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Chapter 7: Problem 86

The following observations are made about two hypothetical elements \(\mathrm{A}\) and \(\mathrm{B}:\) The \(\mathrm{A}-\mathrm{A}\) and \(\mathrm{B}-\mathrm{B}\) bond lengths in the elemental forms of \(\mathrm{A}\) and \(\mathrm{B}\) are 236 and \(194 \mathrm{pm}\), respectively. A and \(B\) react to form the binary compound \(A B_{2}\), which has a linear structure (that is \(\left.\angle \mathrm{B}-\mathrm{A}-\mathrm{B}=180^{\circ}\right) .\) Based on these statements, predict the separation between the two B nuclei in a molecule of \(\mathrm{AB}_{2}\).

Short Answer

Expert verified
The separation between the two B nuclei in a molecule of \(\mathrm{AB_{2}}\) is 430 pm.

Step by step solution

01

Understand the structure of AB2 molecule

In the given molecule AB2, element A is at the center and elements B are bonded to it linearly. This means the bond angle between \(\mathrm{B}-\mathrm{A}-\mathrm{B}\) is given as \(180^{\circ}\). Since the molecule has a linear structure, we can use the geometry of the molecule to predict the separation between the two B nuclei.
02

Use the given bond lengths

We are given the bond lengths in the elemental forms of A and B, which are 236 pm and 194 pm, respectively. We can estimate the bond length of \(\mathrm{A}-\mathrm{B}\) in the AB2 compound using these bond lengths. Since A and B are hypothetical elements, we can assume that their bond length will be the average of the A-A and B-B bond lengths: \[A-B \ bond \ length = \frac{A-A \ bond \ length + B-B \ bond \ length}{2}\]
03

Calculate the A-B bond length

Now, we will substitute the given bond lengths and calculate the A-B bond length: \[A-B \ bond \ length = \frac{236 \ \mathrm{pm} + 194 \ \mathrm{pm}}{2}\] \[A-B \ bond \ length = \frac{430 \ \mathrm{pm}}{2} = 215 \ \mathrm{pm}\]
04

Calculate the separation between the two B nuclei

In the AB2 molecule, two B nuclei are bonded with A at a linear angle. Since the bond angle \(\mathrm{B}-\mathrm{A}-\mathrm{B}\) is \(180^{\circ}\), the \(\mathrm{B}-\mathrm{A}\) and \(\mathrm{A}-\mathrm{B}\) bonds are in a straight line. As a result, the distance between the two B nuclei is the sum of the two A-B bond lengths: \[B-B \ separation = 2 \times (A-B \ bond \ length)\]
05

Calculate the B-B separation

We'll now insert the previously calculated A-B bond length and compute the B-B separation: \[B-B \ separation = 2 \times (215 \ \mathrm{pm}) = 430 \ \mathrm{pm}\] So, the separation between the two B nuclei in a molecule of \(\mathrm{AB_{2}}\) is 430 pm.

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Most popular questions from this chapter

Identify \(a+2\) cation that has the following ground state electron configurations: (a) \([\mathrm{Ne}]\) (b) \([\mathrm{Ar}] 3 d^{9}\) (c) \([\mathrm{Xe}] 4 f^{14} 5 d^{10} 6 s^{2}\)

Write an equation for the first electron affinity of helium. Would you predict a positive or a negative energy value for this process? Is it possible to directly measure the first electron affinity of helium?

Use electron configurations to explain the following observations: (a) The first ionization energy of phosphorus is greater than that of sulfur. (b) The electron affinity of nitrogen is lower (less negative) than those of both carbon and oxygen. (c) The second ionization energy of oxygen is greater than the first ionization energy of fluorine. (d) The third ionization energy of manganese is greater than those of both chromium and iron.

(a) One of the alkali metals reacts with oxygen to form a solid white substance. When this substance is dissolved in water, the solution gives a positive test for hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\). When the solution is tested in a burner flame, a lilac-purple flame is produced. What is the likely identity of the metal? (b) Write a balanced chemical equation for the reaction of the white substance with water.

Write the electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Ti}^{2+},(\mathbf{b})\) (d) \(\mathrm{PO}^{2-}\), (f) \(\mathrm{V}^{3+}\) \(\mathrm{Br}^{-}\) (c) \(\mathrm{Mg}^{2+}\) (e) \(\mathrm{Pt}^{2+}\)
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