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Chapter 14: Problem 112

Two substances with the empirical formula HNO are hyponitrous acid \((\mathscr{A}=62.04 \mathrm{~g} / \mathrm{mol})\) and nitroxyl \((\mathscr{A}=31.02 \mathrm{~g} / \mathrm{mol}) .\) (a) What is the molecular formula of each species? (b) For each species, draw the Lewis structure having the lowest formal charges. (Hint: Hyponitrous acid has an \(\mathrm{N}=\mathrm{N}\) bond. \()\) (c) Predict the shape around the \(\mathrm{N}\) atoms of each species. (d) When hyponitrous acid loses two protons, it forms the hyponitrite ion. Draw cis and trans forms of this ion.

Short Answer

Expert verified
(a) Molecular formulas: Hyponitrous acid: \(\mathrm{H_2N_2O_2}\), Nitroxyl: \(\mathrm{HNO}\). (b) Lewis structures: \(\mathrm{H_2N_2O_2}\): \(\mathrm{HON=NOH}\), \(\mathrm{HNO}\): \(\mathrm{H-N=O}\). (c) Shapes: Hyponitrous acid: trigonal planar; Nitroxyl: bent. (d) Hyponitrite ion: cis and trans forms: \(\text{^-ON=NO^-}\) and \(\text{^-ON=NO^-}\).

Step by step solution

01

Determine the empirical formula mass (part a)

The empirical formula is HNO. Calculate the empirical formula mass by summing the atomic masses of hydrogen, nitrogen, and oxygen: \(1.01 \, \text{g/mol (H)} + 14.01 \, \text{g/mol (N)} + 16.00 \, \text{g/mol (O)} = 31.02 \, \text{g/mol}\)
02

Identify the molecular formula of hyponitrous acid (part a)

Given the molecular mass of hyponitrous acid is 62.04 g/mol and the empirical formula mass is 31.02 g/mol, the ratio is: \(\frac{62.04}{31.02} = 2\)Thus, the molecular formula of hyponitrous acid is \( (\mathrm{HNO})_2 \) or \( \mathrm{H_2N_2O_2} \).
03

Identify the molecular formula of nitroxyl (part a)

Given the molecular mass of nitroxyl is 31.02 g/mol and the empirical formula mass is also 31.02 g/mol, the ratio is: \(\frac{31.02}{31.02} = 1\)Thus, the molecular formula of nitroxyl is \( \mathrm{HNO} \).
04

Draw the Lewis structure of hyponitrous acid (part b)

The hint states that hyponitrous acid has an \(\mathrm{N} = \mathrm{N}\) bond. The Lewis structure is: \( \mathrm{H}\mathrm{O}-\mathrm{N}=\mathrm{N}-\mathrm{O}\mathrm{H} \)Each nitrogen has a lone pair and each oxygen has two lone pairs. Formal charges are minimized this way.
05

Draw the Lewis structure of nitroxyl (part b)

The Lewis structure of nitroxyl can be drawn as:\(\mathrm{H}-\mathrm{N}=\mathrm{O} \)The formal charges on hydrogen, nitrogen, and oxygen are zero when minimizing formal charge. The nitrogen has one lone pair and oxygen has two lone pairs.
06

Predict the shape around the nitrogen atoms in hyponitrous acid (part c)

For hyponitrous acid with an \( \mathrm{N} = \mathrm{N} \) bond and single bonds to oxygen and hydrogen:Each nitrogen is sp2 hybridized, leading to a trigonal planar shape around each nitrogen atom.
07

Predict the shape around the nitrogen atom in nitroxyl (part c)

For nitroxyl with an \( \mathrm{N} = \mathrm{O} \) bond and a hydrogen attachment:The nitrogen in nitroxyl is sp2 hybridized, leading to a bent or V-shaped geometry.
08

Draw cis and trans forms of the hyponitrite ion (part d)

When hyponitrous acid loses two protons, it forms the hyponitrite ion \(\mathrm{N_2O_2^{2-}}\), which has two potential geometric isomers:- cis: \(\mathrm{^-\text{O}N=N\text{O}^-}\)The two oxygen atoms on the same side of the \( \mathrm{N=N} \) bond. - trans:\(\mathrm{^-\text{O}N=N\text{O}^-}\)The two oxygen atoms on opposite sides of the \( \mathrm{N=N} \) bond.

