Problem 84 - Chemistry The Molecular Nature of Matter

Question

A sample of Freon was found to contain \(0.423 \mathrm{~g}\) of \(\mathrm{C}\), \(2.50 \mathrm{~g}\) of \(\mathrm{Cl}\), and \(1.34 \mathrm{~g}\) of \(\mathrm{F}\). What is the empirical formula of this compound?

Step-by-Step Solution

Answer

The empirical formula of the compound is CClF.

Step 1: Calculate moles of each element

First, determine the moles of carbon (C), chlorine (Cl), and fluorine (F) by dividing the mass of each element by its atomic mass (atomic mass of C = 12.01 g/mol, Cl = 35.45 g/mol, F = 19.00 g/mol): - Moles of C = 0.423 g / 12.01 g/mol - Moles of Cl = 2.50 g / 35.45 g/mol - Moles of F = 1.34 g / 19.00 g/mol.

Step 2: Divide by the smallest number of moles

Calculate the mole ratio of each element by dividing the number of moles of each by the smallest number of moles obtained in step 1.

Step 3: Determine the empirical formula

Use the mole ratios to write the empirical formula. The mole ratios may not be whole numbers; if not, multiply all ratios by the same factor to get the smallest whole numbers possible. The empirical formula is then written using these whole number ratios.

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the elements and compounds as they undergo chemical reactions and transformations. It is essentially the math behind chemistry. Stoichiometry allows chemists to make predictions about the outcomes of chemical reactions, including how much product will form and how much reactant is needed to produce a certain amount of product.

To perform stoichiometric calculations, one must first understand the mole concept and molar mass, as they are the foundational pieces. By relating mass to moles and moles to the number of atoms or molecules, we can use stoichiometry to calculate the empirical formula of a compound. In the problem provided, stoichiometry is used to find the ratio of atoms within the Freon sample, leading to the empirical formula. Here, the masses of individual elements are converted to moles, which provide a common measurement for comparing the elemental composition.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a bridge between the atomic world (atoms, molecules) and the macroscopic world we can measure and observe (grams, liters). One mole is defined as the amount of substance that contains as many entities (atoms, ions, molecules) as there are in 12 grams of carbon-12, which is approximately 6.022 x 1023 entities and is known as Avogadro's number.

In practical terms, the mole concept allows chemists to count atoms or molecules by weighing them. For the given Freon sample, each element's mass is divided by its atomic mass (or molar mass) to find out how many moles of each element are present. The mole concept simplifies the calculation by converting different elements' masses, which vary greatly, to a common scale – moles – allowing for an easy comparison and further stoichiometric calculations. In chemical formulas, the mole ratios determine the number of atoms of each element that combine to form a compound.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of the elements present in a molecule as provided on the periodic table. The molar mass of an element is numerically equivalent to its atomic mass and serves as a conversion factor between grams and moles.

Using the molar mass, we can convert the mass of an element in a sample to moles, which is the first step in determining the empirical formula. In the exercise, the molar masses of carbon, chlorine, and fluorine are used to convert the mass of each element in the Freon sample to moles. It's crucial to measure the molar mass accurately, as it directly affects the stoichiometry and the final empirical formula of the compound.