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All elements and compounds generally exist in one of the three states of aggregation, namely, solid, liquid or gas. we have learnt the basic differences between he three states of matter in terms of intermolecular forces. In this chapter we will discuss a few characteristic properties of solids.

This chapter is divided into four sections. Section A deals with solids. We will describe the most characteristic property of solids, namely elasticity or elastic deformation under external forces. The electrical and magnetic properties of solids are outside the scope of the present study. In section B, devoted to fluids, we will discuss properties which are common to both liquids and gases, such as transmission of pressure, buoyancy, viscosity and fluid flow. In section C we will discuss a property called surface tension characteristic only of liquids. In section D we will discuss the relationship between pressure, volume and temperature of a gas. We will conclude this section by describing the postulates and implications of the kinetic theory of gases.

We know that each molecular or atom in a solid is at a fixed average location with respect to other molecules which make up the solid. The average locations of the molecules do not change with time, since the molecules are almost completely lacking in mobility, their kinetic energy is very small; almost negligible. It is this lack of mobility which endows a solid with a – definite shape and appreciable stiffness or rigidity. This rigidity is the cause of elastic behaviour (called elasticity) in solids – which we will discuss. Let us first look at two basic structures in solids.

Interatomic and intermolecular forces

A molecule may consist of a single atom or two or more than two atoms of the same type or of different types. In order to study the three different states of matter and its behaviour, it is necessary to understand the nature of forces between the atoms forming the molecules and also the force between molecules as whole.

The force between two atoms of a molecule (inter-atomic force) is not gravitational in nature. No doubt, the force of gravitation exists between the two atoms but it is too weak to hold them together. For example, two helium atoms separated by a distance of 4 × 10-10 m is of the order of 6 × 10-13 N. The magnitude of gravitational force between two such helium atoms is only 7 × 10-42 N i.e. smaller than a factor of 1029. Therefore, atoms are held together through a different type of force, which is much stronger than gravitational force between the atoms. It is now established that force between atoms and molecules are electrical in nature and origin of such a force may be explained as below:

Interatomic forces

An atom consists of a positive nucleus (size = 10-15 m) surrounded by negatively charged electrons revolving in circular orbits over a distance of the order of 10-10 m. However, an atom is electrically neutral i.e. negative charge of electrons is equal and opposite to the positive charge on the nucleus of the atom. When two atoms are brought close to each other to a distance of the order of 10-10m(atomic size), the distances between their positively and negatively parts i.e. positive nuclei and negative electron clouds become different. Due to this, force between the atoms as well as the potential energy of the system of two atoms change. The variation of potential energy V (r) with separation r between the atoms is found to be as shown in Figure (a). It follows that at large distances, the potential energy is negative and becomes more negative as r is decreases. It implies that force between the atoms is attractive. Further, at a distance r0, the potential energy becomes minimum (maximum negative). At this distance, force between is further decreased, the potential energy starts increasing and then becomes positive. Over this range of separation, the force between the atoms is repulsive.
The force between two atoms at any distance r can be expressed as the negative gradient of the potential energy at that distance i.e.
F (r) = -

Therefore, variation of interatomic force F (r) between the two atoms with distance r can also be known from the graph between V (r) and r by finding slope of the graph at each point and F (r) varies with r as shown in the Figure (b).

Let us now discuss the force between two hydrogen atoms. When they are brought together, the value of r0 is found to be 0.74 Å i.e. at these distance hydrogen atoms will not experience any force and will have minimum potential energy. As the state of minimum potential energy is the state of equilibrium, the two hydrogen atoms can be in equilibrium state, when separation between them is 0.74 Å. Since, the radius of a hydrogen atom is 0.53 Å, the distance between the two atoms should be at least 1.06 Å (equal to the sum of the radii of two atoms). But in the equilibrium state, two hydrogen atoms should be at r0 = 0.74 Å. It can be possible only, if the two atoms share the two electrons.

This chemical sharing of electrons between the combining electrons is called the covalent bond.

