Under special conditions, sulfur reacts with anhydrous...

Under special conditions, sulfur reacts with anhydrous liquid ammonia to form a binary compound of sulfur and nitrogen. The compound is found to consist of $69.6 \% \mathrm{~S}$ and $30.4 \%$ N. Measurements of its molecular mass yield a value of $184.3 \mathrm{~g} \mathrm{~mol}^{-1}$. The compound occasionally detonates on being struck or when heated rapidly. The sulfur and nitrogen atoms of the molecule are joined in a ring. All the bonds in the ring are of the same length. (a) Calculate the empirical and molecular formulas for the substance. (b) Write Lewis structures for the molecule, based on the information you are given. (Hint: You should find a relatively small number of dominant Lewis structures.) (c) Predict the bond distances between the atoms in the ring. (Note: The $\mathrm{S}-\mathrm{S}$ distance in the $\mathrm{S}_{8}$ ring is $2.05 \AA$.) (d) The enthalpy of formation of the compound is estimated to be $480 \mathrm{~kJ} \mathrm{~mol}^{-1}$. $\Delta H_{f}^{\circ}$ of $S(g)$ is $222.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Estimate the average bond enthalpy in the compound.

Key Concepts

Average Bond Enthalpy Determination

Average bond enthalpy represents the energy required to break a bond and is calculated using thermodynamic data, such as the enthalpy of formation, in relation to the number of bonds present in the molecule. This concept allows estimation of bond strength and stability by distributing the total formation energy over the individual bonds.

Resonance and Bond Delocalization

Resonance describes the situation where a single Lewis structure cannot adequately represent the electron distribution within a molecule, resulting in multiple valid structures. In molecules where all bonds in a ring are of equal length, the electrons are delocalized over the entire structure, which is a manifestation of resonance stabilization.

Bond Length Prediction

Bond lengths in a molecule are influenced by factors such as bond order and electron delocalization. When bonds in a ring are equivalent due to resonance, the bond distances tend to be intermediate between typical single and double bond lengths, highlighting the concept that delocalization leads to uniformity in bond lengths.

Empirical and Molecular Formulas

The empirical formula represents the simplest integer ratio of the elements in a compound, while the molecular formula indicates the actual number of atoms present in one molecule. Determining the molecular formula requires comparing the empirical formula mass with the experimentally determined molar mass of the compound.

Percent Composition Analysis

This concept involves using the percentage by mass of each element in a compound to determine the simplest whole number ratio of atoms. It is a fundamental method in analytical chemistry to derive an empirical formula from experimental data regarding the elemental composition of the substance.

Lewis Structures

Lewis structures are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist. They are useful for visualizing the arrangement of electrons, predicting molecular geometry, and understanding reactivity, particularly in structures involving rings or delocalized electrons.

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