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.

Step by step solution

01

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 = \(\frac{30.4}{14.0}\)

02

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.

03

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.

04

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 \(205 \mathrm{pm}\).

05

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.

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