Question

Many foods contain interesting compounds that give them their flavors and smells. Some of these compounds are listed below with the chemical composition given after each name. Write the formulas for these compounds. (a) Allicin gives garlic its flavor (6 carbons, 10 hydrogens, 1 oxygen, and 2 sulfurs). (b) Capsaicin gives peppers their heat (18 carbons, 27 hydrogens, 1 nitrogen, and 3 oxygens). (c) Limonene gives oranges their fragrance (10 carbons and 16 hydrogens).

Short answer

Allicin: \(\text{C}_6\text{H}_{10}\text{OS}_2\), Capsaicin: \(\text{C}_{18}\text{H}_{27}\text{NO}_3\), Limonene: \(\text{C}_{10}\text{H}_{16}\)

Step-by-step solution

Understand the Problem

Identify that each compound's formula must be written using the symbols of the elements provided along with their quantities.

Write the Formula for Allicin

For Allicin, the formula should include 6 carbons (C), 10 hydrogens (H), 1 oxygen (O), and 2 sulfurs (S). The molecular formula is \(\text{C}_6\text{H}_{10}\text{OS}_2\).

Write the Formula for Capsaicin

For Capsaicin, the formula should include 18 carbons (C), 27 hydrogens (H), 1 nitrogen (N), and 3 oxygens (O). The molecular formula is \(\text{C}_{18}\text{H}_{27}\text{NO}_3\).

Write the Formula for Limonene

For Limonene, the formula should include 10 carbons (C) and 16 hydrogens (H). The molecular formula is \(\text{C}_{10}\text{H}_{16}\).

Key concepts

Element Symbols

When writing chemical formulas, it's crucial to know the symbols of each element. Element symbols are one or two letters that represent an element. The first letter is always uppercase, and if there is a second letter, it is lowercase. For example, Carbon is represented by 'C', Hydrogen is 'H', Oxygen is 'O', and Sulfur is 'S'. These symbols make it easy to identify and write out the composition of compounds.
Compound formulas use these symbols along with subscripts to indicate the quantity of each element present. For example, in the formula for water \(\text{H}_2O\), the subscript '2' shows that there are two hydrogen atoms for every one oxygen atom.

Molecular Formulas

Molecular formulas are a shorthand way of representing the types and numbers of atoms in a molecule. They use element symbols followed by subscripts to denote the number of each type of atom. For example, in Allicin's formula \(\text{C}_6\text{H}_{10}\text{OS}_2\), it shows the molecule is made up of 6 carbon atoms, 10 hydrogen atoms, 1 oxygen atom, and 2 sulfur atoms.
Correctly writing molecular formulas requires precise knowledge of how many atoms of each element are involved. Using our exercise, we see:

• \(\text{C}_6\text{H}_{10}\text{OS}_2\) for Allicin
• \(\text{C}_{18}\text{H}_{27}\text{NO}_3\) for Capsaicin
• \(\text{C}_{10}\text{H}_{16}\) for Limonene

This ensures that we accurately represent the chemical composition of each compound.

Chemical Composition

Understanding a molecule's chemical composition helps in writing its formula. The chemical composition tells us which types and how many of each atom make up a molecule. For instance, Allicin's chemical composition is given as 6 carbons, 10 hydrogens, 1 oxygen, and 2 sulfurs. Translating this into a molecular formula gives us \(\text{C}_6\text{H}_{10}\text{OS}_2\).
Breaking down the compounds in our exercise, we identified the specific number of each type of atom required. This allows us to construct molecular formulas:

• Allicin: 6 Carbons (C), 10 Hydrogens (H), 1 Oxygen (O), 2 Sulfurs (S)
• Capsaicin: 18 Carbons (C), 27 Hydrogens (H), 1 Nitrogen (N), 3 Oxygens (O)
• Limonene: 10 Carbons (C), 16 Hydrogens (H)

Knowing the chemical composition is essential for creating accurate molecular formulas and understanding the molecule's structure.