Question

Give the empirical formula that corresponds to each of the following molecular formulas. a. sodium peroxide, \(\mathrm{Na}_{2} \mathrm{O}_{2}\) b. terephthalic acid, \(\mathrm{C}_{8} \mathrm{H}_{6} \mathrm{O}_{4}\) c. phenobarbital, \(\mathrm{C}_{12} \mathrm{H}_{12} \mathrm{~N}_{2} \mathrm{O}_{3}\) d. 1,4 -dichloro- 2 -butene, \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{Cl}_{2}\)

Short answer

a. NaO b. C4H3O2 c. C12H12N2O3 d. C2H3Cl

Step-by-step solution

a. sodium peroxide: Na2O2

Divide each subscript by the greatest common divisor (GCD) of all the subscripts in the molecular formula. In this case, the GCD is 2. \( \frac{\mathrm{Na}_{2}\mathrm{O}_{2}}{2} \) Resulting in the empirical formula: \( \mathrm{Na}\mathrm{O} \)

b. terephthalic acid: C8H6O4

Divide each subscript by the greatest common divisor (GCD) of all the subscripts in the molecular formula. In this case, the GCD is 2. \( \frac{\mathrm{C}_{8} \mathrm{H}_{6} \mathrm{O}_{4}}{2} \) Resulting in the empirical formula: \( \mathrm{C}_{4} \mathrm{H}_{3} \mathrm{O}_{2} \)

c. phenobarbital: C12H12N2O3

Divide each subscript by the greatest common divisor (GCD) of all the subscripts in the molecular formula. In this case, the GCD is 1 (since there are no common divisors for all elements larger than 1). Therefore, the empirical formula remains the same: \( \mathrm{C}_{12} \mathrm{H}_{12} \mathrm{N}_{2} \mathrm{O}_{3} \)

d. 1,4-dichloro 2-butene: C4H6Cl2

Divide each subscript by the greatest common divisor (GCD) of all the subscripts in the molecular formula. In this case, the GCD is 2. \( \frac{\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{Cl}_{2}}{2} \) Resulting in the empirical formula: \( \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl} \)

Key concepts

Molecular Formula

In chemistry, the molecular formula of a chemical substance expresses the exact number of atoms of each element present in a single molecule of that substance. It provides information about the actual numbers and types of atoms that make up the molecule, offering insights into the molecule's composition and potential properties.

An example of a molecular formula is \( \mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6} \), which represents glucose. It tells us that each glucose molecule consists of six carbon atoms (C), twelve hydrogen atoms (H), and six oxygen atoms (O). These figures are critical for understanding the molecule's structure and how it might interact with other chemicals.

Greatest Common Divisor

The greatest common divisor (GCD), also known as the greatest common factor (GCF), is a mathematical concept critical in simplifying ratios and fractions, including those in chemical formulas. To find the empirical formula of a compound from its molecular formula, we look for the GCD of the subscripts (the numbers of atoms of each element) in the molecular formula.

Carefully identifying the GCD helps reduce the molecular formula to the simplest ratio of atoms. For example, in the molecular formula \( \mathrm{C}_{8}\mathrm{H}_{8}\mathrm{O}_{2} \), the GCD of 8, 8, and 2 is 2. Dividing each subscript by 2 gives the empirical formula \( \mathrm{C}_{4}\mathrm{H}_{4}\mathrm{O} \), which reflects the simplest whole-number ratio of atoms in the molecule.

Chemical Composition

Chemical composition refers to the identity and ratio of the elements that make up a chemical compound. Understanding the composition is consequential when characterizing substances and predicting their behavior.

When scientists conduct chemical analysis, they often aim to determine the specific proportions of elements. This knowledge is pivotal for various applications, such as formulating medications, designing materials, and conducting forensic investigations. To elucidate a compound's properties, it's essential to know both its qualitative (which elements are present) and quantitative (how much of each element is present) composition. The empirical formula represents the simplest whole-number ratio of elements, providing a snapshot of the compound's chemical composition.