Intermolecular forces and the three states

Why is water a liquid and methane a gas?

Water and methane have molecules of about the same size. Water boils at $100\ ^\circ\text{C}$ and methane boils at $-162\ ^\circ\text{C}$. Why is the gap so large? Neon, a single atom, boils at $-246\ ^\circ\text{C}$. Xenon, another single atom, boils at $-108\ ^\circ\text{C}$.

The answer lies in two things that work against each other. Attraction between particles pulls them together. Thermal energy, the energy of the random motion, throws them apart. When attraction wins, the substance is a solid or a liquid. When thermal energy wins, it is a gas.

The three states

Here is how the three states compare:

• Solid. The particles touch and stay in fixed positions. A solid has its own shape and its own volume. It is almost not compressed by pressure, and it does not flow.
• Liquid. The particles touch, and they slide past each other. A liquid takes the shape of its container and has a fixed volume. It is almost not compressed by pressure, and it flows.
• Gas. The particles are far apart and move freely. A gas fills the whole container, so it has no fixed shape or volume. It is compressed easily, and it flows.

At $25\ ^\circ\text{C}$ and $1\ \text{bar}$, one mole of gas fills about $24.8\ \text{L}$, while one mole of liquid water fills only $18\ \text{mL}$. The gas takes up about $1400$ times more room. So molecules in a gas are far apart. Each molecule sits in a cube about $3.45\ \text{nm}$ wide, and a molecule is only about $0.3\ \text{nm}$ across. In liquid water the cube is $0.31\ \text{nm}$ wide, and the molecules touch.

Bonds and intermolecular forces

Do not mix up two kinds of attraction. A bond holds the atoms inside one molecule. An intermolecular force acts between different molecules. Boiling water breaks forces between molecules. It does not break the O–H bonds, and the steam is still $\text{H}_2\text{O}$.

Intermolecular forces are much weaker than bonds. Here are typical sizes, in kJ per mole:

• An O–H bond in water: about $460\ \text{kJ/mol}$.
• Hydrogen bonds between water molecules: about $20\ \text{kJ/mol}$ each.
• Dipole-dipole forces: $5$ to $25\ \text{kJ/mol}$.
• London dispersion forces: $0.1$ to $40\ \text{kJ/mol}$, rising with the size of the molecule.

The kinds of intermolecular force

London dispersion forces act between all atoms and molecules, polar or not. The electrons of an atom keep moving. For a moment one side of the atom has slightly more electron charge than the other side. This gives a short-lived dipole, which pushes the electrons of a neighbour and gives it a dipole too. The two dipoles attract. A large atom with many electrons is more easily distorted. We say it is more polarisable. So dispersion forces grow with the number of electrons.

Dipole-dipole forces act between polar molecules. The positive end of one molecule attracts the negative end of the next. Hydrogen chloride and acetone are examples.

Hydrogen bonds are an extra strong kind of dipole-dipole attraction. A hydrogen atom attached to N, O or F is almost bare of electrons. It is pulled towards a lone pair on N, O or F of another molecule. Water, ammonia, hydrogen fluoride and alcohols form hydrogen bonds. Each water molecule can form up to four, which is why water has an unusually high boiling point.

Ion-dipole forces act between an ion and a polar molecule, for example $\text{Na}^+$ and water. They are the strongest of the four and explain why salts dissolve in water.

The order of strength for molecules of similar size is: dispersion, then dipole-dipole, then hydrogen bonding, then ion-dipole. For molecules of very different size, dispersion forces can win. Iodine, $\text{I}_2$, is nonpolar and yet a solid at room temperature, because it has 106 electrons.

Water against its relatives

The hydrides of group 16 show hydrogen bonding clearly. Moving down the group from $\text{H}_2\text{S}$ to $\text{H}_2\text{Te}$, the molar mass rises and the boiling point rises with it:

Water is the lightest, yet it boils far above the others. If the trend continued, water would boil near $200\ \text{K}$, which is $-73\ ^\circ\text{C}$. The extra $173\ \text{K}$ is the effect of hydrogen bonds. The same thing happens in $\text{HF}$ and $\text{NH}_3$, which boil higher than the other hydrides of their groups.

Attraction against thermal energy

The picture shows the energy of two argon atoms as they approach. Far apart, the energy is nearly zero. As they come closer, the attraction lowers the energy until it reaches a minimum, the well, at $0.382\ \text{nm}$. For argon the well is $1.00\ \text{kJ/mol}$ deep. Closer than that, the electron clouds repel each other and the energy shoots up.

A typical particle has thermal energy of about $RT$ per mole. At $300\ \text{K}$ this is $0.008314\ \text{kJ K}^{-1}\ \text{mol}^{-1} \times 300\ \text{K} = 2.49\ \text{kJ/mol}$. That is more than twice the depth of the well, so argon atoms at $300\ \text{K}$ cannot hold on to each other. Argon is a gas. At $87.3\ \text{K}$, its boiling point, $RT$ is $0.73\ \text{kJ/mol}$, which is about three quarters of the well depth. The boiling point of a substance rises with the depth of its well.

Set $T$ to $50\ \text{K}$, and then to $250\ \text{K}$. Watch the dashed line cross the bottom of the well.

Practise with new numbers

Try it in Python

The program fits a straight line through the boiling points of $\text{H}_2\text{S}$, $\text{H}_2\text{Se}$ and $\text{H}_2\text{Te}$, and follows it down to the molar mass of water.

Common mistakes

• Breaking bonds when a liquid boils. Boiling breaks intermolecular forces. The molecules stay whole.
• Calling a hydrogen bond a normal bond. It is about twenty times weaker than a covalent bond. It is a force between molecules.
• Saying that nonpolar molecules have no forces. Every molecule has dispersion forces.
• Saying that a heavier molecule always boils higher. Water is lighter than $\text{H}_2\text{S}$ and boils higher, because of hydrogen bonds.
• Hydrogen bonds with any hydrogen. The hydrogen must be bonded to N, O or F. In $\text{CH}_4$ it is not.

Remember these

• A solid or liquid has attraction that beats thermal energy. A gas has thermal energy that beats attraction.
• Intermolecular forces: London dispersion (all molecules), dipole-dipole, hydrogen bonding (H on N, O or F) and ion-dipole.
• Dispersion forces grow with the number of electrons, so the boiling points of the noble gases rise down the group.
• Thermal energy per mole is $RT$. At $300\ \text{K}$ it is $2.49\ \text{kJ/mol}$.
• The distance of closest approach is where the repulsion starts. The well depth is the strength of the attraction.

Check yourself

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

1. Why does krypton boil at a higher temperature than argon?

2. Ethanol, $\text{CH}_3\text{CH}_2\text{OH}$, boils at $78\ ^\circ\text{C}$. Dimethyl ether, $\text{CH}_3\text{OCH}_3$, has the same formula and boils at $-24\ ^\circ\text{C}$. Explain the difference.

3. What is the thermal energy $RT$ of one mole at $200\ \text{K}$, in kJ/mol?

4. When ice melts, are bonds inside the water molecules broken? What is broken?

5. Argon has a well depth of $1.00\ \text{kJ/mol}$. At $300\ \text{K}$, why is argon a gas?

References

• OpenStax, Chemistry 2e, Chapter 10, section 10.1 (Intermolecular Forces).
• The boiling points of the noble gases and of the hydrides are standard values from the CRC Handbook of Chemistry and Physics.