Question

Given the following molecular formulas, write the empirical formulas. (a) \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2}\) (b) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\) (c) \(\mathrm{N}_{2} \mathrm{O}_{5}\)

Short answer

The empirical formulas for the given molecular formulas are: (a) \( \mathrm{C}_{3} \mathrm{H}_{2} \mathrm{Cl}\), (b) \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\), and (c) \( \mathrm{N}_{2} \mathrm{O}_{5}\)

Step-by-step solution

Identify the Molecular Formula

The molecular formulas are given as \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2}\), \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\), and \(\mathrm{N}_{2} \mathrm{O}_{5}\).

Find the Empirical Formula for \( \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2}\)

The greatest common divisor for 6, 4, and 2 is 2, so divide all the subscripts by this common divisor. This gives the empirical formula as \( \mathrm{C}_{3} \mathrm{H}_{2} \mathrm{Cl}\).

Find the Empirical Formula for \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\)

No common divisor exists between 6, 5 and 1, so the empirical formula is the same as the molecular formula, i.e., \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\).

Find the Empirical Formula for \( \mathrm{N}_{2} \mathrm{O}_{5}\)

The greatest common divisor for 2 and 5 is 1, so the empirical formula is the same as the molecular formula, i.e., \( \mathrm{N}_{2} \mathrm{O}_{5}\).

Key concepts

molecular formula

In chemistry, the molecular formula of a compound shows the exact number of atoms of each element in a molecule. It is like a blueprint that tells you exactly how many atoms make up a compound. For example, the molecular formula \( \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2} \) indicates that in each molecule of the compound, there are 6 carbon atoms, 4 hydrogen atoms, and 2 chlorine atoms. This is different from the empirical formula, which gives the simplest whole-number ratio of these atoms.

• Molecular formulas are specific, representing the actual number of atoms.
• They are crucial for understanding the precise composition of a compound.

Moreover, molecular formulas are important in determining the molecular weight, which is the sum of the atomic weights of all atoms in the molecule. This is fundamental in calculating properties such as the concentration of solutions and reactions.

greatest common divisor

When determining the empirical formula from a molecular formula, one key concept is the greatest common divisor (GCD). The GCD is the largest positive integer that divides each of the numbers in a set without leaving a remainder. In chemistry, you use it to reduce the subscripts in a molecular formula to their simplest whole-number form.
Take the molecular formula \( \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2} \) as an example. Here, you determine the GCD of the subscript numbers 6, 4, and 2, which is 2. Dividing each subscript by this GCD results in the empirical formula \( \mathrm{C}_{3} \mathrm{H}_{2} \mathrm{Cl} \).

• Calculate GCD to find the simplest ratio of elements for the empirical formula.
• A GCD of 1 indicates the molecular formula is also the empirical formula.

Understanding how to find the GCD is essential in simplifying chemical formulas and understanding their basic composition.

subscripts in chemistry

Subscripts in chemistry are the small numbers found in chemical formulas that indicate the number of atoms of each element in a molecule. For instance, in the formula \( \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2} \), the numbers 6, 4, and 2 serve as subscripts. They tell us how many atoms of carbon, hydrogen, and chlorine are present, respectively.

• Subscripts help in determining both molecular and empirical formulas.
• If you change a subscript, you change the compound's identity entirely.

The process of finding the empirical formula involves adjusting these subscripts to the simplest form using the GCD. Additionally, knowing the subscripts allows for calculations of molar mass, which is crucial for stoichiometry in chemical reactions. Therefore, understanding subscripts is vital for anyone studying chemistry, as they form the backbone of chemical notation.