Problem 81 - Chemistry The Central Science

Question

Draw the condensed structural formulas for two different molecules with the formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\) .

Step-by-Step Solution

Answer

The condensed structural formulas for two different molecules with the formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\) are CH\(_2\)=CHOCH\(_2\) and HC≡CCH\(_2\)OH.

Step 1: Draw all possible structural formulas

First, we will draw three different structural formulas that comply with the given molecular formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\). Option 1: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{CH}_{2} \mathrm{O}\) Option 2: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{C}(\mathrm{OH})_{2}\) Option 3: \(\mathrm{HC}\equiv \mathrm{C}- \mathrm{CH}_{2} \mathrm{OH}\)

Step 2: Determine which structures are valid

Now, let's determine if all these structures are valid based on the bonding rules for each atom (C can form four bonds, H forms one bond, and O forms two bonds). Option 1: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{CH}_{2} \mathrm{O}\) In this structure, each carbon atom forms four bonds, the hydrogen atoms form one bond each, and the oxygen atom forms two bonds. Thus, this structure is valid. Option 2: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{C}(\mathrm{OH})_{2}\) In this structure, each carbon and hydrogen atom forms the correct number of bonds, but the oxygen atoms violate the rule since they form only one bond each. Thus, this structure is not valid. Option 3: \(\mathrm{HC}\equiv \mathrm{C}- \mathrm{CH}_{2} \mathrm{OH}\) In this structure, each carbon atom forms four bonds, the hydrogen atoms form one bond each, and the oxygen atom forms two bonds. Thus, this structure is valid.

Step 3: Draw the condensed structural formulas

Now that we have identified the two valid structures, we can draw their condensed structural formulas. Option 1: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{CH}_{2} \mathrm{O}\) Condensed formula: CH\(_2\)=CHOCH\(_2\) Option 3: \(\mathrm{HC}\equiv \mathrm{C}- \mathrm{CH}_{2} \mathrm{OH}\) Condensed formula: HC≡CCH\(_2\)OH These are the condensed structural formulas for two different molecules with the formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\).

Key Concepts

Molecular Formula

The molecular formula is a succinct way to express the exact number of each type of atom present in a molecule. For the problem given, the molecular formula is \( \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O} \). Let’s break this down:

• The \( \mathrm{C}_{3} \) indicates there are three carbon atoms in each molecule.
• The \( \mathrm{H}_{4} \) signifies four hydrogen atoms.
• The \( \mathrm{O} \) stands for one oxygen atom.

A molecular formula like this doesn't tell us how the atoms are arranged or linked together—that’s where structural formulas become essential. It acts like a summary, specifying the information using symbols and numerics but not the actual layout of the atoms.

Bonding Rules

Bonding rules are crucial in verifying if a molecule is viable by ensuring each atom forms the correct number of bonds. Different atoms have distinct capacities for forming bonds based on their electrons. Here are the simplified rules for common atoms:

• Carbon (\( \mathrm{C} \)) typically forms four bonds. This can be single, double, or triple bonds combined, but the total number must add up to four.
• Hydrogen (\( \mathrm{H} \)) can only form one bond because it has just one electron to share.
• Oxygen (\( \mathrm{O} \)) generally forms two bonds—often one double bond or two single bonds. This is due to it having six valence electrons and needing two more to complete its shell.

In the solution, only certain structural formulas followed these rules. For instance, in Option 1, all atoms adhered to their bonding rules, ensuring it was a valid molecule. Observing these physics-based rules helps maintain the stability of the structures formed.

Condensed Structural Formula

Condensed structural formulas provide a streamlined depiction of structural formulas by grouping together atoms and bonds in sequence. They are valuable for writing formulas compactly while retaining essential information about the atom arrangement. Consider Option 1 from the solution, \( \mathrm{H}_{2}\mathrm{C}=\mathrm{C}-\mathrm{CH}_{2}\mathrm{O} \), its condensed formula is expressed as CH\(_2\)=CHOCH\(_2\).

• The equals sign (\( = \)) shows a double bond between atoms.
• Neighboring atoms are shown in the order they are connected.

Option 2, although invalid, would not have a proper condensed formula since it didn’t meet bonding rules. However, Option 3 \( \mathrm{HC}\equiv \mathrm{C}-\mathrm{CH}_{2}\mathrm{OH} \) gets condensed to HC≡CCH\(_2\)OH, highlighting the triple bond with "≡".Condensed formulas allow quick communication of structural information without needing detailed structural diagrams, beneficial for managing complex molecules efficiently.