Chapter 5 : States of Matter
Intermolecular forces are the forces of attraction and repulsion between interacting particles (atoms and molecules).
Topics covered in this snack-sized chapter:
The force of attraction between two temporary dipoles is known as London force. Another name for this force is dispersion force.
5.1.1 Dispersion Forces or London Forces
Dipole-dipole forces act between the molecules possessing permanent dipole. Ends of the dipoles possess “partial charges”.
This interaction is stronger than the London forces but is weaker than ion-ion interaction because only partial charges are involved. The attractive force decreases with the increase of distance between the dipoles.
5.1.2 Dipole - Dipole Forces
This type of attractive forces operate between the polar molecules having permanent dipole and the molecules lacking permanent dipole.
Permanent dipole of the polar molecule induces dipole on the electrically neutral molecule by deforming its electronic cloud. Thus an induced dipole is developed in the other molecule.
5.1.3 Dipole–Induced Dipole Forces
Hydrogen Bond is found in the molecules in which highly polar N–H, O–H or H–F bonds are present. Although hydrogen bonding is regarded as being limited to N, O and F; but species such as Cl may also participate in hydrogen bonding.
Following diagram shows the formation of hydrogen bond.
Thermal energy is the energy of a body arising from motion of its atoms or molecules.
It is directly proportional to the temperature of the substance. It is the measure of average kinetic energy of the particles of the matter and is thus responsible for movement of particles.
This movement of particles is called thermal motion.
Intermolecular forces tend to keep the molecules together but thermal energy of the molecules tends to keep them apart.
Three states of matter are the result of balance between intermolecular forces and the thermal energy of the molecules. When molecular interactions are very weak, molecules do not cling together to make liquid or solid unless thermal energy is reduced by lowering the temperature.
This is the simplest state of matter. There are eleven elements that exist as gases under normal conditions.
The gaseous state is characterized by the following physical properties.
5.3 Intermolecular Forces vs Thermal Interactions arrow_upward
- Gases are highly compressible.
- Gases exert pressure equally in all directions.
- Gases have much lower density than the solids and liquids.
Some gas laws are following:
- The volume and the shape of gases are not fixed. These assume volume and shape of the container.
- Boyle’s Law (Pressure – Volume Relationship)
- Charles’ Law (Temperature – Volume Relationship)
- Gay Lussac’s Law (Pressure- Temperature Relationship)
- Avogadro Law (Volume – Amount Relationship)
At constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume. This is known as Boyle’s law.
5.5.1 Boyle’s Law (Pressure – Volume Relationship)
pV = k1
is the proportionality constant. The value of constant k1
depends upon the amount of the gas, temperature of the gas and the units in which p and V are expressed.
If a fixed amount of gas at constant temperature T occupying volume V1
at pressure p1
undergoes expansion, so that volume becomes V2
and pressure becomes p2
, then according to Boyle’s law:
According to law pressure remaining constant, the volume of a fixed mass of a gas is directly proportional to its absolute temperature
5.5.2 Charles’ Law (Temperature – Volume Relationship)
V = ) T,
Where () is Constant
P = () T,
Where () is Constant
It states that at constant volume, pressure of a fixed amount of a gas varies directly with the temperature. Mathematically,
5.5.3 Gay Lussac’s Law (Pressure- Temperature Relationship)
Pressure vs temperature (Kelvin) graph at constant molar volume is shown in the figure given below. Each line of this graph is called isochore.
It states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules.
This means that as long as the temperature and pressure remain constant, the volume depends upon number of molecules of the gas or in other words amount of the gas.
5.5.4 Avogadro Law (Volume – Amount Relationship)
Where n is the number of moles of the gas.
Number of moles of a gas can be calculated as follows:
Where m = mass of the gas under investigation and M = molar mass
Here ‘d’ is the density of the gas. We can conclude from the above equation that the density of a gas is directly proportional to its molar mass.
A gas that follows Boyle’s law, Charles’ law and Avogadro law strictly is called an ideal gas. Such a gas is hypothetical. It is assumed that intermolecular forces are not present between the molecules of an ideal gas.
