Exercises: Homologous series

Methane ($\text{CH}_4$), ethane ($\text{C}_2\text{H}_6$), propane ($\text{C}_3\text{H}_8$), and butane ($\text{C}_4\text{H}_{10}$) form the homologous series of alkanes. The figure shows their carbon skeletons.

1. a) Check that all four formulas satisfy the general formula $\text{C}_n\text{H}_{2n+2}$ by giving $n$ the values $1$, $2$, $3$, and $4$.
2. b) Write in your own words the definition of a homologous series: compounds of the same type, with the same general formula, whose properties vary gradually.

Compare the formulas of ethane, $\text{C}_2\text{H}_6$, and propane, $\text{C}_3\text{H}_8$. The figure shows what is added when moving from one to the other.

1. a) How do the two molecules differ?
2. b) Two consecutive members of a homologous series are said to differ by a methylene group, $-\text{CH}_2-$: check this also with butane, $\text{C}_4\text{H}_{10}$, and pentane, $\text{C}_5\text{H}_{12}$.
3. c) Calculate the difference in molar mass between two consecutive alkanes (atomic masses: $\text{C} = 12$; $\text{H} = 1$).

Use the general formulas for alkanes ($\text{C}_n\text{H}_{2n+2}$), alkenes ($\text{C}_n\text{H}_{2n}$), and alkynes ($\text{C}_n\text{H}_{2n-2}$) to assign a family to each molecular formula: $\text{C}_5\text{H}_{12}$, $\text{C}_6\text{H}_{12}$, $\text{C}_4\text{H}_6$, $\text{C}_7\text{H}_{16}$, $\text{C}_8\text{H}_{16}$, and $\text{C}_5\text{H}_8$.

The first five alkanes are methane, ethane, propane, butane, and pentane.

1. a) Write down their molecular formulas by setting $n$ to values from $1$ to $5$ in the general formula of the series.
2. b) Comment on which ones you know from everyday life and where they are used (natural gas, lighters, camping gas canisters...).

Alkenes form the homologous series $\text{C}_n\text{H}_{2n}$, with a $\text{C=C}$ double bond in the chain.

1. a) Write down the molecular formulas of the first four alkenes: ethene, propene, butene, and pentene.
2. b) Explain why this series starts at $n = 2$ and cannot have a member with $n = 1$.

Nineteenth-century cavers carried carbide lamps: when calcium carbide reacts with water, ethyne (acetylene), $\text{C}_2\text{H}_2$, is evolved, which burns with a very bright flame.

1. a) Alkynes follow the general formula $\text{C}_n\text{H}_{2n-2}$ and contain a $\text{C}\equiv\text{C}$ triple bond. Check that ethyne satisfies it, and write down the formulas of the next two members, propyne and butyne.
2. b) How many hydrogen atoms does a chain 'lose' when passing from alkane to alkene, and from alkene to alkyne?

Alcohols form the homologous series of general formula $\text{C}_n\text{H}_{2n+2}\text{O}$, with an $-\text{OH}$ group in the chain.

1. a) Check that methanol ($\text{CH}_4\text{O}$) and ethanol ($\text{C}_2\text{H}_6\text{O}$) satisfy the general formula.
2. b) Write down the molecular formula of the $3$-carbon alcohol, propanol, and that of the $4$-carbon alcohol, butanol.
3. c) Also write down the general formula in the form $\text{C}_n\text{H}_{2n+1}\text{-OH}$ and explain what the separately written group represents.

A student claims that ethene, $\text{C}_2\text{H}_4$, and ethane, $\text{C}_2\text{H}_6$, belong to the same homologous series 'because they have the same number of carbon atoms'.

1. a) Explain why he is mistaken: what conditions must a homologous series satisfy regarding the general formula and the type of bond or functional group?
2. b) State two compounds that are indeed consecutive members to ethene in its series, and two others to ethane in its series.

The molar masses of the first five alkanes are $16$, $30$, $44$, $58$, and $72\ \text{g/mol}$.

