Question

What is the "general" formula for an alkane? Show how this general formula can be used to determine the number of hydrogens that would be present for an alkane with twenty carbon atoms.

Short answer

The general formula for an alkane is \(C_nH_{2n+2}\), where n represents the number of carbon atoms. To find the number of hydrogens in an alkane with 20 carbon atoms, substitute n = 20 into the formula: \(2 \times 20 + 2 = 42\). Hence, an alkane with 20 carbon atoms has 42 hydrogen atoms.

Step-by-step solution

Define an alkane and provide its general formula

An alkane is a hydrocarbon consisting of only carbon and hydrogen atoms, with all carbon-carbon and carbon-hydrogen bonds being single bonds. The general formula for an alkane is \(C_nH_{2n+2}\), where n represents the number of carbon atoms in the alkane.

Apply the general formula to find the number of hydrogens in an alkane with 20 carbon atoms

To find the number of hydrogens in an alkane with 20 carbon atoms, substitute n = 20 into the general formula: Number of H atoms = \(2 \times 20 + 2\)

Calculate the number of hydrogens

After substituting the value of n in the formula, we can calculate the number of hydrogens: Number of H atoms = \(2 \times 20 + 2 = 40 + 2 = 42\) So, an alkane with 20 carbon atoms has 42 hydrogen atoms.

Key concepts

Understanding Hydrocarbons

Hydrocarbons are the simplest form of organic compounds, consisting entirely of hydrogen and carbon atoms. They serve as the fundamental building blocks for various organic substances and are categorized based on the types of bonds between carbon atoms. Alkanes form a subset of hydrocarbons where the carbon atoms are connected exclusively by single bonds, making them saturated hydrocarbons.

These compounds are prevalent in natural resources like oil and natural gas and are used as fuels and lubricants due to their energy-rich composition. Hydrocarbons are not only fuel sources but also starting points for creating plastics, synthetic fibers, and pharmaceuticals, showcasing their importance in both energy and materials science.

The Realm of Organic Chemistry

Organic chemistry is the discipline that explores the structure, properties, composition, reactions, and synthesis of carbon-containing compounds. While it includes a vast array of substances, including both naturally occurring and synthetic materials, it's grounded on the understanding of carbon's unique ability to form stable bonds with itself and other elements.

Organic compounds range from simple molecules like methane to complex structures like DNA. Studying organic chemistry equips us with the knowledge to innovate in fields like pharmaceuticals, petrochemicals, and material sciences, reinforcing its importance in both academic and applied sciences.

Deciphering Chemical Formulas

A chemical formula is a symbolic representation of a substance's composition. It indicates the types and numbers of atoms present in the smallest representative unit of a substance. In organic chemistry, this often translates to understanding how many of each atom a molecule contains.

In the context of an alkane, the general formula is pivotal in determining its structure. For alkanes, the formula is represented as CnH2n+2, where n is the number of carbon atoms. This formula is key in predicting the number of hydrogen atoms when given the number of carbon atoms, illustrating the direct relationship between them.

Alkane Structure Explained

Alkanes have a straightforward yet versatile structure that follows the general formula CnH2n+2. This formula reflects that alkanes are composed solely of single bonds between carbon atoms and hydrogen atoms. This simplicity lends alkanes their stability and defines their physical and chemical properties.

An alkane's structure can be envisioned as a tree, where each carbon (C) represents a branch and the hydrogens (H) the leaves. The saturated nature of alkanes, meaning all carbon atoms form four single bonds, allows for a variety of shapes and sizes. For example, methane (CH4) is the simplest alkane with one carbon atom, while eicosane, with twenty carbon atoms (C20H42), shows how the formula scales with size.