STATES OF MATTER: THE GASEOUS STATE

                                                            STATES OF MATTER

• Gases, liquids, and crystalline solids are the primary states of matter or phases.
• The molecules, atoms, and ions in the solid state are held in close proximity by intermolecular, interatomic, or ionic forces.
• Solids with high vapor pressures, such as iodine and camphor, can pass directly from the solid to the gaseous state without melting at room temperature, known as Sublimation. Freeze Drying involves the principles of sublimation. The reverse process is called Deposition.
• There exhibits a fourth phase called as Mesophase, which lies in between the liquid and crystalline states called as Liquid Crystalline State. Supercritical Fluids are also considered a mesophase that lies in between liquids and gases.

GASEOUS STATE:

• In gaseous state, the molecules move randomly with vigorous motion which results in collision not only with themselves but also with the walls of the container due to which they exert a pressure.
• Pressure is defined as force per unit area. The units are dynes/cm² or atm or mm of Hg or bar or pascal.
• Another important characteristic of gases is its volume. It is expressed in litres or cubic centimeters. (1cm³ = 1mL)
• The temperature is given in Kelvin scale. (0⁰C = 273.15K)

THE IDEAL GAS LAW:-

Boyle's Law states that at constant temperature, pressure is indirectly proportional to the volume

                   

                                                                P 𝛂 1/V

                                                                PV = k (constant)

Gay-Lussac and Charles's Law states that at constant pressure, volume is directly proportional to the temperature

                                                                V 𝛂 T

                                                                V = kT

                                       

Then combine both the equations, we get the ideal gas equation, i.e.,  PV/T = k

                                                                 

                                                        P₁V₁/T₁ = P₂V₂/T₂

P₁, V₁, T₁, are the values under one set of conditions and P₂, V₂, T₂ are the values under another set of conditions. It is expressed mathematically as,

              

                                                           PV/T = R

                                                           PV = RT (for one mole of gas), where R = universal gas constant 

                                                           PV = nRT (for n moles of gas) 

This is known as ideal gas law. Real gases do not interact without energy exchange, and therefore do not follow the laws of Boyle, Gay-Lussac and of Charle's. 

The values of R are 0.08205 liter atm/mole K 

                                8.314 joules/mole K

                                8.314 x 10⁶ erg/mole K

                                1.987 cal/mole deg

In gas law problems, R is usually expressed in litre atm/mole deg, whereas in thermodynamic calculations expressed in cal/mole deg or joule/mole deg.

MOLECULAR WEIGHT:-

The molecular weight of a gas is determined using ideal gas equation.

The no. of moles of a gas (n) = no. of grams of gas (g)/ mol. wt of gas (M)

                                                   

                                                PV = gRT/M

                                                M = gRT/PV

The two common methods used to determine the mol. wt of easily vaoprized liquids such as alcohol and chloroform are the Regnault and Victor Meyer methods.

KINETIC MOLECULAR THEORY:- This theory explains the behaviour of gases and to lend additional support to the validity of the gas laws. Important points of the theory are:

• Gases are composed of particles called atoms or molecules, the total volume of gases is so small that it is negligible when compared to the volume of the space in which the molecules are confined.
• The particles of the gas do not attract one another, but move with complete independence.
• The particles exhibit continuous random motion owing to their kinetic energy. The average kinetic energy is directly proportional to the absolute temperature of the gas

                                                                          E = 3/2 RT

• The molecules exhibit perfect elasticity i.e., there is no net loss of speed or transfer of energy after they collide with one another and with the walls of the container.
• From these postulates, the Fundamental kinetic equation is derived:

                                                            PV = 1/3 nmc²

where P - Pressure, V - Volume occupied by any n no. of molecules of mass m having an average velocity of c

• The root mean square velocity is expressed as (c²)½, usually written as 𝛍 

                                                     𝛍 = √3PV/nm = √3RT/M 

for one mole of gas PV becomes RT and n becomes Avagadro's number N_A, and N_A multiplied by the mass of one molecule becomes the molecular weight M.

                                                     𝛍 = √3p/d  (because V/nm = density)

This equation shows that rate of diffusion is inversely proportional to the square of its density. This relation was early found by Graham who showed that a lighter gas diffuses more rapidly through a porous membrane than does a heavier one.

THE VAN DER WAALS EQUATION FOR REAL GASES:-

The equation is  (P + a/V²) (V - b) = RT  (for one mole of gas)

                           (P + an²/V²) (V - nb) = nRT  (for n moles of gas)

a/V² accounts for the  internal pressure denoting intermolecular forces of attraction between the molecules.

b accounts for the incompressibility of the molecules, that is excluded volume, which is about four times the molecular volume.

• Polar liquids have high internal pressures and serve as solvents only for substances of similar internal pressures. Non-polar molecules have low internal pressures and are not able to overcome the powerful cohesive forces of the polar solvent molecules. For ex, Mineral oil is insoluble in water due to its non-polar nature.
• At low pressures and high temperatures real gases behave as an ideal gas.
• Fugacity is a measurement of the activity associated with non-ideal interactions.

Difference between Real gases and Ideal gases 

Reference: Martin