States of Matter

Content

Intermolecular forces

Boyle's law

Charle's law

Gay Lussac's law

Avogadro's law

Dalton's law of partial pressure

Kinetic theory of gases

Vander Waal's equation

Liquid state and its properties

Matter is regarded as a substance that has mass and occupies volume. There are three states of matter solid, liquid and gases.

Three states of the matter are the result of balance between intermolecular forces and the thermal energy of the molecules.

Note:- Thermal energy is the average kinetic energy of the particles of matter and is thus responsible for movement of the particles.


The Gaseous State

Gases are characterized by the following physical properties - Low density and high compressibility, high kinetic energy high diffusibility, large intermolecular space etc.

Behaviour of gases is governed by some general laws.

Boyl's law states at the constant temperature, the pressure of the amount of gas (n) varies inversely with its volume. It can be written as

P 1/v (at constant T and n)

or p₁v₁ = p₂v₂ = constant



Boyle's law (pressure vs volume)

According to the Charle's law, the volume of a given mass of a gas is directly proportional to the absolute temperature at constant pressure. It can be represented as

V T

[ or V₁/T₁ = V₂/T₂ = .....]

Here T is taken in Kelvin scale or absolute temperature scale. Thus 0^oc on the celcius scale is equal to 273.15 K at the absolute scale.

The lowest hypothetical or imaginary temperature at which gases are supposed to occupy zero volume is called absolute zero.

The mathematical relationship between pressure and temperature was given by Gay Lussac and according to his law, at constant volume, pressure of the fixed amount of gas varies

directly with the temperature. It can be represented as

V T

Or V/T= constant

Or V₁/T₁ = V₁/T₂ = ..........


Avogadro combined the conclusion of Dalton's atomic theory and Gay Lussac's law of combining volumes which is now known as Avogadro's law which states that equal volumes

of all gases under the same condition of the temperature and pressure contain equal number of molecules. It can be represented as

V n (where n is the number of moles)

The number of molecules in one mole of a gas has been determined to be 6.022 x 10²³ and is known as Avogadro's constant.


Since volume of the gas is directly proportional to the number of moles; one mole of each gas at standard temperature and pressure (STP) will have same volume.


Hence, at STP, molar volume of an ideal gas is 22.71098 L mol^-1.

STP denotes the temperature of 00c (273.15 k) and pressure of 1 atm.

A gas that follows Boyle's law, Charle's law and Avogadro law strictly is called an ideal gas. Such a gas is hypothetical.

The three gas laws i.e., Boyle's law, Charles law, Avogadro's law can be combined together in a simple equation which is known as ideal gas equation or combined gas laws. It can

be represented as

PV/T = constant or PV = nRT or P₁V₁/T₁ = P₂V₂/T₂

where R = universal gas constant

Note: The value of R depends upon units in which P, V, T are measured. Different units of R include R = 0.0821 L atm K^-1 mol^-1 = 8.314 J K^-1 mol^-1= 8.314 × 10⁵ Pa m³

K^-1 mol^-1 = 8.314 × 102 kPa dm³ K^-1 mol^-1= 8.314 Mpa cm³ K^-1 mol^-1 = 1.987 cal K^-1 mol^-1


Also, The total pressure exerted by the mixture of non reactive gases is equal to the sum of the partial pressures of individual gases. This law is known as Dalton's law of partial

pressure. It can be represented as

P_total = P₁ + P₂ + P₃ (at constant T, V)

Where Ptotal = total pressure exerted by the mixture of gases

P₁ + P₂ + P₃ = partial pressures of the gases



Graham's Law of Diffusion: The rate of diffusion of a gas is inversely proportional to the square root of its density or molar mass. Mathematically, it is expressed as

r

Comparison of the rate of diffusion of two gases under identical conditions provides the relation



where d₁ and d₂ are vapour density of two gases M1 and M2 are molecular mass of two gases.



The phenomenon of converting a gas into liquid is known as liquifaction. The temperature for a given gas below which a continuous increase in pressure will bring liquifaction of gases

and above which no liquifaction is noticed although pressure is increased many folds is known as critical temperature (Tc). The minimum pressure applied on one mole of gas placed at

critical temperature to liquefy the gas is known as critical pressure and the occupied by one mole of gas placed at critical temperature is called critical volume


.
Liquid state:

The liquid state is intermediate betn gaseous and solid states.

The properties of the liquids are as follows:

Vapour pressure is the pressure exerted by the vapour over a liquid when both are in the state of dynamic equilibrium. The temperature at which vapour pressure of a liquid is equal

to the external pressure is called boiling temperature. At 1 atm pressure boiling temperature is called normal boiling point of the liquid. If pressure is 1 bar then the boiling point is called

standard boiling point of the liquid.

Surface tension is defined as force acting per unit length perpendicular to the line drawn on the surface of liquid. Its unit is Nm-1.

Note: The rise of the liquid in capillary tube, spherical shape of the drop of liquid is due to surface tension.


viscosity is the measure of resistance to flow which arise due to internal friction between the layers of the fluids as they pass over each other.

Some other important formulae


1. Root Mean Square Speed

and is given by the expression





2. Average Speed





3. Most Probable Speed


Comparing the three speeds listed above, we find that

u_rms : u_av : u_mp : :

u_rms > u_av > u_mp



4. Average Kinetic Energy

Where k = R/N_A is known as Boltzmann constant.



5. Van der waal's Equation of State:

Van der Waal pointed out that the deviations shown by real gases are due to the following two facts.

1. The volume occupied by the molecules is not negligible in comparison to the total volume of the gas.

2. There exist forces of attraction between the molecules.

Van der Waal systematically corrected the ideal gas equation in the light of the above two facts. The corrected equation is



where Z is known as compressibility factor