Question

How many chlorine atoms are in each of the following? a. \(124 \mathrm{CCl}_{4}\) molecules b. \(38 \mathrm{HCl}\) molecules c. \(89 \mathrm{CF}_{2} \mathrm{Cl}_{2}\) molecules d. \(1368 \mathrm{CHCl}_{3}\) molecules

Short answer

There are 496 chlorine atoms in 124 CCl4 molecules, 38 atoms in 38 HCl molecules, 178 atoms in 89 CF2Cl2 molecules, and 4104 atoms in 1368 CHCl3 molecules.

Step-by-step solution

Analyzing the molecule CCl4

Each molecule of CCl4 contains 4 chlorine atoms. To find the total number of chlorine atoms in 124 CCl4 molecules, multiply the number of molecules by the number of chlorine atoms per molecule.

Calculating the chlorine atoms in CCl4

Multiply 124 molecules of CCl4 by 4 atoms of chlorine per molecule to get the total number of chlorine atoms: 124 * 4 = 496.

Analyzing the molecule HCl

Each molecule of HCl contains 1 chlorine atom. To find the total number of chlorine atoms in 38 HCl molecules, multiply the number of molecules by the number of chlorine atoms per molecule.

Calculating the chlorine atoms in HCl

Multiply 38 molecules of HCl by 1 atom of chlorine per molecule to get the total number of chlorine atoms: 38 * 1 = 38.

Analyzing the molecule CF2Cl2

Each molecule of CF2Cl2 contains 2 chlorine atoms. To find the total number of chlorine atoms in 89 CF2Cl2 molecules, multiply the number of molecules by the number of chlorine atoms per molecule.

Calculating the chlorine atoms in CF2Cl2

Multiply 89 molecules of CF2Cl2 by 2 atoms of chlorine per molecule to get the total number of chlorine atoms: 89 * 2 = 178.

Analyzing the molecule CHCl3

Each molecule of CHCl3 contains 3 chlorine atoms. To find the total number of chlorine atoms in 1368 CHCl3 molecules, multiply the number of molecules by the number of chlorine atoms per molecule.

Calculating the chlorine atoms in CHCl3

Multiply 1368 molecules of CHCl3 by 3 atoms of chlorine per molecule to get the total number of chlorine atoms: 1368 * 3 = 4104.

Key concepts

Chemical Formulas

Understanding chemical formulas is critical when you're looking to count atoms in molecules. Chemical formulas, such as \textbf{CCl\(_4\)}, \textbf{HCl}, \textbf{CF\(_2\)Cl\(_2\)}, and \textbf{CHCl\(_3\)} from the exercise, are shorthand representations of the composition of a substance. Each letter stands for an element from the periodic table, and the subscript numbers indicate how many atoms of each element are present in a molecule. If there is no subscript, it means there is only one atom of that element in the molecule.

For instance, the molecule \textbf{CCl\(_4\)} is composed of one carbon (C) atom and four chlorine (Cl) atoms. It's crucial to understand this representation because it sets the basis for further calculations like counting the total number of a particular atom within a sample of molecules. A common mistake students make is overlooking the subscripts, which can lead to incorrect atom counts. Therefore, always check for and interpret these numbers carefully.

Mole Concept

The mole concept is an essential bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and liters that we observe. One mole (abbreviated as 'mol') is defined as Avogadro's number (\textbf{6.022 x 10\(^{23}\)}) of something, whether they are atoms, molecules, electrons, or any other specified entities. The importance of the mole lies in its ability to relate a chemical formula to a tangible quantity of substance.

When dealing with individual molecules, like in the given exercise, you do not need to dive deeply into the mole concept. However, understanding that a mole represents a set quantity provides a foundation for comprehending more complex scenarios like reacting masses in stoichiometry. Keep in mind, being fluent in the language of moles is crucial for any chemistry student.

Stoichiometry

Stoichiometry is the quantitative study of the reactants and products in a chemical reaction. It is grounded in the law of conservation of mass where the total mass of the reactants equals the total mass of the products. The principles of stoichiometry are employed when you need to predict the amounts of substances consumed and produced in a reaction, much like a recipe tells you how much of each ingredient you need to prepare a dish.

In practice, stoichiometry involves using balanced chemical equations to calculate the mass or volume of a reactant or product, or even the number of atoms or molecules, as demonstrated in the original exercise. It makes use of the mole concept to convert between mass and number of particles since balanced equations indicate the ratio of moles of reactants to moles of products. For instance, if you know the number of molecules you have, you can determine the number of moles and subsequently calculate the mass of substance needed or produced. It's a sequential process that ties together the initial and final stages of a chemical reaction quantitatively.