Two hydrogen atoms combine to form hydrogen molecule due to covalent bonding and the calculations show that the energy of hydrogen molecule decreases by 7.2 × 10-19 J. To dissociate a hydrogen molecule into the two atoms, this energy has to be supplied. Therefore, to dissociate one mole of hydrogen molecules, energy equal to 7.2 × 10-19× 6.0225 × 1023 i.e. 4.4 × 105, J is required.

It may be pointed out that the variations of F (r) and V (r) with r remain qualitatively same for other molecules also. However, the potential energy can be quite different from that of hydrogen molecule. For example, in NaCl molecule, the sodium atom donates its electron in outermost shell to chlorine atom and thus sodium and chlorine ions (Na+ and Cl-) are formed. The attraction between Na+ and Cl- ions results in ionic bond.

The ionic bonds are formed between two atoms by the transfer of one or more valence electrons from one atom to the other.
The ionic bond is formed between sodium and chlorine atom by the transfer of electron, when they are at a distance of about 4 Å. At separation greater than 4 Å, the two atoms cannot transfer electrons and they remain as neutral atoms.

In the molecules formed (due to covalent and ionic bonding), the atoms are at a particular distance r0. Due to this, molecules have definite size. Further, corresponding to separation r0, the energy of the molecule is minimum. It leads to definite shape of the molecule.

Intermolecular forces

Like an atom, a molecule is also electrically neutral. However, it may have non-uniform distribution of positive and negative charges. A molecule, in which the centers of mass of positive and negative charges coincide is called a non-polar molecule. On the other hand, a molecule in which the centers of mass of the positive and negative charges do not coincide is called a polar molecule. Such a molecule behaves as an electric dipole. H2O, NH3, HCl and CO are a few examples of polar molecules, while CH4, CO2,H2 and N2 are a few non-polar molecules. A polar molecule induces electric dipole moment in neighbouring molecules, which results in force of attraction. It is found that force of attraction between molecules varies inversely as seventh power of the distance between them i.e.
or Fatt =
The negative sign indicates that the force is attractive in nature.
When the distance between molecules becomes less than r0(the distance at which net force between molecules is zero), the force becomes repulsive in nature and is found to vary inversely as ninth power of distance between them i.e.
or Frep =

Therefore, force between two molecules is given by
F = Fatt + Frep
or F = -

The values of constants a and b depend upon the structure and nature of molecules.
Now, at r = r0,
- = 0
or r0 = r0 = 1.34 r0

These facts are shown in Figure (c).
It comes out that
at r = 1.5 r0, Fatt =;
at r = 2 r0, Fatt =
and at r = 3 r0, Fatt =

On the other hand,
at r = 0.9 r0, Frep = 5 | Fmax |,
at r = 0.7 r0, Frep = 140 | Fmax |
Thus, molecular force depends strongly on distance and due to this, molecular forces are called range forces.

Difference between interatomic and intermolecular forces. There are following two important points of difference between the two types of forces:
  1. Generally, molecules are not exactly spherical in shape. The separation between two molecules and their potential energy depends on the orientations of the two molecules. As a result, the molecules tumble so often and hence may be treated as effectively spherical.
  2. Forces between two molecules are much weaker than the force between two atoms to a factor of 50 to 100. For example, the two oxygen atoms can come close to each other to a distance of 1.2 Å, whereas two oxygen molecules can come to a distance of 2.9 Å. It is for this reason that energy required to dissociate one mole of oxygen molecules is only 8.4 × 103 J as compared to 4.2 × 105 J mol-1 in case of hydrogen molecules.
The fact that two molecules are in minimum energy state at comparatively larger separation than in case of two atoms. Due to this, one molecule is not restricted to attract only one molecule but can attract many molecules to itself as long as there is enough space i.e. size of the molecules prevents them from getting further close to each other. The origin of molecular attractive forces is attributed to the electric dipole moment of the molecules, which they acquire due to slight shift in the centers of mass of their positive nuclei and the negative cloud. These attractive forces are very weak and are called Vander Waals’ forces. 

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