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 2.05 A.) ( d.) The enthalpy of formation of the compound is estimated to be 480 \(\mathrm{kJ} / \mathrm{mol}^{-1} . \Delta H_{f}^{9}\) of \(\mathrm{S}(g)\) is 222.8 \(\mathrm{kJ} / \mathrm{mol} .\) Estimate the average bond enthalpy in the compound.

Short answer

The compound consists of 69.6% S and 30.4% N by mass and has a molecular mass of 184.3 g/mol. The empirical formula is SN and the molecular formula is S4N4. The most stable Lewis structures comprise alternating single and double bonds between S and N atoms in a ring. The bond distance between S-N atoms is estimated to be 1.5 - 1.8 Å. The average bond enthalpy of the compound is approximately 40 kJ/mol.

Step-by-step solution

1. Calculate the moles of sulfur and nitrogen

From the given data, we know that the compound consists of 69.6% S and 30.4% N by mass. Assuming we have 100g of the compound, then we have 69.6g S and 30.4g N. We can then calculate the number of moles for each element using their molar masses. For sulfur, the molar mass is 32.07g/mol and for nitrogen, it is 14.01g/mol. Moles of S = (69.6g)/(32.07g/mol) = 2.17 mol Moles of N = (30.4g)/(14.01g/mol) = 2.17 mol

2. Determine the empirical formula

The empirical formula is found by determining the simplest whole number ratio between the moles of each element in the compound. In this case, the ratio between moles of S and N is already simplified to 1:1. Therefore, the empirical formula is SN.

3. Determine the molecular formula

Now we can use the molecular mass given (184.3 g/mol) and the empirical formula's molar mass (S: 32.07g/mol and N: 14.01g/mol) to determine the molecular formula. The empirical formula's molar mass is 32.07+14.01 = 46.08 g/mol. Ratio of molecular mass to empirical formula mass = (184.3 g/mol)/(46.08 g/mol) ≈ 4 This tells us that the molecular formula consists of 4 times the empirical formula, i.e., S4N4. b. Lewis structures:

1. Determine the number of valence electrons

In the S4N4 molecule, we have 4 sulfur and 4 nitrogen atoms. Since each sulfur atom has 6 valence electrons, and each nitrogen atom has 5 valence electrons, the total number of valence electrons in the molecule is: Total valence electrons = 4 × 6(S) + 4 × 5(N) = 44

2. Create the Lewis structures

Given that all bonds in the ring are of the same length, the most likely Lewis structures consist of alternating single and double bonds between sulfur and nitrogen atoms. There are two possible structures for this arrangement; one starting with a single S-N bond and another with a double S-N bond. Note that these structures satisfy the octet rule for all atoms and use up all 44 valence electrons, making them the most stable Lewis structures. c. Bond distances:

1. Predict bond distances

Since the molecule has alternating single and double bonds, the bond distance between sulfur and nitrogen will be somewhere between the S-S single bond distance and the N-N single bond distance. The S-S bond distance in the S8 ring is given as 2.05 Å. The N-N bond distance can be approximated to the bond distance in nitrogen gas, which is 1.10 Å. With this information, we can estimate the bond distance between S-N atoms to be 1.5 - 1.8 Å. d. Bond enthalpy:

1. Calculate the enthalpy change per mole

The given enthalpy change per mole is 480 kJ/mol. Since there are 8 bonds in the ring (4 single bonds and 4 double bonds), the total bonds are 12, because double bonds count as two.

2. Estimate the average bond enthalpy

The average bond enthalpy can be estimated by dividing the enthalpy change per mole by the number of bonds. In our case, this would be: Average bond enthalpy = (480 kJ/mol) / 12 = 40 kJ/mol

Key concepts

Empirical Formula

When dealing with molecular compounds, the empirical formula is an essential tool. It represents the simplest ratio of atoms found in the compound. For our compound consisting of sulfur (S) and nitrogen (N), we have 69.6% sulfur and 30.4% nitrogen by mass.
To find the empirical formula, consider 100 grams of the compound, meaning we have 69.6 grams of sulfur and 30.4 grams of nitrogen. We calculate the number of moles for each using their molar masses (Sulfur: 32.07 g/mol and Nitrogen: 14.01 g/mol). Both yield approximately 2.17 moles.
This results in a 1:1 molar ratio, giving us the empirical formula of SN. This formula does not provide the actual number of atoms in a molecule but a simpler form based on the actual elemental composition.

Molecular Formula

The molecular formula reveals the actual number of each type of atom in a molecule. To determine it, we need both the empirical formula and the molecular mass. Here, the empirical formula SN has a mass of 46.08 g/mol.
The molecular mass provided is 184.3 g/mol. Dividing this by the empirical mass gives a ratio of about 4, indicating the molecular formula is a multiple of the empirical formula. Thus, we multiply SN by 4, arriving at the molecular formula S₄N₄.
This formula gives a precise depiction of the molecules' structure and composition, crucial for understanding the compound's chemical properties.

Lewis Structures

Lewis structures are diagrams that show the bonding between atoms and the lone pairs of electrons in a molecule. For S₄N₄, we need to determine the number of valence electrons to begin sketching these structures.
Sulfur contributes 6 valence electrons, and nitrogen 5. With 4 atoms of each element, the total valence electrons add up to 44.
In S₄N₄, all bonds are the same length, which suggests alternating single and double bonds can depict the molecule's ring structure. One possible structure starts with a single S-N bond, followed by a double S-N bond, and alternating. These configurations satisfy the octet rule and utilize all 44 electrons, allowing us to understand their bonding patterns.

Valence Electrons

Valence electrons play a fundamental role in forming chemical bonds. They are found in the outermost shell of an atom and determine how atoms can bond with others. In the S₄N₄ compound, sulfur and nitrogen have 6 and 5 valence electrons respectively.
These electrons are involved in bond formation, creating a stable electronic configuration for the molecule. Bonding in S₄N₄ consumes all available valence electrons, demonstrating their participation in maintaining the integrity and stability of the molecule.

• Sulfur: 4 atoms x 6 electrons = 24
• Nitrogen: 4 atoms x 5 electrons = 20

Each atom's valence electrons are crucial for understanding how molecules achieve stability and what possible structures exist.

Bond Enthalpy

Bond enthalpy represents the energy needed to break a bond between two atoms. It provides insight into the molecule's stability. The enthalpy of formation for the compound is 480 kJ/mol.
In S₄N₄, 8 bonds exist around the ring—accounting for both single and double bonds. The total number of bonds amounts to 12 due to the nature of double bonds.
To estimate the average bond enthalpy, divide the total enthalpy by the number of bonds: 480 kJ/mol divided by 12 gives 40 kJ/mol. This value gives a general understanding of the bond strength within the structure, highlighting the molecule's chemical resilience.