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Chapter 24: Problem 25

The total number of compounds having at least one bridging oxo group among the molecules given below is \(\mathrm{N}_{2} \mathrm{O}_{3}, \mathrm{~N}_{2} \mathrm{O}_{5}, \mathrm{P}_{4} \mathrm{O}_{6}, \mathrm{P}_{4} \mathrm{O}_{7}, \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{5}, \mathrm{H}_{5} \mathrm{P}_{3} \mathrm{O}_{10}, \mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}, \mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{5}\)

Short Answer

Expert verified
5 compounds have at least one bridging oxo group.

Step by step solution

01

- Understand Bridging Oxo Groups

A bridging oxo group is an oxygen atom that connects two metal or nonmetal centers in a molecule. It is represented by an oxygen atom in the chemical structure that has bonds with more than one atom of the other elements present in the compound.
02

- Analyze Given Compounds

Examine the molecular structures of the given compounds to determine if any of them contain oxygen atoms that serve as bridges between two other atoms (usually metals or nonmetals).
03

- Identify Compounds with Bridging Oxo Groups

Determine which of the given compounds have at least one bridging oxo group. 1. \(\mathrm{N}_{2} \mathrm{O}_{3}\) does not have bridging oxo groups. 2. \(\mathrm{~N}_{2} \mathrm{O}_{5}\) contains bridging oxo groups between nitrogen atoms. 3. \(\mathrm{P}_{4}\mathrm{O}_{6}\) has bridging oxo groups connecting phosphorus atoms. 4. \(\mathrm{P}_{4} \mathrm{O}_{7}\) also contains bridging oxo groups between phosphorus atoms. 5. \(\mathrm{H}_{4} \mathrm{P}_{2}\mathrm{O}_{5}\) does not feature bridging oxo groups as oxygen atoms are bonded to a single phosphorus atom. 6. \(\mathrm{H}_{5} \mathrm{P}_{3} \mathrm{O}_{10}\) has bridging oxo groups between phosphorus atoms. 7. \(\mathrm{H}_{2}\mathrm{~S}_{2} \mathrm{O}_{3}\) contains bridging oxo groups between sulfur atoms. 8. \(\mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{5}\) also has bridging oxo groups between sulfur atoms.
04

- Count the Compounds with Bridging Oxo Groups

Upon examination, it is determined that 5 of the provided compounds have at least one bridging oxo group: \(\mathrm{~N}_{2} \mathrm{O}_{5}\), \(\mathrm{P}_{4}\mathrm{O}_{6}\), \(\mathrm{P}_{4} \mathrm{O}_{7}\), \(\mathrm{H}_{5} \mathrm{P}_{3} \mathrm{O}_{10}\), and \(\mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{5}\).

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Key Concepts

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

Chemical Structure Analysis
Understanding the composition and structure of chemical compounds is essential in the realm of chemistry. Chemical structure analysis involves a careful examination of the arrangement of atoms within a molecule, including the presence of specific features such as bridging oxo groups. This process requires a solid grasp of various types of chemical bonds and how they influence molecular structure.

In inorganic chemistry, a bridging oxo group, which involves an oxygen atom that connects two metal or nonmetal atoms, represents a key structural component that can alter a molecule's properties and reactivity. The identification of such groups entails not only recognizing the oxygen atom but also understanding its bonding to neighboring atoms. As illustrated in the exercise, molecules with oxo groups, like (mathrm{N}_2 mathrm{O}_5), contain oxygen atoms that serve as a bridge, and recognizing these is a crucial step in chemical structure analysis.
Inorganic Chemistry
Inorganic chemistry is an expansive field that studies inorganic compounds, which are not based on carbon-hydrogen bonds, unlike organic compounds. This branch of chemistry encompasses a diverse array of substances, ranging from metals and salts to oxides and complexes. Bridging oxo groups are a prevalent feature in many inorganic molecules, especially in the polyoxometalate family.

These bridging groups play a pivotal role in defining the geometry and reactivity of compounds. They can influence the stability and catalytic behaviors of inorganic substances, making them of particular interest in both theoretical studies and practical applications, such as catalysis and material science. Knowing how to identify bridging oxo groups, as highlighted in the original exercise, is an invaluable skill for any student or professional in the field of inorganic chemistry.
Molecular Geometry
The spatial arrangement of atoms in a molecule, defined as molecular geometry, is crucial for understanding a molecule's physical and chemical properties. The presence of bridging oxo groups significantly impacts molecular geometry, as they can allow for the formation of complex polymeric structures.

In the given exercise, compounds like (mathrm{P}_4 mathrm{O}_7) and (mathrm{H}_5 mathrm{P}_3 mathrm{O}_10) demonstrate this concept, as the bridging oxygen atoms transfer the phosphorus atoms from simple tetrahedra to more intricate structures. Learning to predict the shape of a molecule based on its chemical formula and the presence of specific groups is fundamental in understanding chemical reactivity and interactions, making molecular geometry a cornerstone concept in chemistry education.

