Question

Which of the following formulas-NO, ${\mathrm{N}}_2\mathrm{O},{\mathrm{NO}}_2,{\mathrm{N}}_2{\mathrm{O}}_4$ and ${\mathrm{N}}_2{\mathrm{O}}_5-$ represent the empirical and molecular formulas of the same compound? Explain your answer.

Short answer

The compounds NO, N2O, NO2, and N2O5 have the same empirical and molecular formulas, as they are already in their simplest whole-number ratios. Only N2O4 has a different empirical formula (NO2) after dividing the numbers of atoms by the greatest common divisor.

Step-by-step solution

1. NO

NO represents one nitrogen atom and one oxygen atom (N1O1). This is already in its simplest whole-number ratio, so the empirical formula is also NO.

2. N2O

N2O represents two nitrogen atoms and one oxygen atom (N2O1). This is also already in its simplest whole-number ratio, so the empirical formula is also N2O.

3. NO2

NO2 represents one nitrogen atom and two oxygen atoms (N1O2). This is already in its simplest whole-number ratio, so the empirical formula is also NO2.

4. N2O4

N2O4 represents two nitrogen atoms and four oxygen atoms. To obtain the empirical formula, we divide the numbers of atoms by the greatest common divisor (GCD), which is 2 in this case. So, we have N2/2O4/2 -> N1O2, so the empirical formula is NO2. Since the empirical formula is different from the molecular formula, this compound does not meet the criteria.

5. N2O5

N2O5 represents two nitrogen atoms and five oxygen atoms (N2O5). This is already in its simplest whole-number ratio, so the empirical formula is also N2O5. From our analysis, the compounds NO, N2O, NO2, and N2O5 have the same empirical and molecular formulas. Only N2O4 has a different empirical formula (NO2).

Key concepts

Chemical Compounds

Chemical compounds are substances composed of two or more different types of atoms bonded together.
Each compound has a unique composition and properties that distinguish it from other compounds. In chemistry, the types of bonds and the ratio in which atoms combine are critical in defining a compound's characteristics. We often use chemical formulas to represent these compounds symbolically.

• A simple formula is the most basic representation, indicating the types and quantities of atoms in a single molecule of a compound, such as H₂O for water.
• The empirical formula of a compound gives the simplest whole-number ratio of atoms in the compound. It may or may not be the same as the molecular formula.
• The molecular formula indicates the actual number of atoms of each element in a molecule of the compound. For instance, glucose has an empirical formula of CH₂O, while its molecular formula is C₆H₁₂O₆, showing that a single molecule contains six carbon atoms, twelve hydrogen atoms, and six oxygen atoms.

Understanding the difference between molecular and empirical formulas is vital in identifying the composition of a chemical compound.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantities of substances involved in chemical reactions.
It is based on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, atoms are simply rearranged to form new substances. Stoichiometry involves calculating the masses, volumes, and concentrations of reactants and products in a chemical reaction.

• To perform stoichiometric calculations, we must start with a balanced chemical equation that obeys the law of conservation of mass.
• The coefficients in a balanced equation tell us the molar ratio of reactants to products, which is used to calculate the amounts of substances needed or produced in a reaction.
• Often, the empirical formula is used in stoichiometry to determine the simplest ratio of elements in a compound, which then aids in understanding the reaction mechanisms.

For the exercise with nitrogen and oxygen compounds, using principles of stoichiometry, one can determine which formulas represent the empirical and molecular forms based on the atom counts and the simplest integer ratios.

Molecular Composition

Molecular composition refers to the specific arrangement and number of atoms in a molecule.
Knowing the molecular composition is crucial for understanding not only the physical and chemical properties of a substance but also its biological interactions if applicable. The molecular composition determines every unique aspect of a compound, from its reactivity and polarity to its ability to engage in specific chemical reactions.

• When we say a compound's empirical formula, we're referring to the simplest ratio of its elements; however, this may not provide complete information about its true structure as the molecular formula does.
• Molecular formulas contain the exact number of each type of atom in a single molecule and offer more detail about the actual composition.
• Advanced concepts like structural formulas and three-dimensional models give even more precise depictions of molecular composition, elucidating the arrangement of atoms in space.

For example, the analysis in the exercise showed that for most nitrogen-oxygen compounds given, the empirical and molecular formulas were identical, indicating that those representations conveyed the full composition of the molecules.