Problem 54 - Chemistry: An Atoms-Focused Approach

Question

Which of the following nitrogen oxides have the same empirical formulas? (a) \(\mathrm{N}_{2} \mathrm{O} ;\) (b) \(\mathrm{NO} ;\) (c) \(\mathrm{NO}_{2} ;\) (d) \(\mathrm{N}_{2} \mathrm{O}_{2}\) (e) \(\mathrm{N}_{2} \mathrm{O}_{4}\)

Step-by-Step Solution

Answer

Answer: Nitrogen oxides (b) NO and (d) NO, as well as (c) NO2 and (e) NO2 have the same empirical formulas.

Step 1: Write down the given nitrogen oxide formulas

The nitrogen oxides given in the exercise are: (a) N2O (b) NO (c) NO2 (d) N2O2 (e) N2O4

Step 2: Simplify the molecular formulas to get the empirical formulas

Simplify each molecular formula by dividing the subscripts of N and O by their greatest common divisor (GCD). (a) N2O: GCD(2,1) = 1. Dividing both subscripts by 1, we get the empirical formula N2O. (b) NO: There are no further simplifications for this formula, as both subscripts are already 1. The empirical formula is NO. (c) NO2: There are no further simplifications for this formula, as both subscripts are already the simplest. The empirical formula is NO2. (d) N2O2: GCD(2,2) = 2. Dividing both subscripts by 2, we get the empirical formula NO. (e) N2O4: GCD(2,4) = 2. Dividing both subscripts by 2, we get the empirical formula NO2.

Step 3: Identify common empirical formulas

After simplifying the molecular formulas for each nitrogen oxide, we can now identify the ones with the same empirical formulas. (a) N2O (b) NO (c) NO2 (d) NO (e) NO2 Thus, nitrogen oxides (b) NO and (d) NO, as well as (c) NO2 and (e) NO2 have the same empirical formulas.

Key Concepts

Nitrogen Oxides

Nitrogen oxides are a group of chemical compounds composed of nitrogen and oxygen, with varying numbers of these atoms. They play a significant role in both environmental and industrial chemistry. You might encounter them in different contexts, such as environmental discussions about air pollution, since they can contribute to the formation of smog and acid rain.
Nitrogen oxides include compounds like nitrogen monoxide (NO), nitrogen dioxide (NO_2), nitrous oxide (N_2O), and dinitrogen tetroxide (N_2O_4). Each compound has unique chemical properties and uses. For example:

• Nitrogen monoxide (NO) is a gas under standard conditions and can act as a signaling molecule in the body.
• Nitrogen dioxide (NO_2) is a reddish-brown gas, often found in vehicle emissions.
• Nitrous oxide (N_2O), commonly known as laughing gas, is used as an anesthetic.
• Dinitrogen tetroxide (N_2O_4) can exist in equilibrium with nitrogen dioxide and is used in rocket fuels.

Understanding the differences in the nitrogen oxides' formulas helps in determining their properties and potential impacts on the environment.

Molecular Formulas

Molecular formulas provide the exact number of each type of atom present in a compound. They are essential in chemistry as they give insight into the composition of molecules. For nitrogen oxides, knowing the molecular formula allows chemists to predict how these substances will interact in chemical reactions and their behavior in different conditions.
The molecular formula provides information about the compound's structure and potential bonding. Let's use some examples from the exercise:

• N_2O - Two nitrogen atoms bonded to one oxygen atom.
• NO_2 - One nitrogen atom bonded to two oxygen atoms.
• N_2O_4 - Four atoms in a dimer configuration, existing mainly as a pair of NO_2 molecules.

Knowing the molecular formula is the first step in determining the compound's empirical formula, which shows the simplest whole-number ratio of elements. Chemists use this information to infer the properties of the compound and whether different compounds might have similar chemical behaviors if they share the same empirical formula.

Chemistry Problem Solving

Chemistry problem solving often involves simplifying the given information to find solutions or draw conclusions about chemical substances. When working on problems like identifying empirical formulas, chemists use systematic approaches to deduce these simpler formulas from the molecular ones.
Let's take the step-by-step approach seen in the exercise. The goal is to express each compound in its simplest form using the empirical formula. Here are the usual steps in this kind of problem:

• Identify the molecular formula (given in the problem).
• Find the greatest common divisor of the subscripts in the molecular formula.
• Divide each subscript by this greatest common divisor to get the empirical formula.
• Compare empirical formulas to find similarities between different compounds.

For example, N_2O_4 simplifies to NO_2 by dividing the subscripts by their greatest common divisor, 2. This tells us that the formula can be represented in a simpler form, revealing potential relationships between molecules.
Through this methodical process, students learn to critically analyze chemical formulas and recognize patterns, aiding in understanding the broader implications of a compound's chemical structure.