Introduction to Organic Chemistry: Question 6

Worked solution

Step 1: Count every carbon atom

The skeletal formula’s main zigzag chain has five carbon atoms (a pentene-type backbone). Attached to the third carbon of that chain is an ethyl branch, $-\text{CH}_2\text{CH}_3$, which contributes two further carbon atoms.

$\text{Total carbons} = 5 + 2 = 7$

A molecular formula only records the total number of each type of atom present, regardless of how they are arranged into a main chain and a branch, so both the five chain carbons and the two branch carbons count towards the total.

Step 2: Work out the degree of unsaturation

The compound contains one C=C double bond (drawn at the left-hand end of the main chain) and no ring. For a fully saturated, non-cyclic hydrocarbon with 7 carbons, the general formula would be:

$\text{C}_n\text{H}_{2n+2} = \text{C}_7\text{H}_{16}$

Each C=C double bond removes two hydrogen atoms compared with the saturated alkane, because two fewer C-H bonds are needed once two of the carbons are joined by a double bond instead of a single bond plus two extra hydrogens. With one double bond present:

$\text{H count} = 16 - 2 = 14$

Step 3: State the molecular formula

$\textbf{C}_7\textbf{H}_{14}$

This matches the general formula for a non-cyclic alkene with one C=C bond, $\text{C}_n\text{H}_{2n}$, since for $n=7$, $2n=14$.

Why the other options are wrong

• B, C7H16, is the formula of the fully saturated seven-carbon alkane, it ignores the C=C double bond entirely.
• C, C6H12, undercounts the carbon total as six (missing one of the two branch carbons) while still correctly applying the “one double bond” rule ($2\times6=12$); the branch is an ethyl group, contributing two carbons, not one.
• D, C7H12, correctly counts seven carbons but incorrectly removes four hydrogens instead of two, as if branching itself created an extra degree of unsaturation.

Final answer

A. C7H14.