Question

The first sulfur-nitrogen compound was prepared in 1835 and has been used to synthesize many others. In the early \(1980 \mathrm{~s}\) researchers made another such compound that conducts electricity like a metal. Mass spectrometry of the compound shows a molar mass of \(184.27 \mathrm{~g} / \mathrm{mol}\), and analysis shows it to contain 2.288 g of \(\mathrm{S}\) for every \(1.000 \mathrm{~g}\) of \(\mathrm{N}\). What is its molecular formula?

Short answer

The molecular formula is \( \text{S}_4 \text{N}_4 \).

Step-by-step solution

Determine the mass of each element

According to the problem, 2.288 g of sulfur (S) and 1.000 g of nitrogen (N) are given. Start by calculating the molar amounts of each.

Calculate moles of sulfur

The atomic mass of sulfur (S) is approximately 32.06 g/mol.Calculate the moles of sulfur: \[ \text{Moles of S} = \frac{2.288 \text{ g}}{32.06 \text{ g/mol}} \ \text{Moles of S} = 0.0714 \text{ mol} \ \text{(4 significant figures)} \]

Calculate moles of nitrogen

The atomic mass of nitrogen (N) is approximately 14.01 g/mol.Calculate the moles of nitrogen: \[ \text{Moles of N} = \frac{1.000 \text{ g}}{14.01 \text{ g/mol}} \ \text{Moles of N} = 0.0714 \text{ mol} \ \text{(4 significant figures)} \]

Determine the empirical formula

Since the moles of sulfur and nitrogen are in a 1:1 ratio:The empirical formula is \( \text{SN} \).

Determine the molecular formula

Calculate the molar mass of the empirical formula (S = 32.06 g/mol, N = 14.01 g/mol):\[ \text{Empirical Formula Molar Mass} = 32.06 + 14.01 = 46.07 \text{ g/mol} \]Now, use the formula to determine the molecular formula:\[ \text{Molecular Formula} = n \times \text{Empirical Formula} \ n = \frac{Molar Mass (given)}{Empirical Formula Molar Mass} \ n = \frac{184.27 \text{ g/mol}}{46.07 \text{ g/mol}} \ n = 4 \]Finally, multiply the subscripts in the empirical formula by this value:\[ \text{Molecular Formula} = (\text{SN})_4 = \text{S}_4 \text{N}_4 \]

Key concepts

empirical formula

The empirical formula represents the simplest whole-number ratio of the atoms in a compound. Despite its simplicity, it provides crucial information about how elements are combined within a molecule. To find the empirical formula, start with the mass of each element given, convert these masses to moles, and then establish the simplest ratio. In our exercise, we had 2.288 grams of sulfur and 1.000 grams of nitrogen.
By using their atomic masses, we can convert these masses to moles: calculating 2.288 grams of sulfur converts to approximately 0.0714 moles, and 1.000 grams of nitrogen also converts to approximately 0.0714 moles.
Because these values are equal, the ratio of sulfur to nitrogen is 1:1. Thus, the empirical formula for the compound is SN.

molar mass

Molar mass is the mass of one mole of a substance, often measured in grams per mole (g/mol). It is a vital concept for converting between the mass of a substance and the number of moles. In our exercise, the molar mass of the chemical compound was found using mass spectrometry and given as 184.27 g/mol.
To verify the molecular formula using molar mass, take the empirical formula mass (46.07 g/mol for SN) and compare it to the molecular mass. You do this by dividing the given molar mass by the empirical formula mass: \(\frac{184.27 \text{g/mol}}{46.07 \text{g/mol}} = 4\).
This result signifies that the molecular formula contains four times the number of atoms in the empirical formula, leading us to \( \text{S}_4 \text{N}_4 \).

mass spectrometry

Mass spectrometry is an analytical technique used to measure the mass-to-charge ratio of ions. This technique is beneficial in determining the molecular mass of a compound, as it was in our exercise where the molecular mass was found to be 184.27 g/mol.
Mass spectrometry works by ionizing chemical compounds to generate charged molecules or molecule fragments and then measuring these ions with their respective mass-to-charge ratios. The method can precisely pinpoint the molar mass of compounds, crucial for identifying molecular formulas.
For students studying chemical compounds, understanding mass spectrometry can be incredibly beneficial.

Key points include:

• How compounds ionize and break apart
• How to read spectrometry data
• Relating spectrometry data to molecular and empirical formulas

All these make mass spectrometry a powerful tool in modern chemistry.

sulfur-nitrogen compounds

Sulfur-nitrogen compounds are interesting because they exhibit unique chemical and physical properties. They were first synthesized in 1835, and since then, various forms have been discovered. Some of these compounds, like the one highlighted in our exercise, have conductivity properties akin to metals.
The compound in question, with a molecular formula of \(\text{S}_4\text{N}_4 \), illustrates the versatility of sulfur-nitrogen compounds. They serve as synthons in chemical synthesis and have relevance in materials science and electrical engineering.
Studying these compounds involves:

• Understanding their synthesis and properties
• Exploring their uses in different fields
• Appreciating their role in historical and modern chemistry

Whether used for academic purposes or practical applications, sulfur-nitrogen compounds offer a fascinating glimpse into the world of advanced chemical engineering.