1. a) Check that the mass always increases by the same amount and explain why: what group is added at each step in the series and how much does it 'weigh'?
2. b) Deduce the molar mass of the $6$-carbon alkane and that of the $7$-carbon alkane.
3. c) An alkane has a molar mass of $114\ \text{g/mol}$: how many carbon atoms does its molecule have? Hint: its molar mass satisfies $M = 14 \times n + 2$.

The complete combustion of any alkane follows this general pattern:

$\text{C}_n\text{H}_{2n+2} + \frac{3n+1}{2}\ \text{O}_2 \rightarrow n\ \text{CO}_2 + (n+1)\ \text{H}_2\text{O}$

1. a) Check the pattern with methane ($n = 1$) by writing its balanced equation.
2. b) Apply it to butane ($n = 4$) and calculate the moles of $\text{O}_2$ required to burn $1\ \text{mol}$ of butane.
3. c) Explain, by looking at coefficient $\frac{3n+1}{2}$, why oxygen consumption increases by $1.5\ \text{mol}$ for every $-\text{CH}_2-$ group added to the chain.

The boiling points of the first alkanes are: methane $-161.5\ \celsius$, ethane $-88.6\ \celsius$, propane $-42.1\ \celsius$ and butane $-0.5\ \celsius$. The data are plotted in the figure.

1. a) Describe the trend: does the boiling point rise or fall as the chain gets longer?
2. b) Explain this trend in terms of the forces between molecules: what changes as the chain gets longer, and why is it harder to separate them?
3. c) Predict, without consulting tables, whether pentane will boil above or below $0\ \celsius$, and compare your prediction with the actual value: $36.1\ \celsius$.

On Titan, Saturn's moon, the surface temperature is around $-179\ \celsius$ and there are hydrocarbon lakes and rain. Melting and boiling points, in $\celsius$: methane ($-182.5$ and $-161.5$), ethane ($-182.8$ and $-88.6$), propane ($-187.7$ and $-42.1$), and butane ($-138.3$ and $-0.5$).

1. a) For each of the four alkanes, decide its state at $-179\ \celsius$, reasoning whether the temperature is below its melting point, between the two points, or above its boiling point.
2. b) Explain using the results why Titan's lakes can consist of methane and ethane.
3. c) What would butane look like there? Why can it not form lakes?

The boiling points of the first four alcohols are: methanol $64.7\ \celsius$, ethanol $78.4\ \celsius$, propanol $97.2\ \celsius$, and butanol $117.7\ \celsius$. The data are shown in the figure.

1. a) Describe the trend within the series.
2. b) Compare it with that of alkanes: methane ($M = 16\ \text{g/mol}$) boils at $-161.5\ \celsius$ and methanol ($M = 32\ \text{g/mol}$) at $64.7\ \celsius$. Which functional group is responsible for alcohols having much higher boiling points, and what type of intermolecular bond does it form?
3. c) Predict whether the next alcohol, pentanol, will boil above or below $117.7\ \celsius$.

Compare two substances with almost identical molar mass: propane, $\text{C}_3\text{H}_8$ ($M = 44\ \text{g/mol}$, boils at $-42.1\ \celsius$), and ethanol, $\text{C}_2\text{H}_5\text{OH}$ ($M = 46\ \text{g/mol}$, boils at $78.4\ \celsius$). The figure shows two neighboring molecules of each substance (the H atoms bonded to C are omitted). The dashed line indicates an interaction between neighboring molecules.

1. a) Calculate the difference between their boiling points.

1. b) Explain the cause of this difference based on the types of intermolecular forces each substance has, taking into account the figure and the structure of each molecule.

1. c) Draw a general conclusion: what factor does the boiling point mainly depend on within a homologous series, and on what when comparing substances from different families with similar molar masses?

Boiling points of the first alkenes: ethene $-103.7\ \celsius$, propene $-47.6\ \celsius$, $1$-butene $-6.3\ \celsius$, and $1$-pentene $30.0\ \celsius$.

