Problem 22 - Chemistry: An Atoms-Focused Approach

Question

If an alkane and a cycloalkane have equal numbers of carbon atoms per molecule, do they have the same number of hydrogen atoms?

Step-by-Step Solution

Answer

Answer: No, when an alkane and a cycloalkane have equal numbers of carbon atoms per molecule, they do not have the same number of hydrogen atoms. Alkanes have 2 additional hydrogen atoms compared to cycloalkanes with the same number of carbon atoms.

Step 1: Write down the general formulas for alkanes and cycloalkanes

The general formula for alkanes is CnH2n+2, and the general formula for cycloalkanes is CnH2n.

Step 2: Compare the number of hydrogen atoms in both formulas

Given that the number of carbon atoms in both alkane and cycloalkane molecules is the same, we can denote this number with just 'n'. So, we just need to compare H2n+2 and H2n to see if they are equal.

Step 3: Determine if the number of hydrogen atoms is the same for both molecules

The number of hydrogen atoms in alkanes is H2n+2, while the number of hydrogen atoms in cycloalkanes is H2n. We can observe that they are different (H2n+2 ≠ H2n) because there are always 2 additional hydrogen atoms in alkanes compared to cycloalkanes with the same number of carbon atoms. Therefore, when an alkane and a cycloalkane have equal numbers of carbon atoms per molecule, they do not have the same number of hydrogen atoms.

Key Concepts

Alkanes

Alkanes are a fundamental class of hydrocarbons. These are the simplest type of organic molecules consisting only of carbon (C) and hydrogen (H) atoms. The carbon atoms in alkanes are connected through single bonds, creating a saturated structure. This means that each carbon atom forms the maximum number of single covalent bonds possible. The general formula for alkanes is \( \text{C}_n\text{H}_{2n+2} \). Here, \( n \) represents the number of carbon atoms, and the formula indicates that for every carbon atom, there are two hydrogen atoms plus two additional hydrogens.

Important characteristics of alkanes include:

• Saturation: Alkanes are also known as saturated hydrocarbons because they only have single bonds, making them quite stable and less reactive compared to other hydrocarbons.
• Physical state: Smaller alkanes, such as methane and ethane, are gases at room temperature, while larger alkanes can be liquids or solids.
• Usage: Alkanes are commonly used as fuels. Examples include propane (used in BBQ grills) and butane (found in lighters).

Alkanes form the backbone of organic chemistry, and understanding them is crucial for grasping more complex organic compounds.

Cycloalkanes

Cycloalkanes are another fascinating group of hydrocarbons. These molecules also consist of carbon and hydrogen, forming closed ring structures. This circular formation creates a distinct category of saturated hydrocarbons with the general formula \( \text{C}_n\text{H}_{2n} \). Each vertex of the ring represents a carbon atom bonded to two hydrogens when the ring is simple and contains no double or triple bonds.

Key features of cycloalkanes include:

• Ring Formation: Unlike alkanes, cycloalkanes form rings of carbon atoms which significantly affects their properties and reactivity.
• Isomerism: Cycloalkanes exhibit structural isomerism due to their ring structures. For example, cyclohexane and hexane have the same molecular formula but different structures.
• Physical Properties: Depending on the size, cycloalkanes can be gases, liquids, or solids, similar to alkanes.

Understanding cycloalkanes is essential for exploring the structural diversity of organic compounds, especially those in biological and synthetic materials.

Molecular Formulas

Molecular formulas provide a straightforward method to represent molecules, indicating the exact number of each type of atom present in a compound. For hydrocarbons like alkanes and cycloalkanes, molecular formulas reflect the ratio of carbon and hydrogen.For example:

• In an alkane, the molecular formula \( \text{C}_n\text{H}_{2n+2} \) suggests that for a compound with three carbon atoms, the formula would be \( \text{C}_3\text{H}_{8} \) (propane).
• For a cycloalkane with the same number of carbon atoms (three), the molecular formula is \( \text{C}_3\text{H}_{6} \) (cyclopropane).

This formulaic difference highlights how the presence of a ring in cycloalkanes affects the number of hydrogen atoms their structures can accommodate compared to open-chain alkanes.

This concise way of denoting compounds is vital for predicting chemical properties and reactions efficiently. Molecular formulas serve as the basis of understanding molecular structures and help in identifying both composition and potential reactivity in different chemical environments.