Problem 8 - Chemistry A Guided Inquiry

Question

a) What number of carbon atoms are found in one dozen methane, \(\mathrm{CH}_{4}\), molecules? b) What number of carbon atoms is found in one dozen carbon tetrachloride, \(\mathrm{CCl}_{4}\), molecules?

Step-by-Step Solution

Answer

There are 12 carbon atoms in a dozen methane molecules and 12 carbon atoms in a dozen carbon tetrachloride molecules.

Step 1: Understand the Composition of Molecules

First, it's required to understand the composition of the given molecules. For a molecule of Methane (\(\mathrm{CH}_{4}\)), there's only one carbon atom and in a molecule of Carbon Tetrachloride (\(\mathrm{CCl}_{4}\), there's just one carbon atom as well.

Step 2: Calculate the Carbon Atoms for Methane

To calculate the number of carbon atoms in a dozen Methane molecules, multiply the number of molecules (a dozen, which is 12) by the number of carbon atoms in one molecule of Methane, which is 1. This gives 12 x 1 = 12 carbon atoms.

Step 3: Calculate the Carbon Atoms for Carbon Tetrachloride

Similarly, to calculate the number of carbon atoms in a dozen Carbon Tetrachloride molecules, multiply the number of molecules (a dozen, which is 12) by the number of carbon atoms in one molecule of Carbon Tetrachloride, which is 1. This again gives 12 x 1 = 12 carbon atoms.

Key Concepts

Understanding Carbon Atoms

Carbon atoms are fundamental building blocks in organic chemistry. Each carbon atom has the ability to form four covalent bonds with other atoms. This tetravalency allows carbon to form a vast array of complex structures, permitting enormous diversity in organic molecules. For instance, in molecules like methane and carbon tetrachloride, the carbon atom forms bonds with different atoms.

• In methane (\(\mathrm{CH}_{4}\)), a single carbon atom bonds with four hydrogen atoms.
• In carbon tetrachloride (\(\mathrm{CCl}_{4}\)), a single carbon atom forms bonds with four chlorine atoms.

Recognizing the number of carbon atoms in a molecule is crucial when performing calculations in molecular chemistry.

Methane and Its Molecular Structure

Methane is one of the simplest organic compounds and provides a fundamental way to understand carbon bonding. In methane, represented by the formula \(\mathrm{CH}_{4}\), the molecule consists of one carbon atom bonded to four hydrogen atoms. The arrangement results in a tetrahedral shape, which is one of the most stable configurations for molecules in chemistry.

In practical calculations, if you have a dozen methane molecules, you simply multiply 12 (the number of molecules in a dozen) by 1 (the number of carbon atoms per molecule). This gives you a total of 12 carbon atoms. Methane serves as an essential example in chemistry due to its simple structure and abundance in natural gas.

Carbon Tetrachloride and Its Composition

Carbon tetrachloride is another key molecule in studying carbon's interaction with other elements. Notably, it consists of one carbon atom bonded to four chlorine atoms, represented chemically as \(\mathrm{CCl}_{4}\). Similar to methane, the carbon atom forms tetrahedral bonds, but in this case with chlorine atoms that are larger than hydrogen, making the molecule denser.

To calculate the total number of carbon atoms in a dozen carbon tetrachloride molecules, the process mirrors that of methane. Multiply 12 (the dozen molecules) by 1 (the single carbon atom per molecule), resulting in 12 carbon atoms. This understanding can help students visualize molecular interactions and the nature of covalent bonding in more complex organic chemistry structures.