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Key Concepts

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

Empirical Formula
The empirical formula represents the simplest whole-number ratio of the elements in a compound. For instance, if we have a substance with the empirical formula HNO, this formula tells us that for every one hydrogen (H) atom, there is one nitrogen (N) atom and one oxygen (O) atom. It's crucial to calculate the empirical formula mass, which adds up the atomic masses of the constituent elements. In our example, that calculation is: 1.01 g/mol (H) + 14.01 g/mol (N) + 16.00 g/mol (O) = 31.02 g/mol. This basic formula helps us in understanding the actual molecular composition when we compare it to the molecular mass.
Molecular Formula
The molecular formula shows the actual number of atoms of each element in a molecule. To find it, we need the molecular mass and the empirical formula mass. For hyponitrous acid with a molecular mass of 62.04 g/mol and the empirical formula mass of HNO being 31.02 g/mol, the ratio is \[ \frac{62.04}{31.02} = 2 \]. Hence, the molecular formula of hyponitrous acid is \[ (\text{HNO})_2 \] or \[ \text{H}_2\text{N}_2\text{O}_2 \]. For nitroxyl, with both molecular and empirical formula masses at 31.02 g/mol, the molecular formula remains HNO.
Lewis Structure
The Lewis structure represents the valence electrons of atoms within a molecule, typically visualized as dots around the atomic symbols. For hyponitrous acid, given the \[\text{N} = \text{N} \] bond, its Lewis structure is: \[ \text{H}-\text{O}-\text{N}=\text{N}-\text{O}-\text{H} \]. Both nitrogen atoms have lone pairs, ensuring minimal formal charges. For nitroxyl, the Lewis structure is: \[ \text{H}-\text{N}=\text{O} \] with one lone pair on nitrogen and two lone pairs on oxygen. Lewis structures help us visualize bonding interactions and lone pairs.
Formal Charge
Understanding formal charge helps us determine the most stable Lewis structure. The formal charge is calculated using the formula: \[ \text{Formal Charge} = \text{Valence Electrons} - (\text{Non-bonding Electrons} + \frac{\text{Bonding Electrons}}{2}) \]. In hyponitrous acid's structure, the formal charges on nitrogen and oxygen are minimized to zero, which indicates stability. Similarly, in nitroxyl, careful placement of lone pairs and bonds yields formal charges of zero for all atoms, reinforcing it as the most stable configuration.
Molecular Geometry
Molecular geometry describes the 3D shape of a molecule. For hyponitrous acid, each nitrogen, sp2 hybridized, displays a trigonal planar shape due to the \[\text{N}=\text{N} \] bond and attachments to oxygen and hydrogen. In nitroxyl, the nitrogen is also sp2 hybridized, but the shape is bent or V-shaped because of the presence of a lone pair. Understanding molecular geometry helps predict molecular behavior and interaction.
Cis-Trans Isomerism
Cis-trans isomerism occurs when molecules have the same formula but different spatial arrangements around a double bond. For the hyponitrite ion \[\text{N}_2\text{O}_2^{2-} \], which forms after hyponitrous acid loses two protons, there are two isomers:
  • Cis: The two oxygen atoms on the same side of the \[ \text{N}=\text{N} \] bond: \[ ^-\text{O}-\text{N}=\text{N}-\text{O}^- \].
  • Trans: The two oxygen atoms on opposite sides of the \[ \text{N}=\text{N} \] bond: \[ ^-\text{O}-\text{N}=\text{N}-\text{O}^- \].
These different arrangements can significantly affect the chemical properties and behaviors of the molecules.

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Most popular questions from this chapter

Indium (In) reacts with \(\mathrm{HCl}\) to form a diamagnetic solid with the formula \(\ln \mathrm{Cl}_{2}\). (a) Write condensed electron configurations for \(\mathrm{In}, \mathrm{In}^{+}, \mathrm{In}^{2+}\) and \(\mathrm{In}^{3+}\) (b) Which of these species is (are) diamagnetic and which paramagnetic? (c) What is the apparent oxidation state of In in \(\mathrm{InCl}_{2}\) ? (d) Given your answers to parts (b) and (c), explain how \(\mathrm{InCl}_{2}\) can be diamagnetic.

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Rank the following hydrides in order of increasing acid strength: \(\mathrm{H}_{2} \mathrm{~S}, \mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2} \mathrm{Te} .\)

The bond angles in the nitrite ion, nitrogen dioxide, and the nitronium ion \(\left(\mathrm{NO}_{2}^{+}\right)\) are \(115^{\circ}, 134^{\circ},\) and \(180^{\circ},\) respectively. Explain these values using Lewis structures and VSEPR theory.

Give the name and symbol or formula of a Group \(3 \mathrm{~A}(13)\) element or compound that fits each description or use: (a) Component of heat-resistant (Pyrex-type) glass (b) Largest temperature range for liquid state of an element (c) Elemental substance with three-center, two-electron bonds (d) Metal protected from oxidation by adherent oxide coat (e) Toxic metal that lies between two other toxic metals.
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