Problem 80 - Chemistry Matter and Change

Question

The general formula for alkanes is \(\mathrm{C}_{n} \mathrm{H}_{2 n+2} .\) Determine the general formula for cycloalkanes.

Step-by-Step Solution

Answer

The general formula for cycloalkanes is \(C_nH_{2n}\).

Step 1: Understanding Alkanes Formula

The formula for alkanes is given as \( C_nH_{2n+2} \). In this formula, \(n\) represents the number of carbon atoms.

Step 2: Closed Ring Structure of Cycloalkanes

Cycloalkanes are alkanes that have one or more rings of carbon atoms. Each ring decreases the number of hydrogen atoms because a pair of hydrogen atoms is removed to allow the end carbon atoms to join.

Step 3: Derive the Cycloalkane Formula

For each ring in a cycloalkane, two hydrogen atoms are removed compared to the alkane structure. Therefore, for a single ring cycloalkane, the formula is \(CnH_{2n}\), because we remove two hydrogens from the original formula \(CnH_{2n+2}\).

Step 4: State the Formula for Cycloalkanes

The general formula for cycloalkanes is \(C_nH_{2n}\), indicating that they are saturated hydrocarbons with one ring structure.

Key Concepts

Alkanes

Alkanes are a fundamental category of hydrocarbons. They consist entirely of carbon and hydrogen atoms joined together by single bonds. These molecules are known as "saturated" because they have the maximum number of hydrogen atoms possible, given the number of carbon atoms in the molecule. Alkanes are the simplest type of hydrocarbon and form the basis of many organic compounds.
Key features include:

• Single covalent bonds between carbon atoms.
• General chemical formula: \(C_nH_{2n+2}\).
• They are nonpolar molecules, making them insoluble in water but soluble in organic solvents.
• Typically found in natural gas and petroleum.

Chemical formula

Chemical formulas allow us to understand the composition of molecules at a glance. For alkanes, the formula \(C_nH_{2n+2}\) provides essential information. Here, \(n\) stands for the number of carbon atoms in the molecule, and according to this formula, the number of hydrogen atoms is twice the number of carbon atoms, plus two.
When converting alkanes to cycloalkanes, which form a ring structure, this formula changes because each ring requires the removal of two hydrogens to close the loop. Understanding these formulas helps in predicting molecular structures and reactions in organic chemistry.

Carbon rings

Carbon rings are an intriguing aspect of organic molecules, formed when carbon atoms link together at their ends to create a closed loop or "ring." Cycloalkanes contain one or more of these rings, altering the molecular formula compared to their straight-chain counterparts.
Key aspects of carbon rings include:

• The formation of rings leads to a reduction of hydrogen atoms. For cycloalkanes, the formula becomes \(C_nH_{2n}\).
• Rings can have varying numbers of carbon atoms, with the most common being five or six.
• The chemical properties of the molecules often change once a ring is formed, affecting reactivity and interactions with other compounds.

Saturated hydrocarbons

Saturated hydrocarbons are compounds that contain only single bonds between carbon atoms. Alkanes and cycloalkanes fall under this category.
Key points to remember about saturated hydrocarbons are:

• They have no double or triple bonds, making them chemically stable.
• Both alkanes and cycloalkanes are saturated, but cycloalkanes have rings, which can affect their physical properties.
• Saturated hydrocarbons typically have higher melting and boiling points compared to unsaturated hydrocarbons.
• They are used widely in fuels, lubricants, and in the manufacturing of various chemicals.