At constant T and n;
At constant p and n;
At constant p and T;
- Where R is proportionality constant. On rearranging the equation (5.16) we obtain
pV = nRT
This equation is called ideal gas equation. R is called gas constant. It is same for all gases. Therefore it is also called Universal Gas Constant.
Ideal gas equation is a relation between four variables and it describes the state of any gas, therefore, it is also called equation of state.
If temperature, volume and pressure of a fixed amount of gas vary from T1
then we can write
This equation is also known as Combined gas law.
Ideal gas equation can be rearranged as follows:
5.6.1 Density and Molar Mass of a Gaseous Substance arrow_upward
Replacing n by m/M, we get
It states that the total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases i.e., the pressures which these gases would exert if they were enclosed separately in the same volume and under the same conditions of temperature.
In a mixture of gases, the pressure exerted by the individual gas is called partial pressure.
+...... (at constant T, V)
is the total pressure exerted by the mixture of gases and p1
etc. are partial pressures of gases.
– Aqueous tension
Assumptions or postulates of the Kinetic Molecular Theory of gases are given below:
- Gases consist of large number of identical particles (atoms or molecules) that are so small and so far apart on the average that the actual volume of the molecules is negligible in comparison to the empty space between them. They are considered as point masses. This assumption explains the great compressibility of gases.
- There is no force of attraction between the particles of a gas at ordinary temperature and pressure.
- Particles of a gas are always in constant and random motion.
- At any particular time, different particles in the gas have different speeds and hence different kinetic energies. This assumption is reasonable because as the particles collide, we expect their speed to change.
The figure given below shows such a plot constructed from actual data for several gases at 273 K.
pV vs p plot for real gases is not a straight line. There is a significant deviation from ideal behaviour.
Two types of curves are seen. In the curves for dihydrogen and helium, as the pressure increases the value of pV also increases.
For ideal gas Z = 1 at all temperatures and pressures because pV = n RT.
5.8 Behavior of Real Gases: Deviation from Ideal Gas Behavior arrow_upward
At very low pressures all gases shown have and behave as ideal gas. At high pressure all the gases have Z > 1. These are more difficult to compress. At intermediate pressures, most gases have Z < 1.
Thus gases show ideal behavior when the volume occupied is large so that the volume of the molecules can be neglected in comparison to it.
At high temperatures isotherms look like that of an ideal gas and the gas cannot be liquefied even at very high pressure.
The figure given below shows the isotherms of carbon-di-oxide at various temperatures.
As the temperature is lowered, shape of the curve changes and data shows considerable deviation from ideal behaviour.
At 30.98 °C carbon dioxide remains gas upto 73 atmospheric pressure. (Point E). At 73 atmospheric pressure, liquid carbon dioxide appears for the first time. The temperature 30.98 °C is called critical temperature (TC
) of carbon dioxide. This is the highest temperature at which liquid carbon dioxide is observed.
Intermolecular forces are stronger in liquid state than in gaseous state. Molecules in liquids are so close that there is very little empty space between them and under normal conditions liquids are denser than gases.
Molecules of liquids are held together by attractive intermolecular forces. Liquids have definite volume because molecules do not separate from each other.
However, molecules of liquids can move past one another freely, therefore, liquids can flow, can be poured and can assume the shape of the container in which these are stored.
Vapor pressure or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with itscondensed phases (solid or liquid) at a given temperature in a closed system
The temperature at which vapour pressure of liquid is equal to the external pressure is called boiling temperature at that pressure.
At 1 atm pressure boiling temperature is called normal boiling point.
If pressure is 1 bar then the boiling point is called standard boiling point of the liquid.
Surface tension is defined as the force acting per unit length perpendicular to the line drawn on the surface of liquid. It is denoted by Greek letter (Gamma). It has dimensions of kg s–2
and in SI unit it is expressed as N m–1
The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress. For liquids, it corresponds to the informal concept of "thickness". For example, honey has a much higher viscosity than water.
If the velocity of the layer at a distance dz is changed by a value du then velocity gradient is given by the amount du/dz.
A force is required to maintain the flow of layers. This force is proportional to the area of contact of layers and velocity gradient i.e.
Where is proportionality constant and is called coefficient of viscosity.