Problem 106 - Chemistry The Central Science In Si Units

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 \(S-S\) distance in the \(S_{8}\) ring is 205 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.

Step-by-Step Solution

Answer

Empirical formula: SN; Molecular formula: \( \text{S}_4\text{N}_4 \); Average bond enthalpy: 60 kJ/mol. Bond distances ~205 pm.

Step 1: Calculate Empirical Formula

First, assume a 100 g sample of the compound for ease of calculation. This means you have 69.6 g of sulfur (S) and 30.4 g of nitrogen (N) per 100 g of compound. Next, convert these masses to moles using their atomic masses (S = 32.07 g/mol, N = 14.01 g/mol):\[ \text{Moles of } S = \frac{69.6 \, g}{32.07 \, g/mol} \approx 2.17 \, mol \]\[ \text{Moles of } N = \frac{30.4 \, g}{14.01 \, g/mol} \approx 2.17 \, mol \]The ratio of moles of S to N is 1:1, so the empirical formula is \( \text{SN} \).

Step 2: Calculate Molecular Formula

The empirical formula mass of SN is:\[ 32.07 \, g/mol + 14.01 \, g/mol = 46.08 \, g/mol \]Next, determine how many empirical formula units make up the molecular formula using the molar mass:\[ \frac{184.3 \, g/mol}{46.08 \, g/mol} \approx 4 \]Thus, the molecular formula is \( \text{S}_4\text{N}_4 \).

Step 3: Draw Lewis Structures

The compound \( \text{S}_4\text{N}_4 \) forms a ring structure with alternating sulfur and nitrogen atoms. Considering it is a ring and the bonds are described to have the same length, one possible Lewis structure is a square with alternating single bonds connecting S and N atoms, with lone pairs on each atom ensuring the octet rule is considered.

Step 4: Predict Bond Distances

Given that all bonds in the ring are the same length, and knowing the \( S-S \) distance in \( S_8 \) is 205 pm, you can approximate the \( S-N \) bond distances to also be close to this measurement due to similar bonding environments.

Step 5: Estimate Average Bond Enthalpy

Use the estimated enthalpy of formation for the compound and bond enthalpies. If \( \Delta H_f^{\circ}(\text{S}(g)) = 222.8 \, kJ/mol \), the formation of one molecule \( \text{S}_4\text{N}_4 \) (molar mass = 184.3 g/mol) is given as 480 kJ/mol.Since there are 8 bonds (4 S-N and 4 N-S) involved in forming the ring, you can estimate the average bond enthalpy as:\[ \frac{\Delta H_f^{\circ}}{\text{number of bonds}} \approx \frac{480 \, kJ/mol}{8} = 60 \, kJ/mol \]

Step 6: Conclusion

The empirical formula is SN, the molecular formula is \( \text{S}_4\text{N}_4 \), the bonds in this ring are approximately 205 pm (like S-S bonds in \( S_8 \)), and the average bond enthalpy is estimated to be 60 kJ/mol.

Key Concepts

Empirical and Molecular Formulas

To find the empirical formula, we assume a 100 g sample, making it easier to calculate percentages as direct masses. Given that we have a composition of 69.6% sulfur (S) and 30.4% nitrogen (N), we convert these percentages to grams:

• Sulfur: 69.6 g
• Nitrogen: 30.4 g

Next, we convert these masses to moles:

• Moles of S = \( \frac{69.6 \, g}{32.07 \, g/mol} \approx 2.17 \, mol \)
• Moles of N = \( \frac{30.4 \, g}{14.01 \, g/mol} \approx 2.17 \, mol \)

Thus, the mole ratio of S to N is 1:1. This results in an empirical formula of \( \text{SN} \). The molecular formula is determined using the compound's molecular weight of 184.3 g/mol. The empirical formula mass for SN is 46.08 g/mol:

• \( \frac{184.3 \, g/mol}{46.08 \, g/mol} \approx 4 \)

Therefore, the molecular formula is \( \text{S}_4\text{N}_4 \).

Lewis Structures

Lewis structures are diagrams representing the arrangement of electrons in a molecule. For \( \text{S}_4\text{N}_4 \), the Lewis structure shows alternating sulfur and nitrogen atoms, forming a ring. Each atom needs to follow the octet rule, meaning each atom should be surrounded by eight electrons.The structure for \( \text{S}_4\text{N}_4 \) can be visualized as a square, with single bonds connecting alternating sulfur and nitrogen atoms. Each atom will have lone pairs to satisfy the octet:

• Lone pairs on sulfur and nitrogen
• All atoms achieving an octet
• Reinforcement of single bonds due to ring structure symmetry

Drawing the structure often involves understanding that errors can occur if you don't make sure all atoms have the correct number of bonds and lone pairs.

Bond Enthalpy

Bond enthalpy is a measure of bond strength in a chemical bond. It is defined as the amount of energy required to break one mole of bonds in gaseous molecules. The provided enthalpy of formation for \( \text{S}_4\text{N}_4 \) is 480 kJ/mol, and it involves 8 bonds due to its \( \text{S-N} \) and \( \text{N-S} \) connections.To estimate the average bond enthalpy, we calculate:\[\text{Average bond enthalpy} = \frac{\Delta H_f^{\circ}(\text{compound})}{\text{Number of bonds}} = \frac{480 \, kJ/mol}{8} = 60 \, kJ/mol\]This calculation gives us an approximation of how much energy would be needed to break each bond within the molecule, helping understand the compound's stability and reactivity.

Ring Structures

Ring structures feature atoms connected in a closed loop, impacting the molecule's geometry and properties. In \( \text{S}_4\text{N}_4 \), the sulfur and nitrogen atoms form a four-membered ring, producing unique chemical behavior.A ring's bond lengths typically depend on the type of atoms and their bonding interactions. Here, the rings are described as having bonds of the same length. By comparison, the \( S-S \) distance in the \( S_8 \) ring is 205 pm. Due to similar bonding environments, the \( S-N \) and \( N-S \) bonds in \( \text{S}_4\text{N}_4 \) are expected to be around the same length.Understanding ring structures can provide insight into:

• Chemical stability
• Potential for high energy release
• Unique reactivity patterns due to strain and symmetry in small rings

These characteristics can lead to the explosive nature of some ring compounds, like \( \text{S}_4\text{N}_4 \), especially when exposed to stresses like impact or heat.