Carbon, shapes and structural formulae

Carbon, the element of many compounds

Wood, cotton, plastic, petrol, sugar, soap, medicines and the DNA in your cells are all carbon compounds. Chemists have named many millions of them. Their study is organic chemistry. Carbon itself, its oxides and the carbonates usually belong to inorganic chemistry.

Carbon forms so many compounds for four reasons.

• Four bonds. A carbon atom has four outer electrons and shares them in four covalent bonds.
• Catenation. Carbon atoms join in straight chains, branched chains and rings. The C-C bond is strong, about 350 kJ/mol, so these chains are stable.
• Multiple bonds. Two carbon atoms can share one, two or three pairs of electrons.
• Isomerism. The same atoms can be joined in different orders. The third lesson shows how.

From orbitals to shapes

In its ground state carbon is $1s^2\,2s^2\,2p^2$, with only two unpaired electrons. Yet it makes four bonds. One 2s electron moves to the empty 2p orbital. The s and p orbitals then mix into equal hybrid orbitals. The mix sets the shape.

A bond made by head-on overlap along the line between two nuclei is a sigma bond (σ). Sideways overlap of two p orbitals makes a pi bond (π).

• $sp^3$ (one s and three p): four orbitals pointing to the corners of a tetrahedron, 109.5 degrees apart. Methane has four sigma bonds from carbon to hydrogen.
• $sp^2$ (one s and two p): three orbitals in a plane, 120 degrees apart, and one p orbital left over. In ethene the leftover p orbitals overlap sideways, above and below the plane, and make a pi bond. All six atoms lie in one plane.
• $sp$ (one s and one p): two orbitals, 180 degrees apart, and two p orbitals left over. Ethyne has one sigma and two pi bonds. It is a straight line.

What a pi bond changes

• A double bond is one sigma and one pi bond. A triple bond is one sigma and two pi bonds.
• The pi cloud lies outside the line of the nuclei, so it is easy to attack. This is why alkenes and alkynes react more readily than alkanes.
• Atoms can spin about a sigma bond, but not about a double bond. This gives cis and trans isomers.
• More bonds pull the carbons closer. C-C is 154 pm, C=C is 134 pm and C≡C is 120 pm.

Set the slider to 1, 2 and then 3. Which readout changes the most?

Practise with new numbers

Four ways to write a structure

1. Complete structural formula: every atom and every bond.
2. Condensed formula: each carbon with its hydrogen atoms, as in $\text{CH}_{3}\text{CH(OH)CH}_{2}\text{CH}_{3}$. Repeats go in brackets, $\text{CH}_{3}\text{(CH}_{2}\text{)}_{3}\text{CH}_{3}$, and a branch goes in brackets after its carbon, $\text{CH}_{3}\text{CH(CH}_{3}\text{)CH}_{3}$.
3. Bond-line formula: the one chemists draw most.
   • Every end and every corner is a carbon atom.
   • Hydrogen atoms on carbon are not drawn. A carbon has four bonds, so its hydrogen count is four minus the lines drawn to it.
   • Other atoms are written out with their hydrogen atoms, as in OH.
   • A double bond is two lines and a triple bond is three.
4. Wedge and dash: a plain line is in the page, a solid wedge comes towards you and a dashed wedge goes away.

The molecular formula, such as $\text{C}_{4}\text{H}_{10}\text{O}$, only counts the atoms. It does not say how they are joined.

Try it in Python

The program counts the sigma and pi bonds of a molecule given as a list of bonds. It finds the hybridisation of each carbon from the number of atoms around it.

Common mistakes

• Counting bonds instead of atoms around a carbon. A double bond to one atom still counts as one neighbour. The neighbours decide the hybridisation.
• Forgetting that a double bond holds a sigma bond. It is one sigma and one pi, not two pi.
• Missing a carbon at a bond-line corner. Every corner and every end is a carbon.
• Drawing five bonds on a carbon. If the lines add up to more than four, something is wrong.

Remember these

• Carbon forms four bonds and joins to itself, so it makes chains, rings and many compounds.
• $sp^3$ is tetrahedral, 109.5 degrees. $sp^2$ is planar, 120 degrees. $sp$ is linear, 180 degrees.
• A double bond is one sigma and one pi. A triple bond is one sigma and two pi.
• In a bond-line drawing, the corners and ends are carbons and the hydrogen atoms on carbon are not drawn.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Carbon is $1s^2\,2s^2\,2p^2$ in its ground state. Why does it form four bonds, not two?

2. What is the hybridisation of each carbon in $\text{CH}_{3}\text{CH=CH}_{2}$?

3. How many sigma bonds and how many pi bonds are in ethyne, $\text{CH}\equiv \text{CH}$?

4. A bond-line drawing is a zigzag of four lines with nothing else on it. How many carbon and hydrogen atoms does the molecule have?