Question

Given the following molecular formulas, write the empirical formulas. (a) \(\mathrm{N}_{2} \mathrm{O}_{4}\) (b) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (c) \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)

Short answer

The empirical formulas for the given molecular forms are: (a) \(\mathrm{NO}_{2}\) (b) \(\mathrm{HCO}_{2}\) (c) \(\mathrm{CH}_{2}\mathrm{O}\)

Step-by-step solution

Identify the Number of Atoms of Each Element for N2O4

For \(\mathrm{N}_{2}\mathrm{O}_{4}\), there are 2 atoms of Nitrogen (N) and 4 atoms of Oxygen (O).

Simplify the Ratio for N2O4

The ratio between Nitrogen and Oxygen for \(\mathrm{N}_{2}\mathrm{O}_{4}\) can be simplified to 1:2, therefore the empirical formula is \(\mathrm{NO}_{2}\).

Identify the Number of Atoms of Each Element for H2C2O4

For \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\), there are 2 atoms of Hydrogen (H), 2 atoms of Carbon (C) and 4 atoms of Oxygen (O).

Simplify the Ratio for H2C2O4

The ratio between Hydrogen, Carbon and Oxygen for \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\) can be simplified to 1:1:2, therefore the empirical formula is \(\mathrm{HCO}_{2}\).

Identify the Number of Atoms of Each Element for CH3CO2H

For \(\mathrm{CH}_{3}\mathrm{CO}_{2}\mathrm{H}\), there are 4 atoms of Hydrogen (H), 2 atoms of Carbon (C) and 2 atoms of Oxygen (O).

Simplify the Ratio for CH3CO2H

The ratio between Hydrogen, Carbon and Oxygen for \(\mathrm{CH}_{3}\mathrm{CO}_{2}\mathrm{H}\) can be simplified to 2:1:1, therefore the empirical formula is \(\mathrm{CH}_{2}\mathrm{O}\).

Key concepts

Molecular Formulas

Molecular formulas are an essential aspect of chemistry as they convey the types and numbers of atoms present in a molecule. A molecular formula reveals the exact number of each type of atom in a molecule. For instance, in the formula \( \mathrm{N}_{2}\mathrm{O}_{4} \), it indicates the presence of 2 nitrogen atoms and 4 oxygen atoms in a molecule.
It gives important information on the actual composition of a chemical substance. This offers a clear understanding of the substance's chemical nature and potential chemical reactions it can undergo.
Molecular formulas can be quite complex, and in some cases, it's helpful to simplify them. This simplification leads us to another related concept, the empirical formula. The molecular formula is significant as it provides the detailed atomic composition of the compound, which is crucial when discussing or calculating chemical reactions.

Chemical Ratios

Chemical ratios are at the heart of understanding molecular and empirical formulas. They express the relative proportions of different atoms in a molecular formula or empirical formula. For example, in \( \mathrm{N}_{2}\mathrm{O}_{4} \), the chemical ratio is 2 nitrogen atoms to 4 oxygen atoms.
This can be simplified to a 1:2 ratio as seen in the empirical formula \( \mathrm{NO}_{2} \). Simplifying a chemical ratio involves finding the greatest common divisor of the amounts of each element and then reducing the ratio accordingly.

• This simplification helps to understand the basic building blocks of compounds.
• It also provides insight into how different molecules might combine or be rearranged in chemical reactions.

By focusing on these ratios, chemists can make predictions about the properties and behavior of a compound in different chemical scenarios.

Atomic Composition

Atomic composition refers to the specific kinds and amounts of atoms that make up a molecule or compound. It is the basis for deriving both molecular and empirical formulas. Consider the compound \( \mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4} \), which consists of 2 hydrogen, 2 carbon, and 4 oxygen atoms.
In constructing a molecular formula, the atomic composition is directly listed with each element symbol followed by a subscript denoting the number of atoms.

• Empirical formulas represent the simplest integer ratio of these atoms.
• They can differ from the molecular formula if the molecule is composed of repeating subunits.

The atomic composition is critical, as it not only tells us what is present in the compound but also guides chemists in determining the reactivity, stability, and conformation of molecules.