Question

Determine the empirical formula for the compound represented by each molecular formula. $$ \text { a. }\mathrm{C}_{2} \mathrm{H}_{4} \quad \text { b. } \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \quad \text { c. } \mathrm{NH}_{3} $$

Short answer

a. CH2, b. CH2O, c. NH3

Step-by-step solution

Determine the Empirical Formula for C2H4

The molecular formula for C2H4 can be simplified by finding the greatest common divisor of the subscripts for C and H. Since the subscripts are already at their lowest ratio (2:4 can be simplified to 1:2), the empirical formula is CH2.

Determine the Empirical Formula for C6H12O6

For C6H12O6, find the greatest common divisor for the subscripts of C, H, and O, which is 6. Divide each subscript by 6 to find the simplest whole number ratio. The empirical formula is CH2O.

Determine the Empirical Formula for NH3

The molecular formula NH3 is already at its lowest whole number ratio, so the empirical formula is the same as the molecular formula: NH3.

Key concepts

Molecular Formula

Understanding the molecular formula of a compound is critical to grasping its entire chemical identity. A molecular formula represents the actual number of atoms of each element in a molecule of a substance. For example, in the case of ethylene given by the molecular formula \( C_2H_4 \), this indicates that each molecule consists of 2 carbon atoms and 4 hydrogen atoms.

The specifics of a molecular formula include not only the types of atoms but also how many of each type are found in a single molecule. Though it reflects the exact number of atoms, it does not necessarily convey the simplest ratio between them, nor does it illustrate the structure of the molecule, which is where other forms of chemical representation, such as structural formulas, come into play.

Chemical Composition

Delving into the chemical composition of a substance involves understanding the elements present and their proportions in the substance. Every sample of a given pure compound will always contain the same elements in the same mass proportion - this is known as the Law of Definite Proportions. For instance, the molecular formula \( C_6H_{12}O_6 \) indicates that in glucose, there are 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms, showing a precise fixed mass ratio of these elements as they combine to form the compound.

This chemical composition helps predict the properties of the substance, such as its reactivity, phase at room temperature, and how it interacts with other chemicals. By understanding the chemical composition, students can also infer different types of chemical bonds within the molecule, which in turn affect the compound's physical and chemical behaviors.

Stoichiometry

The concept of stoichiometry is one of the foundational pillars of chemistry and serves as an invaluable tool for scientists. Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. In the context of the empirical formula, stoichiometry allows us to determine the simplest whole number ratio of elements in a compound, derived from the compound's molecular formula.

Through stoichiometry, we can also calculate the amounts of substances consumed and produced in a reaction, which is crucial for laboratory preparations and industrial processes alike. Stoichiometry is not only about counting atoms but also involves the conservation of mass and charge, the use of Avogadro's number in mole-to-atom conversions, and the role of molar masses in converting between grams and moles.

Chemical Formula Simplification

The skill of chemical formula simplification is essential for students to transition from the molecular formula to the empirical formula of a compound. The empirical formula is the most simplified version of the chemical formula, showing the simplest whole number ratio of atoms of each element. To achieve this, identify the greatest common divisor of the atoms' subscripts and divide by it, as seen in the exercise for glucose where the molecular formula \( C_6H_{12}O_6 \) simplifies to the empirical formula \( CH_2O \).

Practical Applications

Such simplifications are not merely academic exercises; they have real-world applications in identifying compounds, understanding reactions, and even designing drugs in pharmacology. Mastering chemical formula simplification can significantly improve a student’s competence in various areas of chemistry.