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Three elements, \(X, Y,\) and \(Z,\) have the electron configurations: \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}\) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}\) The first ionization energies are known to be (not in any order \(): 0.4188 \mathrm{MJ} / \mathrm{mol}, 0.7377 \mathrm{MJ} / \mathrm{mol},\) and \(1.5205 \mathrm{MJ} / \mathrm{mol}\). The covalent radii of these elements are (not in any order): \(0.094 \mathrm{nm}, 0.136 \mathrm{nm},\) and \(0.202 \mathrm{nm}\) (a) Identify each element and match the appropriate values of ionization energy and atomic radius to each configuration. (b) Which of \(X, Y,\) and \(Z\) has the smallest AVEE? (c) Which is(are) paramagnetic?

Short Answer

Expert verified
(a) X: Mg, 0.7377 MJ/mol, 0.136 nm; Y: Ar, 1.5205 MJ/mol, 0.094 nm; Z: K, 0.4188 MJ/mol, 0.202 nm. (b) Z (K) has the smallest AVEE. (c) Z (K) is paramagnetic.

Step by step solution

01

Identify the Elements by Configuration

First, let's identify each element based on the provided electron configurations:- The configuration \(1s^2 2s^2 2p^6 3s^2 3p^6\) corresponds to Argon (Ar), which is a noble gas with a filled outer shell.- \(1s^2 2s^2 2p^6 3s^2\) corresponds to Magnesium (Mg), with its outermost electrons in the 3s orbital.- \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\) corresponds to Potassium (K), with its outer electron in the 4s orbital.
02

Match Ionization Energies to Elements

Ionization energy is related to the energy required to remove the outermost electron. Usually, noble gases (like Argon) have the highest ionization energies because they have complete outer shells, making them stable. Thus, \(1.5205\ \mathrm{MJ/mol}\) corresponds to Argon. Magnesium, being closer to a full outer shell than Potassium, has a moderately high ionization energy, \(0.7377\ \mathrm{MJ/mol}\), leaving Potassium with the lowest ionization energy, \(0.4188\ \mathrm{MJ/mol}\).
03

Match Covalent Radii to Elements

Covalent radius increases with increasing atomic size. Potassium, having the largest size, matches the largest covalent radius, \(0.202\ \mathrm{nm}\). Magnesium is smaller, with a covalent radius of \(0.136\ \mathrm{nm}\), and Argon, being a noble gas at the end of its period, has the smallest covalent radius, \(0.094\ \mathrm{nm}\).
04

Determine Which Element Has the Smallest AVEE

AVEE (Average Valence Electron Energy) is typically smaller for metals than for nonmetals because metals hold their valence electrons less tightly. Potassium should have the smallest AVEE due to its low ionization energy and larger atomic size, indicating its valence electron is less tightly bound.
05

Determine Paramagnetic Elements

An element is paramagnetic if it has unpaired electrons. Potassium (configuration \(4s^1\)) has an unpaired electron and is thus paramagnetic. Argon and Magnesium, with no unpaired electrons in their outer shells, are diamagnetic.

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Key Concepts

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

Ionization Energy
Ionization energy is the energy required to remove an electron from an atom in the gaseous state. It is a key factor in understanding the reactivity of elements. In general, ionization energy increases across a period on the periodic table because the valence electrons are closer to the nucleus and more tightly bound. Conversely, it decreases down a group as the outer electrons are further from the nucleus, making them easier to remove.

For example, noble gases have high ionization energies due to their stable, full valence shells. This is why Argon, with the electron configuration of a noble gas, displays the highest ionization energy among the three elements in the exercise. Potassium, with an easily removable outer electron in the 4s orbital, has the lowest ionization energy, making it relatively more reactive compared to Magnesium or Argon.

Remember, ionization energy can provide useful insights into the chemical properties of an element, including its tendency to gain or lose electrons during chemical reactions.
Covalent Radius
The covalent radius of an atom refers to the size measure of an atom that forms part of a single covalent bond. It's essentially the part of the atom that interacts when forming a molecule. The covalent radius can hint at how atoms bond and interact with other atoms.

As you move down a group in the periodic table, the covalent radius increases. This is because new electron shells are added as we go down, increasing the atomic size and thereby the covalent radius. For instance, Potassium, with more electron shells, has a larger covalent radius compared to Magnesium or Argon.
  • Potassium = 0.202 nm
  • Magnesium = 0.136 nm
  • Argon = 0.094 nm

These differences in size can affect how atoms form chemical bonds. A larger covalent radius usually suggests that the valence electrons are further from the nucleus, which could influence the element's reactivity and bonding characteristics.
Noble Gases
Noble gases are elements found in Group 18 of the periodic table. These elements, like Argon, have completely filled outer electron shells, which gives them remarkable stability. This stable configuration makes them largely non-reactive or "inert."

