Problem 36 - Chemistry for Allied Health

Question

How many moles of carbon are in \(0.75\) moles of \(\mathrm{CCl}_{4}\) ? How many moles of chlorine?

Step-by-Step Solution

Answer

0.75 moles of carbon; 3.0 moles of chlorine.

Step 1: Identify the Components of Molecule

The molecule \(\mathrm{CCl}_{4}\) consists of one carbon atom and four chlorine atoms. We will first consider the contributions of each atom individually.

Step 2: Determine Moles of Carbon in Molecule

Since \(\mathrm{CCl}_{4}\) has one carbon atom per molecule, the number of moles of carbon is directly equal to the number of moles of \(\mathrm{CCl}_{4}\).

Step 3: Calculate Moles of Carbon

Given \(0.75\) moles of \(\mathrm{CCl}_{4}\), the moles of carbon are also \(0.75\) because each molecule has one C atom.

Step 4: Determine Moles of Chlorine in Molecule

Each \(\mathrm{CCl}_{4}\) molecule contains 4 chlorine atoms.

Step 5: Calculate Moles of Chlorine

To find the moles of chlorine, we multiply the moles of \(\mathrm{CCl}_{4}\) by the 4 Chlorine atoms per molecule: \(0.75 \, \text{moles of} \, \mathrm{CCl}_{4} \times 4 = 3.0\) moles of chlorine.

Key Concepts

Atomic Composition

When discussing chemical substances, atomic composition refers to the types and numbers of atoms that make up a molecule. For instance, the molecular formula \(\mathrm{CCl}_{4}\) describes the compound known as carbon tetrachloride. This molecule is composed of:

• 1 carbon atom
• 4 chlorine atoms

The representation of a molecule with these numbers is crucial because it helps us understand the molecule's structure and how it participates in chemical reactions. Knowing the atomic composition allows chemists to calculate important properties, like the number of moles of each atom in a given quantity of the compound.

Chemical Formulas

A chemical formula conveys information about the different types of atoms that are present in a chemical compound and their respective quantities. Using \(\mathrm{CCl}_{4}\) as an example, the formula tells us that each molecule consists of one carbon atom and four chlorine atoms. These formulas are akin to a "recipe" for molecules and are vital in identifying and comparing substances.The subscript numbers in a chemical formula indicate the number of each type of atom within a single molecule (if no subscript is present, it is understood as 1). Understanding and interpreting chemical formulas is the first step in carrying out mole calculations,allowing us to relate the mass of a compound to the count of constituent atoms.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. It relies on the law of conservation of mass, where mass is neither created nor destroyed in a closed system. This concept extends to mole calculations, where the quantities of reactants and products can be predicted from the balanced equation.To find out how many moles of a particular element are in a compound, such as \(\mathrm{CCl}_{4}\), stoichiometry involves using the mole ratio derived from the compound's chemical formula. For example, knowing that each molecule of \(\mathrm{CCl}_{4}\) contains four chlorine atoms allows us to multiply the moles of \(\mathrm{CCl}_{4}\) by 4 to calculate the total moles of chlorine. Hence, with \(0.75\) moles of \(\mathrm{CCl}_{4}\), multiplying by the 4 chlorine atoms gives \(3.0\) moles of chlorine, illustrating the application of stoichiometric relationships seamlessly.