questions from this chapter

(a) Which ion is smaller, \(\mathrm{Co}^{3+}\) or \(\mathrm{Co}^{4+} ?\) (b) In a lithium-ion battery that is discharging to power a device, for every \(\mathrm{Li}^{+}\) that inserts into the lithium cobalt oxide electrode, a \(\mathrm{Co}^{4+}\) ion must be reduced to a \(\mathrm{Co}^{3+}\) ion to balance charge. Using the CRC Handbook of Chemistry and Physics or other standard reference, find the ionic radii of \(\mathrm{Li}^{+}, \mathrm{Co}^{3+},\) and \(\mathrm{Co}^{4+}\). Order these ions from smallest to largest. (c) Will the lithium cobalt oxide cathode expand or contract as lithium ions are inserted? (d) Lithium is not nearly as abundant as sodium. If sodium ion batteries were developed that function in the same manner as lithium ion batteries, do you think "sodium cobalt oxide" would still work as the electrode material? Explain. (e) If you don't think cobalt would work as the redox-active partner ion in the sodium version of the electrode, suggest an alternative metal ion and explain your reasoning.

In the chemical process called electron transfer, an electron is transferred from one atom or molecule to another. (We will talk about electron transfer extensively in Chapter 20.) A simple electron transfer reaction is $$ \mathrm{A}(g)+\mathrm{A}(g) \longrightarrow \mathrm{A}^{+}(g)+\mathrm{A}^{-}(g) $$ In terms of the ionization energy and electron affinity of atom A, what is the energy change for this reaction? For a representative nonmetal such as chlorine, is this process exothermic? For a representative metal such as sodium, is this process exothermic?

Write a balanced equation for the reaction that occurs in each of the following cases: (a) White phorphrous, \(\mathrm{P}_{4}(\mathrm{~s})\), reacts with chlorine gas. (b) Sodium metal reacts with water. (c) Hydrogen bromide gas reacts with chlorine gas. (d) Aluminum trichloride reacts with aqueous sodium hydroxide.

Detailed calculations show that the value of \(Z_{\text {eff }}\) for the outermost electrons in \(\mathrm{Si}\) and \(\mathrm{Cl}\) atoms is \(4.29+\) and \(6.12+,\) respectively. (a) What value do you estimate for \(Z_{\text {eff }}\) experienced by the outermost electron in both Si and Cl by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant? (b) What values do you estimate for \(Z_{\text {eff }}\) using Slater's rules? (c) Which approach gives a more accurate estimate of \(Z_{\text {eff }} ?\) (d) Which method of approximation more accurately accounts for the steady increase in \(Z_{\text {eff }}\) that occurs upon moving left to right across a period? (e) Predict \(Z_{\text {eff }}\) for a valence electron in P, phosphorus, based on the calculations for \(\mathrm{Si}\) and \(\mathrm{Cl}\).

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Potassium metal is exposed to 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 reacts with molten sulfur.
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