Problem 61 - Chemistry: An Atoms-Focused Approach

Question

How many carbon atoms are there in one molecule of each of the following compounds? (a) \(\mathrm{CH}_{4} ;\) (b) \(\mathrm{C}_{3} \mathrm{H}_{8} ;\) (c) \(\mathrm{C}_{6} \mathrm{H}_{6}\) (d) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)

Step-by-Step Solution

Answer

(a) CH4 (b) C3H8 (c) C6H6 (d) C6H12O6 Answer: (a) CH4: 1 carbon atom (b) C3H8: 3 carbon atoms (c) C6H6: 6 carbon atoms (d) C6H12O6: 6 carbon atoms

Step 1: Identify the carbon atoms in each molecule

For each molecule given, look for the chemical symbol C, which represents carbon atoms. The subscript next to the C symbol will tell you the number of carbon atoms in that specific molecule.

Step 2: Find the number of carbon atoms in \(\mathrm{CH}_{4}\)

In the molecule \(\mathrm{CH}_{4}\), we can see that there is one carbon atom (C) and four hydrogen atoms (H). So, the number of carbon atoms in this molecule is 1.

Step 3: Find the number of carbon atoms in \(\mathrm{C}_{3} \mathrm{H}_{8}\)

For the molecule \(\mathrm{C}_{3} \mathrm{H}_{8}\), we can see that there are three carbon atoms (C) and eight hydrogen atoms (H). So, the number of carbon atoms in this molecule is 3.

Step 4: Find the number of carbon atoms in \(\mathrm{C}_{6} \mathrm{H}_{6}\)

In the molecule \(\mathrm{C}_{6} \mathrm{H}_{6}\), we can see that there are six carbon atoms (C) and six hydrogen atoms (H). So, the number of carbon atoms in this molecule is 6.

Step 5: Find the number of carbon atoms in \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)

For the molecule \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), we can see that there are six carbon atoms (C), twelve hydrogen atoms (H), and six oxygen atoms (O). So, the number of carbon atoms in this molecule is 6.

Step 6: Summary

Now we have found the number of carbon atoms in each given molecule as follows: (a) \(\mathrm{CH}_{4}:\) 1 carbon atom (b) \(\mathrm{C}_{3} \mathrm{H}_{8}:\) 3 carbon atoms (c) \(\mathrm{C}_{6} \mathrm{H}_{6}:\) 6 carbon atoms (d) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}:\) 6 carbon atoms

Key Concepts

Chemical Formulas

Chemical formulas are a way of representing chemical substances using symbols for their constituent elements. Each element is represented by its chemical symbol, a one or two-letter shorthand derived from its name. For instance, carbon is denoted by 'C', and hydrogen is denoted by 'H'. These symbols are used in formulas to depict the composition of compounds.

Subscripts are small numbers written to the right and slightly below each chemical symbol. They indicate the number of atoms of that particular element in one molecule of the compound. For example, in the formula \( \mathrm{CH}_{4} \), the '4' is a subscript indicating there are four hydrogen (H) atoms attached to one carbon (C) atom. This representation provides a quick glance at the makeup of a molecule, showcasing what elements are involved and in what amounts.

Reading and understanding chemical formulas is crucial for determining a molecule's molecular structure and behavior in reactions. They serve as a universal language for chemists across the globe.

Molecular Composition

Molecular composition refers to the identities and ratios of atoms present in a chemical compound. It is the detailed structural blueprint that informs us how molecules are constructed from individual elements.

Knowing a compound's molecular composition allows us to understand its properties and how it might interact with other substances. For instance,

• \( \mathrm{CH}_{4} \) has one carbon and four hydrogen atoms, making it methane, a simple hydrocarbon.
• \( \mathrm{C}_{3} \mathrm{H}_{8} \), or propane, consists of three carbon atoms and eight hydrogen atoms, making it a more complex hydrocarbon compared to methane.
• \( \mathrm{C}_{6} \mathrm{H}_{6} \), known as benzene, contains six carbon atoms arranged in a ring, partnered with six hydrogen atoms, illustrating its aromatic nature.
• \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \), which is glucose, consists of carbon, hydrogen, and oxygen in a specific arrangement necessary for energy storage in cells.

With this information, chemists can predict chemical behavior, potential energy changes, and molecule reactivity.

Counting Atoms

Counting atoms in chemical formulas is a fundamental step in understanding how molecules are constructed and function. It requires recognizing the symbols of elements and interpreting the subscripts correctly.

Here's a simple guide to count atoms:

• Identify the chemical symbol for the atom you're examining, such as 'C' for carbon.
• Look for a subscript beside the symbol. This number indicates how many atoms of that element are present.
• If there's no subscript next to a symbol, it implies there is only one atom of that element in the molecule. For example, in \( \mathrm{CH}_{4} \), there is no subscript with 'C', meaning there's 1 carbon atom.

To count carbon atoms specifically, you would examine each chemical formula for the symbol 'C' and observe the subscript. For example:

• In \( \mathrm{CH}_{4} \), there is 1 carbon atom.
• In \( \mathrm{C}_{3} \mathrm{H}_{8} \), there are 3 carbon atoms.
• In \( \mathrm{C}_{6} \mathrm{H}_{6} \), there are 6 carbon atoms.
• In \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \), there also are 6 carbon atoms.

Counting atoms correctly allows us not only to understand single molecules but also to scale up to larger quantities, facilitating advancements in chemical equations and stoichiometry.