Argon's electron configuration ( 1s^2 2s^2 2p^6 3s^2 3p^6 ) exemplifies why noble gases are so stable—they have eight electrons in their outer shell. This full valence shell satisfies what is known as the "octet rule," which states that atoms tend to be more stable when they have eight electrons in their valence shell.
  • High ionization energies due to stable configurations
  • Low reactivity compared to other elements
  • Used in lighting and as inert environments for chemical reactions

Understanding the behavior and properties of noble gases is crucial for comprehending why elements like Argon behave the way they do in chemical and physical contexts.
Paramagnetism
Paramagnetism is the tendency of a chemical species to be attracted to a magnetic field, which is a result of unpaired electrons in its electron configuration. When an atom has unpaired electrons, these electrons can align parallel to an external magnetic field, causing the substance to be attracted to it.

Among the given elements, Potassium is paramagnetic because it has an unpaired electron in its 4s orbital. This single unpaired electron makes Potassium paramagnetic, allowing it to respond to magnetic fields. In contrast, Argon and Magnesium have all their electrons paired, making them diamagnetic and not influenced by magnetic fields.
  • Potassium: paramagnetic due to unpaired electron (4s^1)
  • Magnesium and Argon: diamagnetic (all electrons paired)

Recognizing whether an element or compound is paramagnetic or diamagnetic is important for predicting and explaining its reactions and interactions with other substances and in various applied technologies.

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Most popular questions from this chapter

Some elements, such as tin and lead, have more than one common ion. Use the electron configurations to predict the most likely ions of \(\mathrm{Sn}\) and \(\mathrm{Pb}\).

Determine the number of orbitals in the \(n=3, n=4\), and \(n=5\) shells.

Which of the following is the correct electron configuration for the \(\mathrm{P}^{3-}\) ion? (a) [Ne] (b) \([\mathrm{Ne}] 3 \mathrm{~s}^{2}\) (c) \([\mathrm{Ne}] 3 s^{2} 3 p^{3}\) (d) \([\mathrm{Ne}] 3 s^{2} 3 p^{6}\)

Relate to the following data. An atom with an equal number of spin-up and spindown electrons is said to be diamagnetic because the atom is repelled by a magnetic field. In this case we say that all of the electrons are "paired." If this is not the case - if there are one or more unpaired electrons on an atom - the atom is attracted to a magnetic field, and it is said to be paramagnetic. The strength of the attraction is an experimentally measurable quantity known as the magnetic moment. The magnitude of the \(m a g-\) netic moment (measured in magnetons) is related to (but not proportional to) the number of unpaired electrons present. In other words, the larger the number of unpaired electrons, the larger the magnetic moment. Here are some experimental data collected by an investigator of this phenomenon. $$ \begin{array}{llc} {3}{c} {\text { Magnetic Moments of Several Elements }} \\ \hline & & \\ \text { Element } & \text { Type } & \begin{array}{c} \text { Magnetic Moments } \\ \text { (magnetons) } \end{array} \\ \hline \mathrm{H} & \text { Paramagnetic } & 1.7 \\ \mathrm{He} & \text { Diamagnetic } & 0 \\ \mathrm{~B} & \text { Paramagnetic } & 1.7 \\ \mathrm{C} & \text { Paramagnetic } & 2.8 \\ \mathrm{~N} & \text { Paramagnetic } & 3.9 \\ \mathrm{O} & \text { Paramagnetic } & 2.8 \\ \mathrm{Ne} & \text { Diamagnetic } & 0 \\ \hline \end{array} $$ An ion, \(X^{2+}\), is known to be from the first transition metal series. The ion is paramagnetic, with four unpaired electrons. What two possible elements could \(X\) be?

Consider the following ions/atoms: \(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Ne}, \mathrm{Na}^{+}\), and \(\mathrm{Mg}^{2+}\). Arrange them in order of increasing ionization energy. Also arrange them in order of increasing radius. Now consider the following atoms: \(\mathrm{O}, \mathrm{F}, \mathrm{Ne},\) Na, Mg. Arrange them in order of increasing ionization energy. Also arrange them in order of increasing radius.

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