Question

What is the total number of atoms in a molecule of each of the following compounds? (a) citric acid (in citrus fruit), \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{OH}(\mathrm{COOH})_{3}\) (b) lactic acid (in sore muscles), \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{OH}) \mathrm{COOH}\)

Short answer

Citric acid has 21 atoms, and lactic acid has 12 atoms.

Step-by-step solution

Break Down the Chemical Formula of Citric Acid

The given chemical formula for citric acid is \( \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{OH}(\mathrm{COOH})_{3} \). First, identify each component in this compound: \( \mathrm{C}_3 \), \( \mathrm{H}_4 \), \( \mathrm{OH} \), and \( (\mathrm{COOH})_3 \).

Key concepts

Citric Acid Formula

Citric acid is a naturally occurring compound found in citrus fruits and plays a significant role in their acidic taste. Understanding its chemical formulation is key to comprehending its structure and properties. The molecular formula of citric acid is represented as \( \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{OH}(\mathrm{COOH})_{3} \), and here's how we can break it down:

• \( \mathrm{C}_{3} \) indicates three carbon atoms.
• \( \mathrm{H}_{4} \) suggests four hydrogen atoms attached to carbon atoms.
• \( \mathrm{OH} \) presents a hydroxyl group, contributing one oxygen and one hydrogen atom.
• \((\mathrm{COOH})_{3} \) encapsulates three carboxyl groups, each consisting of one carbon, two oxygen, and one hydrogen atom.

The presence of the carboxyl groups is what gives citric acid its "acidic" characteristic, making it a vital part of metabolic pathways, such as the citric acid cycle.
Breaking down the formula helps to visualize and understand the specific components that give citric acid its unique features and behavior in chemical reactions.

Lactic Acid Formula

Lactic acid is another important organic compound commonly associated with muscle soreness after intense physical activity. Its molecular composition is expressed as \( \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{OH}) \mathrm{COOH} \). Let's dissect this formula step by step:

• \( \mathrm{C}_{2} \) reflects a pair of carbon atoms at its core.
• \( \mathrm{H}_{4} \) comprises four hydrogens spread within the molecule.
• \( \mathrm{(OH)} \) is an additional hydroxyl group, which adds another oxygen and hydrogen to the structure.
• \( \mathrm{COOH} \) is a standalone carboxyl group, imparting the acid characteristic due to its carbon, hydroxyl (OH), and double-bonded oxygen components.

In the body, lactic acid is formed during anaerobic respiration when oxygen levels are low. This formula breakdown helps elucidate the balance and interaction of atoms in lactic acid, explaining how it functions in both biological and chemical contexts.
Understanding lactic acid's structure aids in grasping why it accumulates during exercise and how it’s used in food and pharmaceutical industries.

Chemical Formula Breakdown

Breaking down a chemical formula involves identifying and counting each type of atom present in a compound. This process is crucial for understanding how different molecules are structured and react with each other. Let’s illustrate this with both citric and lactic acid as examples.

In citric acid \( \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{OH}(\mathrm{COOH})_{3} \), each group of atoms contributes to the compound's overall characteristics:

• The three carbon atoms in the \( \mathrm{C}_{3} \) and additional carbons in \((\mathrm{COOH})_{3} \) define the backbone of the molecule.
• Hydrogen atoms from \(\mathrm{H}_{4}\), \(\mathrm{OH} \), and carboxyl groups provide the necessary polar characteristics and binding versatility.
• Overall, this formula compiles to give citric acid a total of 21 atoms.

Lactic acid \( \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{OH}) \mathrm{COOH} \), on the other hand, has fewer components but still forms a complex structure:

• Carbon and hydrogen work together with oxygen from \( \mathrm{OH} \) and \( \mathrm{COOH} \) to form 12 atoms in total.

By understanding the breakdown, we examine how each atom contributes to the chemical identity, influencing properties such as reactivity, acidity, and solubility. It’s a fundamental skill in chemistry that aids in the design and optimization of chemical compounds.​