1. a) State which ones are gases and which one is a liquid in a laboratory at $20\ \celsius$.
2. b) Compare ethene with ethane ($-88.6\ \celsius$) and propene with propane ($-42.1\ \celsius$): does the double bond significantly affect the boiling point? Relate this to the fact that all of them are non-polar hydrocarbons.

You know the boiling points of hexane ($68.7\ \celsius$) and octane ($125.6\ \celsius$), but not that of heptane, which lies between them in the alkane series. The situation is shown in the figure.

1. a) Estimate the boiling point of heptane, assuming it lies halfway between them (interpolation), and express the result to one decimal place.
2. b) The actual value is $98.4\ \celsius$: calculate the error in your estimate and assess whether the method was reasonable.
3. c) Repeat the interpolation to estimate the boiling point of nonane from octane and decane ($174.1\ \celsius$).

Boiling points of straight-chain alkanes, in $\celsius$: methane $-161.5$; ethane $-88.6$; propane $-42.1$; butane $-0.5$; pentane $36.1$; hexane $68.7$; heptane $98.4$; octane $125.6$.

1. a) Calculate the difference in boiling point between each pair of consecutive members.
2. b) Check that the differences become progressively smaller and suggest an explanation: think about how much the mass increases proportionally from methane to ethane (from $16$ to $30\ \text{g/mol}$, almost doubling) compared to from heptane to octane (from $100$ to $114\ \text{g/mol}$).
3. c) Draw in your notebook the graph of boiling point against number of carbon atoms and describe its shape: is it a straight line?

You can do it on paper and send a photo with your answer.

Inside a transparent lighter, liquid can be seen, even though the flame burns gas: butane (boiling point $-0.5\ \celsius$) is liquefied by the internal pressure and evaporates when the valve is opened. Construction site gas cylinders use propane ($-42.1\ \celsius$) and town natural gas is methane ($-161.5\ \celsius$).

1. a) Explain, using boiling points, why butane can be liquefied under pressure inside a lighter at room temperature, but methane cannot be liquefied under household conditions.
2. b) Reason what happens to a butane lighter on a winter morning at $-5\ \celsius$ and why patio heaters work better with propane.
3. c) Methane travels through pipes as a gas: explain the advantage of this for distribution and the disadvantage for storing it in small containers.

In a laboratory analysis, an unknown alcohol is found to have a molar mass of $74\ \text{g/mol}$.

1. a) Apply the general formula for alcohols, $\text{C}_n\text{H}_{2n+2}\text{O}$, to write its molar mass in terms of $n$ (atomic masses: $\text{C} = 12$; $\text{H} = 1$; $\text{O} = 16$).
2. b) Solve the equation and deduce the molecular formula of the alcohol.
3. c) Knowing that the series boils at $64.7\ \celsius$ (methanol), $78.4\ \celsius$ (ethanol), and $97.2\ \celsius$ (propanol), predict an approximate boiling point for this alcohol and compare it with the actual value for butanol: $117.7\ \celsius$.

Compare three gaseous fuels containing $2$ carbon atoms: ethane, $\text{C}_2\text{H}_6$ (alkane); ethene, $\text{C}_2\text{H}_4$ (alkene); and ethyne, $\text{C}_2\text{H}_2$ (alkyne).

1. a) Calculate for each one the hydrogen-to-carbon ratio (atoms of $\text{H}$ per atom of $\text{C}$) and the mass percentage of carbon (atomic masses: $\text{C} = 12$; $\text{H} = 1$).
2. b) Order the three flames from cleanest to sootiest, knowing that the higher the percentage of carbon, the more incandescent particles (soot) are formed during combustion.
3. c) The flame of natural gas (alkanes) is blue and clean, whereas that of ethyne is very bright but produces soot if oxygen is deficient: relate this to the calculated percentages.

Methane ($M = 16\ \text{g/mol}$) boils at $-161.5\ \celsius$ and methanol ($M = 32\ \text{g/mol}$) at $64.7\ \celsius$.

