Question

Carbohydrates, a class of compounds containing the elements carbon, hydrogen, and oxygen, were originally thought to contain one water molecule \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) for each carbon atom present. The carbohydrate glucose contains six carbon atoms. Write a general formula showing the relative numbers of each type of atom present in glucose.

Short answer

The general formula for glucose, based on the relative numbers of each type of atom, is \[C_6H_{12}O_6\].

Step-by-step solution

Identify the number of carbon atoms

We are given that glucose has 6 carbon atoms, so our formula will include 6 Carbon atoms represented as C_6.

Determine the number of hydrogen atoms

Since there is one water molecule (H2O) for each carbon atom and glucose has 6 carbon atoms, we can say there are 6 water molecules. Considering there are 2 hydrogen atoms in a water molecule, we will have a total of 2*6=12 hydrogen atoms, which we will represent as H12 in the formula.

Determine the number of oxygen atoms

We know each water molecule contains 1 oxygen atom. We have 6 water molecules, so there are 6 oxygen atoms associated with the water molecules. We represent this as O6 in the formula.

Write the general formula

Now, we know the proportions of each type of atom present in glucose. We just need to combine them in a formula. The resulting general formula for glucose is: \[C_6H_{12}O_6\] This formula represents the molecular structure of glucose, with 6 carbon, 12 hydrogen, and 6 oxygen atoms present.

Key concepts

Carbohydrates

Carbohydrates are a vital class of organic compounds composed of carbon, hydrogen, and oxygen. They play essential roles in biological processes, mainly acting as a primary source of energy for both plants and animals. These compounds are generally divided into three main types: **sugars**, **starch**, and **fibers**. Glucose is a type of sugar, which is a simple carbohydrate or **monosaccharide**. Unlike starchy carbohydrates, which consist of multiple sugar units, monosaccharides are single-unit sugars.

One key feature of carbohydrates is their general empirical formula \( ext{C}_n( ext{H}_2 ext{O})_n \), which explains why they are sometimes described as "hydrates of carbon." This formula highlights the 2:1 ratio of hydrogen to oxygen, similar to water. However, not all carbohydrates strictly adhere to this formula, especially more complex ones.

Chemical Formulas

Chemical formulas, such as the one for glucose, \( ext{C}_6 ext{H}_{12} ext{O}_6 \), express the composition of molecules in terms of the atoms they contain. These formulas give us a clear understanding of the proportions of each element within the compound.

By looking at the chemical formula of glucose, we can determine it contains:

• 6 Carbon atoms
• 12 Hydrogen atoms
• 6 Oxygen atoms

These formulas not only tell us the number of atoms but also allow us to infer other properties, such as molecular mass. In glucose, the arrangement and bond distribution of these atoms define its specific properties and functionalities.

Molecular Structure

The molecular structure of a compound like glucose refers to the three-dimensional arrangement of its atoms in space. This structure heavily influences the compound's biological and chemical properties. In the case of glucose, each carbon atom is tetrahedrally bonded, facilitating its ability to form various structural isomers that can perform different functions in living organisms.

One critical aspect of the glucose molecular structure is its **ring formation**, which arises in aqueous solutions when the molecule forms a cyclic compound, a pyranose ring. This arrangement has significant implications for glucose's metabolism and functionality within biological systems. The distinctive structural arrangements contribute to glucose's role as an essential energy source in cellular respiration.

Organic Chemistry

Organic chemistry is the branch of chemistry that deals with the structure, properties, and reactions of organic compounds containing carbon. Glucose and its chemical formula \( ext{C}_6 ext{H}_{12} ext{O}_6 \) is a classic example of an organic molecule studied within this field. Organic chemistry explores how glucose interacts with other molecules, participates in biochemical reactions, and supports life.

• The study of glucose involves understanding its synthesis paths and breakdown processes, such as glycolysis and photosynthesis.
• Organic chemists also investigate how glucose's structure leads to different reactivity patterns and serves as a building block for more complex carbohydrates.

Organic chemistry not only explains the properties of glucose itself but also its transformations and roles in broader biological systems. Understanding these aspects helps us utilize carbohydrates in medicine, agriculture, and industry.