# 8.6.1: Boiling Points

## Correlating Polarity and Physical Properties: Boiling Points

### Introduction

Understanding the nature of intermolecular interactions enables us to understand many chemical and physical phenomena. In fact, it was the investigation of such phenomena that led to our understanding of intermolecular interactions in the first place. In the discussion that follows, we will refer to Coulomb's law several times, so it may be worthwhile to review the mathematical statement of that law:

Coulomb's Law

##### $$F_{c}\propto\frac{q_{1}q_{2}}{r^{2}}$$

In terms of intermolecular interactions, the law says that the force of attraction between two molecules increases as the distance between them decreases. It also states that the force of attraction increases as the magnitude of the opposite charges increase.

### Boiling Points

In the gas phase, the distance between molecules is large in comparison to the size of the molecules. Since the distance is very large, Coulomb's law tells us that the force of attraction between the molecules is very small. In gases it is essentially zero.

In the liquid state, the separation between molecules is much smaller, and the interactions between them much larger than in the gas phase. The boiling point of a liquid is a measure of the amount of energy required to overcome these intermolecular Coulombic attractions. Let's compare the boiling points of three small molecules, dihydrogen, methane and water. Dihydrogen boils at -259oC, methane boils at -164oC, water at +100oC. Obviously the intermolecular forces holding water molecules together are much stronger than those holding dihydrogen or methane molecules together. If we assume that in the liquid phase the intermolecular distances are about the same for all three molecules, then it must be differences in the values of q1 and q2 that are responsible for the differences in boiling points. It is important to remember that in this situation q1 and q2 are the charges associated with the bond dipoles. Figure 1 serves as a reminder of the interactions that we are considering. Here X represents any atom or group and the dashed red lines indicate the Coulombic attractions between opposite charges.

Figure 1: Even Partial Charges Attract

Let's compare water and methane first. Because oxygen is more electronegative than carbon, an $$\ce{O-H}$$ bond has a larger bond dipole than a $$\ce{C-H}$$ bond. Hence the force of attraction between two water molecules is greater than it is between two methane molecules. Water has the higher boiling point.

Now let's compare methane and dihydrogen. We could invoke the same argument here that we did in comparing methane and water. The $$\ce{C-H}$$ bond has a larger bond dipole than the $$\ce{H-H}$$ bond. Therefore, methane has the higher boiling point. The real question is why does dihydrogen become a liquid at any temperature? It has no permanent bond dipole, so the values of q1 and q2 should be zero, and the force of attraction between dihydrogen molecules should also be zero. The key word here is permanent. As we have seen, the motion of the electrons in the H-H bond induces transient dipoles. The distortion of the electron distribution in one molecule of dihydrogen induces complementary distortions in other , nearby dihydrogen molecules. It is this fleeting development of charge that we call upon to rationalize the fact that dihydrogen does finally liquefy at -259oC.

Finally, let's consider the boiling points of a series of alkanes and a comparable series of alcohols. Figure 2 presents plots of the boiling points of a homologous series of linear alkanes and linear alcohols.

Figure 2: Comin' to a Boil

There are several trends in this figure that are noteworthy.

• First, it's obvious that alcohols have higher boiling points than alkanes of comparable size.
• Second, the differences in boiling points become smaller as n increases. (When n = 1, the difference in boiling points is 156oC. When n = 10, the difference is 26 oC.)
• Third, in both series, the boiling points increase as n increases.

Exercise 1 What factor is responsible for the first trend?

Figure 3 offers a pictorial rationalization of the correlation between boiling points and n.

Figure 3: Touch Me, Touch Me

Here the dashed red lines represent the induced dipole-induced dipole interactions between molecules. The more interactions, the higher the boiling point.

Finally, it's important to understand that the different types of interactions we have been discussing are not mutually exclusive. It is possible to have several types of intermolecular interactions occuring simultaneously. In discussing the solubility of 1-bromobutane in ethanol, we alluded to the idea that there were intermolecular forces in addition to dipole-dipole interactions. Figure 4 illustrates the idea.

Figure 4: Different Strokes

Here the narrow dashed red lines represent induced dipole-induced dipole interactions, while the broad dashed lines highlight the stronger dipole-dipole interactions.

### Contributors

• Otis Rothenberger (Illinois State University) and Thomas Newton University of Southern Maine)