Home >> Matter, intermolecular force & P.E.

Molecules and atoms (considered the same)

While the kinetic theory of matter considers the motion of molecules to be free and random, there are forces between molecules.

The force acting between molecules is an electrostatic force. If we consider two molecules, the force is:

repulsive between opposite electron clouds
repulsive between opposite nuclei
attractive between one electron cloud and the opposing nucleus

As molecules have forces between them they must have potential energy.
It is convenient to think of two molecules as having zero P.E. at infinite distance, where the attractive force between them is also zero.
Work is done when two attracting molecules are separated. So their P.E. must increase when they are parted.
However, since molecules at infinite distance have zero P.E., those at intermediary distances have negative P.E. relative to this level.
Conversely, repelling molecules have positive P.E. . Repulsive forces do work to move molecules apart.

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Relation between force (F) and P.E. change (δE - delta E)

Consider two attracting molecules(X & Y). The force of attraction F of Y on X moves X a small distance δr (delta 'r') towards Y.
The distance δr is so small that the force F may be considered constant.

The work done W in moving the force F a distance δr is given by: (remember work = force x distance force moves)

If the change in the P.E. of X is δE (delta E), then:

Note the minus sign signifies the decrease in P.E. of X as it is attracted towards Y.

Elimenating δW from the first two equations:

in the limit, as δEand δr tend to zero,

This means that the negative of the gradient of an E-r graph equals the force F acting.

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Curve of molecular P.E. (E) vs molecular separation (r)

The value of the equilibrium separation r_o depends on the solid and temperature. An approximate value is 3 x 10^-10 m.

The point of inflexion is where the gradient is maximum on the right hand side of the graph.

P.E. and K.E. changes between molecules

If two molecules in a solid are at absolute zero, they have no kinetic energy and their separation is r_o . Now consider the two molecules at a higher temperature, with a shared kinetic energy ε . This energy creates an imbalance between the attractive and repulsive forces.

B         r maximum    molecules attracted     PE max, KE zero

BC       PE converted into KE

C        r = r_o equilibrium position     PE min     KE max

CA      KE converted into PE

A        r minimum    molecules repelled     PE max, KE zero

AC      PE converted into KE

C       r = r_o equilibrium position     PE min     KE max

CB      KE converted into PE

In solids molecules can only vibrate small distances about fixed positions. The reason is that the kinetic energy ε is much smaller than the potential energy ε_o (approx. 10%) . Hence a solid has a fixed shape and volume.

Effect of temperature on equilibrium position

C represents the equilibrium position r_o at absolute zero. In this state the molecules have no kinetic energy and consequently do not oscillate.

Consider a low temperature P.E. level at AB. The mid-point of AB moves r_o to the right.

At a higher P.E. level A^'B^' corresponding to a higher temperature. The mid-point A^'B^' of moves r_o even further to the right.

So as the temperature rises, r_o increases. The molecules move apart and the solid is observed to expand.

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Curve of intermolecular force (F) vs molecular separation (r)

Force is the negative of the gradient of the E-r graph.

When F is positive, the force is repulsive.
When F is negative, the force is attractive.

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