Question

A \(0.77-\mathrm{mg}\) sample of nitrogen reacts with chlorine to form \(6.61 \mathrm{mg}\) of the chloride. What is the empirical formula of the nitrogen chloride?

Short answer

The empirical formula of the nitrogen chloride is NCl3.

Step-by-step solution

Identify the Masses of the Elements

First, we take the masses as given in the exercise. The mass of nitrogen is 0.77 mg, and the mass of nitrogen chloride formed is 6.61 mg.

Find the Mass of Chlorine in the Compound

Subtract the mass of nitrogen from the total mass of the nitrogen chloride to find the mass of chlorine in the compound: 6.61 mg - 0.77 mg = 5.84 mg.

Convert Masses to Moles

Use the molar masses of nitrogen (14.007 g/mol) and chlorine (35.453 g/mol) to convert the masses from milligrams to moles. For nitrogen: (0.77 mg) / (14.007 g/mol * 1000 mg/g) = 5.50 * 10^-5 moles. For chlorine: (5.84 mg) / (35.453 g/mol * 1000 mg/g) = 1.65 * 10^-4 moles.

Determine the Simplest Mole Ratio

Divide each number of moles by the smallest number of moles to find the simplest whole number ratio. For nitrogen: (5.50 * 10^-5 moles) / (5.50 * 10^-5) = 1. For chlorine: (1.65 * 10^-4 moles) / (5.50 * 10^-5) = 3. This gives us a ratio of nitrogen to chlorine of 1:3.

Write the Empirical Formula

Using the simplest mole ratio, we write the empirical formula of the nitrogen chloride as NCl3.

Key concepts

Stoichiometry

Stoichiometry is a section within chemistry that deals with the quantitative relationships between the substances involved in a chemical reaction. It's the cornerstone for understanding reactions and finding out how much of each substance is needed or produced. For example, determining the empirical formula involves stoichiometry as it requires the balancing of elements based on their mass and the number of moles.

To grasp the stoichiometry in the context of the given problem, consider a dance where each nitrogen atom needs to partner with chlorine atoms to form the compound. The empirical formula is like the list of dance pairs - it shows the simplest ratio of the partners, reflecting how many chlorine atoms 'dance' with each nitrogen atom. Thanks to the stoichiometric calculations, we can deduce that one nitrogen atom pairs with three chlorine atoms, giving us the empirical formula NCl3.

Understanding stoichiometry is vital because it doesn't just tell us the proportions; it also guides us in predicting product formation and is the basis for many quantitative analyses in chemistry.

Mole Concept

The mole concept is a way of counting particles at the atomic and molecular scale, much like counting eggs by the dozen. One mole is defined as the amount of substance that contains as many particles, atoms, molecules, ions, or electrons, as there are atoms in 12 grams of carbon-12 (Avogadro's number, approximately 6.022 x 10^23).

In the exercise, we use the mole concept to convert the mass of nitrogen and chlorine to moles. This step is crucial as it allows us to compare atoms on a per-particle basis, rather than mass, because atoms combine in fixed ratios of particles, not mass. Knowing that the mass of nitrogen is 0.77 mg, we convert this mass to moles by dividing by the molar mass of nitrogen. We repeat this process for chlorine to achieve a mole ratio, which is the heart of stoichiometry. The mole concept, therefore, bridges the gap between the macroscopic world we see and the microscopic world of atoms and molecules.

Chemical Composition

Chemical composition refers to the identity and ratio of the elements that make up a chemical compound. It is determined by the types of atoms and the number of each type of atom in the compound. In our textbook example, we are finding the chemical composition of a nitrogen chloride compound.

To establish this, we first separate the total mass of the compound into the masses of its constituent elements, nitrogen, and chlorine. After calculating their respective moles, we can express the chemical composition as a ratio or formula that is most simplified, which in this instance is NCl3. This is an empirical formula, which shows the simplest whole number ratio of elements within the compound.

By understanding the chemical composition through the empirical formula, students can predict many properties of the compound, such as reactivity, phase at room temperature, polarity, and even color. Therefore, chemical composition is not just an abstract concept; it has real-world implications in understanding the substances around us.