# Example: Boiling hydrogen bonds

## Understanding the situation

Let's explore how the energetics of molecular bonding can give us insight into the properties of matter. In liquid water, water molecules are continually forming and breaking hydrogen bonds.

In water, a hydrogen bond has a bond energy of about 0.2 eV (binding energy of -0.2 eV). Two water molecules are shown forming a hydrogen bond (dashed line) in the figure at the right.

Energy has to be put into water to convert it from a liquid to a gas. Does that energy go towards the breaking of the hydrogen bonds in liquid water? It takes about 2.3 x 106 J to boil 1 kg of water.

## Sample problem and solution

1. Is the formation of the hydrogen bond exothermic (releases energy, reducing the internal energy of the molecules) or endothermic (absorbs energy, increasing the internal energy of the molecule)? Explain briefly.

Exothermic. When a bond forms, energy has to be put in to break it, therefore the energy of the bonded system is lower than the energy of the separated system. When the bond is formed, energy would be released in order to conserve total energy. This released energy could be thermal (kinetic energy of molecules), or a photon could be emitted.

Let's see whether hydrogen bonds can account for the energy needed to boil water.  Assume the model that when water boils, the energy that has to be put in is the energy needed to break the hydrogen bonds.

2.  Figure out how many water molecules there are in 1 kg of water. (Hint: The atomic mass of water is 18D* and Avogadro's number is ~ 6 x 1023 molecules/mole.)

Since 1 kg of water has 1000 g, that corresponds to 1000/18 moles. That would have (103/18) x (6 x 1023) ~ 3 x 1025 molecules of water.

3. Do you expect that there would be more hydrogen bonds than water molecules or fewer? Explain your reasoning.

You can't really tell, but since water is pretty cohesive, I expect each molecule has at least one hydrogen bond to another water molecule. Since two is the maximum each can have, we would expect somewhere between 1 and 2 bonds per molecule.

4. Next, figure out in our model of boiling, how many hydrogen bonds are broken in order to boil 1 kg of water.

To boil 1 kg of water we need 2.3 x 106 J. Each hydrogen bond requires an input of 0.2 eV to break it. Converting that to Joules we get (0.2 eV) x (1.6 x 10-19 J / 1 eV) = 0.32 x 10-19 J per hydrogen bond. So if all our energy of boiling is breaking hydrogen bonds, we must be breaking

N = (2.3 x 106 J) / (0.32 x 10-19 J/bond) ~ 7 x 1025 bonds.

5. Does your calculation support our simple model or not? Why?

It's not 100% convincing, but it is satisfying that the number we get is pretty close to 2 bonds per molecule. This suggests that the model is not totally unreasonable.

* "D" or Dalton is the official unit often called an "AMU" or "Atomic Mass Unit". It is the mass of an atom or a molecule in the system where the mass of a carbon atom is taken to be 12 D.

Joe Redish 12/16/16

Article 471