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.

Step by step solution

01

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

02

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.

03

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:

04

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

05

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:

06

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:

07

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.

08

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

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