Problem 9 - Chemistry A Guided Inquiry

Question

a) What number of hydrogen atoms is found in one dozen methane molecules? b) What number of chlorine atoms is found in one dozen carbon tetrachloride molecules? c) Explain how you arrived at your answer to part b using grammatically correct sentences.

Step-by-Step Solution

Answer

a) There are 48 hydrogen atoms in a dozen methane molecules.\nb) There are 48 chlorine atoms in a dozen carbon tetrachloride molecules.\nc) The answer was arrived at by understanding the molecular structure of carbon tetrachloride, counting the number of chlorine atoms in one molecule, and then multiplying by the given quantity (one dozen).

Step 1: Number of Hydrogen Atoms in a Methane molecule

A methane molecule consists of 1 carbon atom and 4 hydrogen atoms. So, every molecule of methane has 4 atoms of hydrogen.

Step 2: Calculate Hydrogen Atoms in One Dozen Methane Molecules

A dozen equals 12. Therefore, in one dozen methane molecules, there will be 12 (dozen) multiplied by 4 (number of hydrogen atoms in one molecule), which equals 48 hydrogen atoms.

Step 3: Determine the Number of Chlorine Atoms in a Carbon Tetrachloride molecule

A carbon tetrachloride (CCl4) molecule consists of 1 carbon atom and 4 chlorine atoms. Hence, every molecule of carbon tetrachloride has 4 atoms of chlorine.

Step 4: Calculate Chlorine Atoms in One Dozen Carbon Tetrachloride Molecules

As established previously, a dozen equals 12 items. Therefore, there would be 12 (dozen) multiplied by 4 (number of chlorine atoms in one molecule), which equals 48 chlorine atoms.

Step 5: Formulate Your Explanation for Part B

In order to answer part b, consider the molecular structure of carbon tetrachloride. It consists of 1 carbon atom and 4 chlorine atoms. Therefore, in a single molecule of carbon tetrachloride there are 4 chlorine atoms. Given that we were looking for the number of chlorine atoms in a dozen such molecules, we multiplied the 4 chlorine atoms by 12. So, there are 48 chlorine atoms in a dozen carbon tetrachloride molecules.

Key Concepts

Chemical Formulas

Understanding chemical formulas is crucial in chemistry as they provide information about the types and numbers of atoms in a molecule. Each element in a formula is represented by chemical symbols that correspond to elements on the periodic table. These symbols are often accompanied by subscript numbers, which denote the number of atoms of each element in the compound.
For example, the chemical formula for methane is CH extsubscript{4}, indicating one carbon (C) atom bonded to four hydrogen (H) atoms. Similarly, the formula for carbon tetrachloride is CCl extsubscript{4}, showing one carbon atom bonded to four chlorine (Cl) atoms. By interpreting these formulas, you can quickly determine the atomic composition of a molecular compound, which is essential for stoichiometric calculations.

Molecular Compounds

Molecular compounds are made up of molecules, which are groups of atoms bonded together. These compounds consist typically of nonmetals. For instance, in methane (CH extsubscript{4}) and carbon tetrachloride (CCl extsubscript{4}), nonmetals such as carbon, hydrogen, and chlorine are interconnected by chemical bonds to form stable compounds.
The structure of a molecule can be represented by its formula, which notifies for both the ratio and quantity of the atoms forming the compound. Recognizing these molecular structures helps in identifying how atoms are arranged and in determining their stoichiometry. This is particularly useful when conducting chemical reactions, as it aids in predicting product quantities and reacting proportions.

Atomic Counting

Atomic counting involves determining the number of individual atoms of each element present in a given amount of a molecular compound. This is a foundational skill for performing stoichiometric calculations.
The process involves interpreting chemical formulas and using simple multiplication to extend these counts over multiple molecules. For example, knowing that a single molecule of methane contains four hydrogen atoms allows you to calculate the total number of hydrogen atoms in a dozen (12) methane molecules: 4 hydrogen atoms per molecule multiplied by 12 molecules equals 48 hydrogen atoms.
Through atomic counting, you not only count the atoms in individual molecules but also scale this count for larger quantities of the substance, allowing you to understand the full makeup of the sample.

Chemical Calculations

Chemical calculations employ mathematical techniques to predict quantifiable outcomes in chemical reactions. These calculations include determining the amounts of reactants and products involved.
In stoichiometry, which deals extensively with chemical calculations, you often use the concept of the mole as a base unit to relate mass quantities to the number of molecules or atoms. For exercises such as determining the number of atoms in a dozen molecules, the dozen concept simplifies calculations by ensuring a clear-cut conversion.
In our example exercise, determining the number of atoms within a defined set (dozen) involved basic multiplication with known quantities—the atomic ratio given by the molecular formula was pivotal here. Understanding and mastering these down-to-earth calculations are essential for executing more complex chemical stoichiometry efficiently.