15.2 Representation of Organic Molecules

Organic compounds often have structures that are more complex than those of inorganic compounds. Consequently, several different types of chemical formulae are used to represent them, each providing a different level of detail.

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15.2.1 Molecular Formula

The molecular formula is a representation that shows the type of atoms and the actual whole number of atoms for each element present in one molecule of a compound. It provides the exact composition of the molecule but gives no information about its structure.

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15.2.2 Empirical Formula

The empirical formula represents the simplest whole-number ratio of atoms of the different elements in a compound.

Interesting Information: Inorganic compounds typically have simple structures, so their empirical formula is often sufficient for representation.

Comparison of Molecular and Empirical Formulae

Note: The empirical formula can sometimes be misleading. For example, both ethanoic acid and glucose share the same empirical formula ($C{H}_{2}O$), making it impossible to distinguish between them using only this information.

Determination of Empirical and Molecular Formulae

The empirical and molecular formulas can be determined experimentally, often through combustion analysis. This process is fundamental to stoichiometry.

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Worked Examples

Example 1: Determining Empirical Formula from Percentage Composition

An organic compound has the following percentage composition by mass: C = 38.4%, H = 4.8%, and Cl = 56.8%. Calculate the empirical formula of this compound.

Solution:

1. Assume 100 g of the substance and calculate the moles of each element.
   (The percentage by mass is equivalent to the mass in grams for a 100 g sample).

   • Moles of Carbon (C): $\frac{38.4g}{12.0gmo{l}^{-1}}=3.2mol$
   • Moles of Hydrogen (H): $\frac{4.8g}{1.0gmo{l}^{-1}}=4.8mol$
   • Moles of Chlorine (Cl): $\frac{56.8g}{35.5gmo{l}^{-1}}=1.6mol$

2. Divide the moles of each element by the smallest mole value to find the simplest ratio.
   The smallest value is 1.6 mol.

   • Carbon (C): $\frac{3.2}{1.6}=2$
   • Hydrogen (H): $\frac{4.8}{1.6}=3$
   • Chlorine (Cl): $\frac{1.6}{1.6}=1$

3. Write the empirical formula.
   The ratio of atoms is C:H:Cl = 2:3:1.
   Therefore, the empirical formula is $C_2{H}_{3}Cl$.

Example 2: Determining Molecular Formula from Empirical Formula and Molecular Mass

An organic compound has the empirical formula "CH" and a molecular mass of 78 amu. Calculate its molecular formula.

Solution:

1. Calculate the empirical formula mass.

   • Empirical formula mass of CH = $12+1=13$ amu.

2. Find the integer multiple 'n' relating the molecular mass to the empirical formula mass. $n=\frac{\text{molecular mass}}{\text{empirical formula mass}}=\frac{78}{13}=6$

3. Calculate the molecular formula.

   • Molecular Formula = $n\times (\text{Empirical Formula})$
   • Molecular Formula = $6\times (CH)=C_6{H}_6$

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15.2.3 Structural Formulae

Since molecular and empirical formulae do not show how atoms are connected, structural formulae are used to illustrate the arrangement of atoms and identify functional groups within a molecule.

1. Condensed Structural Formula

This formula shows the relative positions of all atoms without explicitly drawing the single covalent bonds. Each carbon atom is written with the hydrogen atoms attached to it. Branches and functional groups are often shown in brackets.

• Example: Acetic acid ($C{H}_{3}COOH$) shows three hydrogens on the first carbon, which is bonded to a carboxyl group ($COOH$).
• Key Information: Side chains or functional groups are written in brackets next to the carbon they are attached to.

2. Full Structural Formula (2D Displayed Formula)

This formula is a two-dimensional representation that indicates all atoms and all the covalent bonds between them.

• Key Information: A 2D formula is ideal for showing the connectivity in planar molecules, representing atoms in the x and y planes.

Ethane ($C_2{H}_6$)

Ethanol ($C_2{H}_{5}OH$)

3. Skeletal Formula

For large and complex organic molecules, the skeletal formula (also called bond-line formula) is the easiest and quickest representation to draw.

Rules for skeletal formulae:

• Carbon atoms are not written explicitly; each vertex (bend) and each line-end represents one carbon atom.
• Hydrogen atoms bonded to carbon are not shown.
• Heteroatoms (O, N, S, halogens, etc.) and any hydrogen atoms bonded directly to them are written explicitly.
• The number of implied hydrogens on each carbon is determined by the tetravalency of carbon (4 bonds total).

Example: Pentane ($C_5{H}_{12}$) is drawn as a zigzag line with 5 points (2 ends + 3 vertices), each representing one carbon.

4. Three-Dimensional (3D) Structural Formula

To represent the actual three-dimensional arrangement of atoms in space, wedge-and-dash notation is used:

This notation is essential for representing stereochemistry and the tetrahedral geometry of $s{p}^3$ carbon atoms.

5. Dot-and-Cross Diagram

A dot-and-cross diagram (electron diagram) shows the distribution of valence electrons between atoms:

• Dots represent electrons from one atom.
• Crosses represent electrons from another atom.
• Both bonding pairs and lone pairs are shown.

This representation is useful for understanding the electronic structure of covalent bonds but is rarely used for large organic molecules due to complexity.

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Summary: Types of Formulae