Question

Write the chemical formula for each of the following compounds: (a) vitamin A: 20 carbon, 30 hydrogen, and 1 oxygen atom (b) vitamin \(\mathrm{K}: 31\) carbon, 46 hydrogen, and 2 oxygen atoms

Short answer

Vitamin A: \( \text{C}_{20}\text{H}_{30}\text{O} \); Vitamin K: \( \text{C}_{31}\text{H}_{46}\text{O}_{2} \).

Step-by-step solution

Understand Chemical Formulas

Chemical formulas are representations of compounds where the symbols of the elements are used along with numerical subscripts indicating the number of atoms of each element in the molecule.

Organize Element Information

List the elements present in each compound along with the number of atoms for each element given in the problem. For vitamin A, list carbon (20 atoms), hydrogen (30 atoms), and oxygen (1 atom). For vitamin K, list carbon (31 atoms), hydrogen (46 atoms), and oxygen (2 atoms).

Write the Chemical Formula for Vitamin A

To write the formula for vitamin A, start with the element with the highest atomic number, carbon, then hydrogen, followed by oxygen. Combine them into a formula: \( \text{C}_{20}\text{H}_{30}\text{O} \).

Write the Chemical Formula for Vitamin K

Similarly, for vitamin K, start with carbon, then hydrogen, and finally oxygen. Write the formula as: \( \text{C}_{31}\text{H}_{46}\text{O}_{2} \).

Key concepts

Understanding Chemical Compounds

Chemical compounds are substances formed when two or more elements are chemically bonded together. These bonds can be ionic, covalent, or metallic. What's fascinating about chemical compounds is how they bring together various atoms to create entirely new substances with unique properties. For instance, vitamin A and vitamin K, both essential to various bodily functions, are just specific arrangements of carbon, hydrogen, and oxygen atoms.

• Ionic compounds involve the transfer of electrons and result in positive and negative ions.
• Covalent compounds consist of shared electron pairs between atoms, creating a molecule.
• Metallic compounds are formed by the pooling of electrons among a lattice of metal atoms.
  

Next time you encounter a compound's formula, remember it's more than just letters and numbers; it's a combination of elements holding hands through chemical bonds.

Significance of Element Symbols

Element symbols are shorthand representations of chemical elements derived from their English or Latin names. These one or two-letter abbreviations offer a way to quickly identify elements in chemical equations and formulas. For example, in the case of vitamin A and K, we use the symbols C, H, and O to represent carbon, hydrogen, and oxygen, respectively.
These symbols are universal in the scientific community, making it easier to communicate and understand formulas globally. The periodic table provides these symbols for all known elements.

• C for carbon: A key element found in many compounds essential for life.
• H for hydrogen: The lightest and most abundant element in the universe.
• O for oxygen: Critical for processes like respiration and combustion.
  

Remembering these symbols is crucial for anyone studying chemistry or related fields.

Purpose of Numerical Subscripts in Chemical Formulas

Numerical subscripts in chemical formulas indicate the number of atoms of each element present in a compound. These little numbers are crucial because they change the entire substance's identity and properties if altered. For the chemical formulas of vitamins A and K, the subscripts are vital in describing the exact number of carbon, hydrogen, and oxygen atoms.
For example:

• In vitamin A, the formula is \( \text{C}_{20}\text{H}_{30}\text{O} \), highlighting 20 carbons, 30 hydrogens, and 1 oxygen atom.
• In vitamin K, the formula \( \text{C}_{31}\text{H}_{46}\text{O}_{2} \) shows 31 carbons, 46 hydrogens, and 2 oxygens.

Subscripts must be applied correctly since even a small mistake can represent an entirely different compound. Hence, attention to detail when writing chemical formulas is essential, as it ensures precise communication in the world of chemistry. Whether solving an exercise or working in a lab, those tiny subscripts play a massive role in understanding and predicting chemical behavior.