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Chapter 8: Problem 98

The \(\mathrm{Ti}^{2+}\) ion is isoelectronic with the Ca atom. (a) Write the electron configurations of \(\mathrm{Ti}^{2+}\) and Ca. (b) Calculate the number of unpaired electrons for Ca and for \(\mathrm{Ti}^{2+}\). (c) What charge would Ti have to be isoelectronic with \(\mathrm{Ca}^{2+}\) ?

Short Answer

Expert verified
(a) Electron configurations: Ti²⁺: \([Ar] 3d^2\), Ca: \([Ar] 4s^2\). (b) Unpaired electrons: Ca has 0, Ti²⁺ has 2. (c) Ti must have a charge of 4+ (Ti⁴⁺) to be isoelectronic with Ca²⁺.

Step by step solution

01

Determine electron configurations of Ti²⁺ and Ca

First, let's find the electron configurations for Ti and Ca, after this we will derive Ti²⁺ configuration from the Ti atom. Titanium (Ti) has an atomic number of 22, and calcium (Ca) has an atomic number of 20. Their electron configurations are as follows: Ti: \([Ar] 4s^2 3d^2\) Ca: \([Ar] 4s^2\) When titanium loses 2 electrons to form the Ti²⁺ ion, its electron configuration becomes: Ti²⁺: \([Ar] 3d^2\) Now we have the electron configurations of Ti²⁺ and Ca.
02

Calculate the number of unpaired electrons

Unpaired electrons are the electrons that do not have a partner with the opposite spin in the same orbital. For Ca (\([Ar] 4s^2\)), there is 1 orbital (4s) with 2 electrons. Both electrons have paired spins, so there are 0 unpaired electrons. For Ti²⁺ (\([Ar] 3d^2\)), there are 2 electrons in the 3d orbital. These electrons will occupy separate orbitals with the same spin direction (Hund's rule), so there are 2 unpaired electrons. To summarize, Ca has 0 unpaired electrons, and Ti²⁺ has 2 unpaired electrons.
03

Determine the charge of Ti to be isoelectronic with Ca²⁺

Isoelectronic means having the same number of electrons or the same electronic structure. Calcium (Ca) has 20 electrons. When it loses 2 electrons (forming Ca²⁺), it will have 18 electrons. To be isoelectronic with Ca²⁺, titanium (Ti) must also have 18 electrons. Since titanium (Ti) has an atomic number of 22, it must lose 4 electrons to have 18 electrons. Therefore, Ti must have a charge of 4+ (Ti⁴⁺) to be isoelectronic with Ca²⁺.

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Most popular questions from this chapter

(a) Draw the dominant Lewis structure for the phosphorus trifluoride molecule, \(\mathrm{PF}_{3}\). (b) Determine the oxidation numbers of the \(\mathrm{P}\) and \(\mathrm{F}\) atoms. \((\mathbf{c})\) Determine the formal charges of the \(\mathrm{P}\) and \(\mathrm{F}\) atoms.

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