Ch.7 - Periodic Properties of the Elements

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.7 - Periodic Properties of the Elements

Problem 31b

Chapter 7, Problem 31b

Consider the isoelectronic ions F- and Na+. (b) Using Equation 7.1 and assuming that core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant, S, calculate Zeff for the 2p electrons in both ions.

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Identify the isoelectronic ions: F^- and Na^+ both have the same number of electrons, which is 10.

Determine the atomic numbers: Fluorine (F) has an atomic number of 9, and Sodium (Na) has an atomic number of 11.

Use the formula for effective nuclear charge, Z_{eff} = Z - S, where Z is the atomic number and S is the screening constant.

Calculate the screening constant, S, for each ion. Since core electrons contribute 1.00 and valence electrons contribute 0.00, identify the core and valence electrons for each ion. For both ions, the core electrons are the 1s^2 electrons, contributing 2.00 to S.

Substitute the values into the Z_{eff} formula for each ion: For F^-, Z_{eff} = 9 - 2.00; for Na^+, Z_{eff} = 11 - 2.00.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isoelectronic Species

Isoelectronic species are atoms or ions that have the same number of electrons and, therefore, the same electronic configuration. In this case, F- and Na+ both have 10 electrons, making them isoelectronic. Understanding this concept is crucial for comparing their effective nuclear charges (Zeff) since they experience similar electron-electron interactions despite differing nuclear charges.

Effective Nuclear Charge (Zeff)

Effective nuclear charge (Zeff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge minus the shielding effect of other electrons. Calculating Zeff helps in understanding how strongly the nucleus attracts its electrons, which is essential for predicting chemical behavior and properties of ions like F- and Na+.

Screening Constant (S)

The screening constant (S) quantifies the extent to which inner electrons shield outer electrons from the full effect of the nuclear charge. In the context of the question, core electrons contribute a value of 1.00 to S, while valence electrons contribute 0.00. This distinction is important for accurately calculating Zeff for the 2p electrons in the ions, as it directly influences the perceived nuclear charge experienced by these electrons.

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Related Practice

Textbook Question

Which neutral atom is isoelectronic with each of the following ions? Ga³⁺, Zr⁴⁺, Mn⁷⁺, I⁻, Pb²⁺.

Consider S, Cl, and K and their most common ions. (a) List the atoms in order of increasing size.

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Textbook Question

For each ion, identify the neutral atom that is isoelectronic with it.

a. Cl−

b. Sc3+

c. Fe2+

d. Zn2+

e.Sn4+

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Textbook Question

For each set of atoms and ions, pick the smallest one.

a. I, I+, I−

b. Be2+, Ca2+, Mg2+

c. Fe, Fe2+, Fe3+

Textbook Question

Consider S, Cl, and K and their most common ions. (b) List the ions in order of increasing size. (c) Explain any differences in the orders of the atomic and ionic sizes.

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