Question

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 \(30.4 \% \mathrm{~N}\). Measurements of its molecular mass yield a value of \(184.3 \mathrm{~g} / \mathrm{mol}\). 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 \(205 \mathrm{pm} .\) ) \((\mathbf{d})\) The enthalpy of formation of the compound is estimated to be \(480 \mathrm{~kJ} / \mathrm{mol}^{-1} . \Delta H_{f}^{\circ}\) of \(\mathrm{S}(g)\) is \(222.8 \mathrm{~kJ} / \mathrm{mol}\). Estimate the average bond enthalpy in the compound.

Short answer

The empirical formula of the compound is S\(_2\)N\(_2\), and the molecular formula is S\(_4\)N\(_4\). The Lewis structures show double bonds between the sulfur and nitrogen atoms, forming an eight-membered ring. The bond distances between the atoms in the ring are about \(205 \mathrm{pm}\). The average bond enthalpy in the compound is approximately \(361.9 \mathrm{~kJ/mol}\).

Step-by-step solution

Calculate moles of sulfur (S) and nitrogen (N)

Firstly, let's assume that we have 100 g of the compound. Therefore, we have \(69.6\) g of sulfur and \(30.4\) g of nitrogen. Now, let's find the moles of \(\mathrm{S}\) and \(\mathrm{N}\). Molar mass of S = \(32.1 \mathrm{~g/mol}\) Moles of S = \(\frac{69.6}{32.1}\) Molar mass of N = \(14.0 \mathrm{~g/mol}\) Moles of N = \(\frac{30.4}{14.0}\)

Determine the empirical formula and molecular formula of the compound

To find the empirical formula, we need to divide the moles of each element by the smallest number of moles present. \(\frac{\mathrm{moles~of~S}}{\mathrm{smallest~number~of~moles}}: \frac{\mathrm{moles~of~N}}{\mathrm{smallest~number~of~moles}}\) Choose the smallest number of moles between S and N, and then calculate the ratio of moles in the compound. This will give us the empirical formula. Then, we can find the molecular formula using the empirical formula and the given molecular mass of the compound.

Draw the Lewis structures for the molecule

Knowing the molecular formula, we can draw possible Lewis structures for the molecule. Keep in mind that sulfur and nitrogen atoms are joined in a ring, and all the bonds in the ring are of the same length.

Predict the bond_distances between the atoms in the ring

Since all the bonds in the ring are of the same length, we can predict the bond distances using the information given. Note that the S-S distance in the S\(_8\) ring is \(205 \mathrm{pm}\).

Calculate the average bond enthalpy in the compound

We are given the enthalpy of formation, \(\Delta H_{f}^{\circ}\), of the compound \((480 \mathrm{~kJ/mol})\) and that of \(\mathrm{S}(g)\) \((222.8 \mathrm{~kJ/mol})\). Using these values and the enthalpy conservation principle, we can estimate the average bond enthalpy in the compound.

Key concepts

Lewis structures

When discussing chemical structures, Lewis structures are a convenient way to depict molecules and their bonds. They illustrate the arrangement of atoms in a molecule, highlighting which atoms are bonded together and how many electrons are involved in creating those bonds.

For a molecule made of sulfur and nitrogen reacting under special conditions, like in the given nitrogen-sulfur compound, Lewis structures will show atoms connected in a ring. To construct a valid Lewis structure for this scenario, we must ensure each atom achieves a stable, noble gas-like electron configuration. Sulfur and nitrogen both aim to complete their valence shells, following the octet rule, though sulfur can sometimes have expanded octets.

In this particular compound, the information regarding the ring structure and equal bond lengths suggest resonance structures. These are multiple Lewis structures depicting various arrangements of electrons that achieve the same molecular geometry, enhancing our understanding of the molecule's behavior.

bond enthalpy

Bond enthalpy, also known as bond energy, is a measure of the strength of a chemical bond. It is the energy required to break one mole of a bond in a molecule in the gas phase. Knowing the bond enthalpy is essential for predicting the energy changes that occur during chemical reactions.

In the nitrogen-sulfur compound described, estimating the average bond enthalpy allows us to understand the stability and reactivity of the compound. Given the enthalpy of formation data provided, we can infer some insights. The enthalpy of formation, \(\Delta H_f^{\circ}\), indicates the energy change when one mole of the compound forms from its constituent elements in their standard states.

By using the known enthalpy of elemental sulfur and the overall formation enthalpy provided, we can estimate the average bond enthalpy for the compound. This gives a rough measure of the energy stored in its bonds and shows why the compound may be prone to detonation given enough energy input.

molar mass calculation

Molar mass calculation is crucial for determining empirical and molecular formulas. Molar mass is the mass of one mole of a substance, giving the combined weight of atoms involved.

For the nitrogen-sulfur compound with a given molar mass of 184.3 g/mol, we begin by calculating the moles of each element present. Assuming a 100 g sample:

• Sulfur is 69.6 g, using molar mass of sulfur (32.1 g/mol), calculate moles = 69.6 / 32.1.
• Nitrogen is 30.4 g, using molar mass of nitrogen (14.0 g/mol), calculate moles = 30.4 / 14.0.

These calculations allow us to find the empirical formula by determining the ratio of moles of nitrogen to sulfur.

Once the empirical formula is known, we can relate it to the molar mass of the compound to determine the molecular formula. The molecular formula can be a multiple of the empirical formula units, showing the actual number of atoms in a molecule. This step connects the percentage composition and the physical properties like molar mass.

nitrogen-sulfur compound

A nitrogen-sulfur compound showcases an interesting chemistry under particular conditions, forming molecules with a unique set of properties. In this exercise, we deal with a binary compound composed solely of nitrogen and sulfur. It is essential to understand the characteristics and implications of this composition.

Such compounds can often form ring structures where atoms are interconnected, exhibiting equal bond lengths as specified in the problem. These features suggest a fascinating balance between differing atomic sizes and bonding capabilities, indicative of resonance and possibly aromatic characteristics in similar compounds.

The given compound is reactive enough to explode upon impact or heat due to the energy that is stored in its chemical bonds, which we refer to as enthalpy. The special conditions mentioned for the creation and behavior of this compound underscore its dynamic and energetically rich nature, emphasizing why it catches interest in both research and application contexts.