Question

Arrange these four molecules in increasing order of their biological energy content per mole: (a) Mannose (b) Stearic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{COOH}\) (c) Fructose (d) Palmitic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{14} \mathrm{COOH}\)

Short answer

Mannose ≈ Fructose < Palmitic acid < Stearic acid.

Step-by-step solution

Understand the Molecules

To find the biological energy content, first, consider the types of molecules: Mannose and Fructose are carbohydrates, while Stearic acid and Palmitic acid are fatty acids. Generally, fatty acids are more energy-dense than carbohydrates due to their higher numbers of C-H bonds.

Compare Carbohydrates

Compare Mannose and Fructose. Both are similar in structure, as they are monosaccharides with the same chemical formula, C6H12O6. Hence, their energy content is comparable.

Analyze Fatty Acids

Stearic acid (18 carbon chain) and Palmitic acid (16 carbon chain) are both long-chain saturated fatty acids. Longer chains generally have more energy due to more C-H bonds. Therefore, Stearic acid will have more energy per mole than Palmitic acid.

Rank Based on Energy Content

Fatty acids have greater energy content compared to carbohydrates. Among fatty acids, Stearic acid has more energy than Palmitic acid due to its longer carbon chain. Carbohydrates (Mannose and Fructose) have a lower energy content than fatty acids.

Arrange Molecules

Based on steps 2 through 4, the increasing order of energy content per mole is as follows: Mannose ≈ Fructose < Palmitic acid < Stearic acid.

Key concepts

Carbohydrates

Carbohydrates are essential macromolecules found in foods and living tissues. They are composed of carbon, hydrogen, and oxygen atoms, typically in a 1:2:1 ratio. Carbohydrates are vital because they serve as the body's primary energy source.

Monosaccharides like glucose, fructose, and mannose are the simplest forms of carbohydrates. These molecules usually have the formula \( C_6H_{12}O_6 \), which means they contain the same number of carbon and oxygen atoms. Although they share this formula, their structure varies slightly, leading to different properties and reactivity.

Carbohydrates release energy during metabolism, especially glucose, which plays a key role in cellular respiration. However, when compared to fatty acids, carbohydrates generally have lower energy content because each carbon atom is bonded to more oxygen—meaning less available energy per gram.

Fatty Acids

Fatty acids are long-chain hydrocarbons with a carboxyl group \( \text{(-COOH)} \) at one end. They are primarily found in fats and oils and are a significant energy source in the diet.

Fatty acids can be classified as saturated and unsaturated. In the context of our discussion, we focus on saturated fatty acids like stearic and palmitic acids. These fatty acids have no double bonds between carbon atoms, allowing the maximum number of hydrogen atoms to attach to the carbon chain.

This high number of C-H bonds makes fatty acids denser in energy compared to carbohydrates. When metabolized, these bonds release substantial amounts of energy, providing a more intense form of fuel for bodily processes, particularly during prolonged physical activity or fasting. Fatty acids are stored in the body in the form of triglycerides.

Molecular Structure

The structure of a molecule profoundly influences its biological roles and energy content. The molecular structure determines how many bonds a molecule can form, affecting its stability and energy release potential.

Carbohydrates like mannose and fructose have a ring-like structure with numerous hydroxyl groups \(( -\text{OH} )\). This arrangement impacts their solubility in water and means they readily participate in chemical reactions necessary for life. Their energy release is quick but not as potent as that from fatty acids.

In contrast, fatty acids with extended chains—like stearic and palmitic acid—contain numerous C-H bonds. These bonds store more energy and release it when broken during metabolism. The length of the carbon chain in fatty acids further enhances energy storage, as longer chains mean more bonds.

Energy Density

Energy density refers to the amount of energy stored in a given mass of substance. In the context of biology and nutrition, understanding energy density helps determine how much energy we obtain from different foods.

Carbohydrates generally have an energy density of about 4 kilocalories per gram. Their energy is quickly accessible, making them suitable for immediate energy demands. Despite this quick energy release, their shorter carbon chains and higher oxygen content limit the total energy they can provide.

On the other hand, fats, primarily made up of fatty acids like stearic and palmitic acid, have a much higher energy density, about 9 kilocalories per gram. The lack of oxygen atoms per carbon in fatty acids means more energy is released during oxidation. As such, fats serve as a longer-term energy source and contribute significantly to thermal regulation and cell structure maintenance.