1. a) Break down the difference in boiling point between the two into two effects: that of mass, which doubles, and that of the $-\text{OH}$ group, which enables hydrogen bonding. Which of the two dominates? Justify this by comparing with ethane ($M = 30\ \text{g/mol}$, boils at $-88.6\ \celsius$), which has almost the same mass as methanol.
2. b) Predict qualitatively the boiling point of ethene ($M = 28\ \text{g/mol}$, hydrocarbon) and that of ethanol ($M = 46\ \text{g/mol}$, alcohol), and compare with the actual values: $-103.7\ \celsius$ and $78.4\ \celsius$.

In an oil refinery, crude oil is separated by fractional distillation: petrol contains alkanes with approximately $5$ to $12$ carbon atoms; kerosene, $12$ to $16$; and diesel, $15$ to $20$. The diagram of the fractionating column is shown in the figure.

1. a) Order the three fractions by their boiling point and justify the order using the trend in the alkane homologous series.
2. b) Explain why, in the fractionating column, petrol is collected near the top and diesel near the bottom.
3. c) In winter, some diesel lorries break down because the diesel thickens or crystallises in the cold, something that does not happen to petrol: relate this to chain length and intermolecular forces.

The molar masses and boiling points of four consecutive members of a homologous series are measured: $72\ \text{g/mol}$ and $36.1\ \celsius$; $86\ \text{g/mol}$ and $68.7\ \celsius$; $100\ \text{g/mol}$ and $98.4\ \celsius$; $114\ \text{g/mol}$ and $125.6\ \celsius$.

1. a) Check that the masses increase from $14$ in steps of $14$ and explain what this reveals about the series.
2. b) Find out which series it is by checking that the masses satisfy $M = 14 \times n + 2$, the alkane rule, and deduce the number of carbon atoms in each member.
3. c) Predict the molar mass of the next member and estimate its boiling point, bearing in mind that the differences in boiling point become somewhat smaller.

A student claims: 'in the alkane series, the boiling point is proportional to the molar mass'.

1. a) Test it with methane ($16\ \text{g/mol}$, $-161.5\ \celsius$) and butane ($58\ \text{g/mol}$, $-0.5\ \celsius$): if it were proportional, what boiling point would correspond to butane, whose mass is about $3.6$ times that of methane? Why is the result absurd? Think about what happens when you multiply a negative temperature.
2. b) Repeat the test in kelvin ($T(\text{K}) = T(\celsius) + 273$): calculate the quotient of the boiling point and the molar mass for methane and for octane ($114\ \text{g/mol}$, $125.6\ \celsius$) and check that it is not constant.
3. c) Conclude what can actually be stated: the boiling point increases with mass, but not proportionally; rather, at a progressively slower rate.

Unit challenge. How do structure and functional groups determine the macroscopic properties of carbon compounds?

1. Research: Look up the boiling point ($T_e$) of the first five members of the 1-alcohol homologous series (from methanol to pentan-1-ol) in the PubChem database. Create a data table and plot $T_e$ ($^\circ\text{C}$) against the number of carbons ($N_C$).

2. Experimental measurement: On a clean plate, place a small drop ($V \approx 0.05\text{ mL}$) of rubbing alcohol ($96\,\%$ ethanol) and, separately, one of nail polish remover whose label lists acetone as the main component. Measure the time it takes for each to evaporate completely using your mobile phone's stopwatch ($u = \pm 0.2\text{ s}$). Repeat the experiment $3$ times to calculate the mean value and the dispersion uncertainty. Safety: both liquids are flammable; work with small drops in a well-ventilated place, away from any flame or heat source.

3. Final report: Prepare a brief report including the measurement table with its uncertainties, the plot of the homologous series, and a theoretical justification: explain how molecular mass, chain length, and intermolecular forces (such as hydrogen bonding) influence the observed volatility.

Evaluation criteria:

• Rigorous collection of bibliographic and experimental data with uncertainty analysis.

• Technical quality in the creation and interpretation of the homologous series plot.

• Coherent scientific argumentation relating functional groups to intermolecular forces.