IGCSE Chemistry 0620: General Formulae and the Homologous Series Idea

A school science technician finds three unlabelled gas cylinders left over from a delivery. A supplier's note confirms that each cylinder contains a pure hydrocarbon, and gives its molecular formula:

Gas L: $\text{C}_4\text{H}_{10}$
Gas M: $\text{C}_4\text{H}_8$
Gas N: $\text{C}_7\text{H}_{16}$

(a) State the general formula of the alkane homologous series and the general formula of the alkene homologous series, using $n$ for the number of carbon atoms in one molecule. [2]

(b) Using the general formulae from part (a), state whether each of Gas L, Gas M and Gas N belongs to the alkane homologous series or the alkene homologous series. [3]

(d) Ethane, $\text{C}_2\text{H}_6$ , is the simplest member of the alkane homologous series after methane. Describe, in words, the displayed formula of ethane, stating the number of carbon atoms, hydrogen atoms, carbon–carbon bonds and carbon–hydrogen bonds it contains, and show that this is consistent with the general formula for $n=2$ . [2]

Part (a): General formulae

The two general formulae to know for this pair of homologous series, using $n$ for the number of carbon atoms in one molecule, are:

$\text{Alkanes: } C_nH_{2n+2} \qquad \text{Alkenes: } C_nH_{2n}$

Part (b): Classifying Gas L, Gas M and Gas N

For each gas, substitute its number of carbon atoms into both general formulae and compare with the given number of hydrogen atoms.

Gas L, $C_4H_{10}$ : here $n=4$ .

Alkane check: $2n+2 = 2(4)+2 = 10$ , matches.
Alkene check: $2n = 2(4) = 8$ , does not match.

So Gas L is an alkane.

Gas M, $C_4H_8$ : here $n=4$ .

Alkane check: $2n+2 = 10$ , does not match.
Alkene check: $2n = 8$ , matches.

So Gas M is an alkene.

Gas N, $C_7H_{16}$ : here $n=7$ .

Alkane check: $2n+2 = 2(7)+2 = 16$ , matches.
Alkene check: $2n = 14$ , does not match.

So Gas N is an alkane.

Part (c): Defining “homologous series”

A homologous series is a family of similar compounds that share the same functional group (and can be described by the same general formula), and which therefore show similar chemical properties.

Part (d): The displayed formula of ethane

Ethane’s molecular formula is $C_2H_6$ . Its displayed formula shows every atom and every bond:

2 carbon atoms, joined to each other by 1 single carbon–carbon (C–C) bond.
Each carbon atom is also joined to 3 hydrogen atoms, each by its own single carbon–hydrogen (C–H) bond, giving 6 hydrogen atoms and 6 C–H bonds in total.

Checking this against the alkane general formula for $n=2$ : $2n+2 = 2(2)+2 = 6$

This matches the 6 hydrogen atoms described above, confirming that ethane’s displayed formula is consistent with the alkane general formula.

Final answers

(a) Alkanes: $C_nH_{2n+2}$ ; Alkenes: $C_nH_{2n}$ .
(b) Gas L = alkane, Gas M = alkene, Gas N = alkane.
(c) A homologous series is a family of similar compounds with the same functional group and general formula, showing similar chemical properties.
(d) Ethane has 2 carbon atoms joined by 1 C–C bond, and 6 hydrogen atoms joined by 6 C–H bonds (3 to each carbon), consistent with $2n+2=6$ for $n=2$ .