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Most popular questions from this chapter

Let \(s, t, r\) be non-zero complex numbers and \(L\) be the set of solutions \(z=x+i y\) \((x, y \in \mathbb{R}, i=\sqrt{-1})\) of the equation \(s z+t \bar{z}+r=0\), where \(\bar{z}=x-i y\). Then, which of the following statement \((\mathrm{s})\) is (are) TRUE? (A) If \(L\) has exactly one element, then \(|s| \neq|t|\) (B) If \(|s|=|t|\), then \(L\) has infinitely many elements (C) The number of elements in \(L \cap\\{z:|z-1+i|=5\\}\) is at most 2 (D) If \(L\) has more than one element, then \(L\) has infinitely many elements

Let \(f:(0, \pi) \rightarrow \mathbb{R}\) be a twice differentiable function such that $$ \lim _{t \rightarrow x} \frac{f(x) \sin t-f(t) \sin x}{t-x}=\sin ^{2} x \text { for all } x \in(0, \pi) $$ If \(f\left(\frac{\pi}{6}\right)=-\frac{\pi}{12}\), then which of the following statement \((\mathrm{s})\) is (are) TRUE? (A) \(f\left(\frac{\pi}{4}\right)=\frac{\pi}{4 \sqrt{2}}\) (B) \(f(x)<\frac{x^{4}}{6}-x^{2}\) for all \(x \in(0, \pi)\) (C) There exists \(\alpha \in(0, \pi)\) such that \(f^{\prime}(\alpha)=0\) (D) \(f^{\prime \prime}\left(\frac{\pi}{2}\right)+f\left(\frac{\pi}{2}\right)=0\)

Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on \(\left[\mathrm{H}^{+}\right]\) are given in LIST-II. (Note: Degree of dissociation \((\alpha)\) of weak acid and weak base is \(<<1\); degree of hydrolysis of salt \(\left\langle<1 ;\left[\mathrm{H}^{+}\right]\right.\) represents the concentration of \(\mathrm{H}^{+}\) ions \()\) LIST-I P. \((10 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{NaOH}+20 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) acetic acid) diluted to \(60 \mathrm{~mL}\) Q. \((20 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{NaOH}+20 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) acetic acid) diluted to \(80 \mathrm{~mL}\) R. \((20 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{HCl}+20 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) ammonia solution) diluted to \(80 \mathrm{~mL}\) S. \(10 \mathrm{~mL}\) saturated solution of \(\mathrm{Ni}(\mathrm{OH})_{2}\) in equilibrium with excess solid \(\mathrm{Ni}(\mathrm{OH})_{2}\) is diluted to \(20 \mathrm{~mL}\) (solid \(\mathrm{Ni}(\mathrm{OH})_{2}\) is still present after dilution). LIST-II 1\. the value of \(\left[\mathrm{H}^{+}\right]\) does not change on dilution 2\. the value of \(\left[\mathrm{H}^{+}\right]\) changes to half of its initial value on dilution 3\. the value of \(\left[\mathrm{H}^{+}\right]\) changes to two times of its initial value on dilution 4\. the value of \(\left[\mathrm{H}^{+}\right]\) changes to \(\frac{1}{\sqrt{2}}\) times of its initial value on dilution 5\. the value of \(\left[\mathrm{H}^{+}\right]\) changes to \(\sqrt{2}\) times of its initial value on dilution

Consider an electrochemical cell: \(\mathrm{A}(\mathrm{s})\left|\mathrm{A}^{\mathrm{n}+}(\mathrm{aq}, 2 \mathrm{M}) \| \mathrm{B}^{2 \mathrm{n}+}(\mathrm{aq}, 1 \mathrm{M})\right| \mathrm{B}(\mathrm{s})\). The value of \(\Delta H^{\ominus}\) for the cell reaction is twice that of \(\Delta G^{\theta}\) at \(300 \mathrm{~K}\). If the emf of the cell is zero, the \(\Delta S^{\theta}\) (in \(\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}\) ) of the cell reaction per mole of \(\mathrm{B}\) formed at \(300 \mathrm{~K}\) is (Given: \(\ln (2)=0.7, R\) (universal gas constant) \(=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \cdot H, S\) and \(G\) are enthalpy, entropy and Gibbs energy, respectively.)

A planet of mass \(M\), has two natural satellites with masses \(m_{1}\) and \(m_{2}\). The radii of their circular orbits are \(R_{1}\) and \(R_{2}\) respectively. Ignore the gravitational force between the satellites. Define \(v_{1}, L_{1}, K_{1}\) and \(T_{1}\) to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1 ; and \(v_{2}, L_{2}, K_{2}\) and \(T_{2}\) to be the corresponding quantities of satellite 2. Given \(m_{1} / m_{2}=2\) and \(R_{1} / R_{2}=1 / 4\), match the ratios in List-I to the numbers in List-II. LIST-I P. \(\frac{v_{1}}{v_{2}}\) Q. \(\frac{L_{1}}{L_{2}}\) \(\mathbf{R} \quad \frac{K_{1}}{K_{2}}\) S. \(\frac{T_{1}}{T_{2}}\) LIST-II 1\. \(\frac{1}{8}\) 2\. 1 3\. 2 4\. 8
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