Thermo & Stat Mech - Spring 2006 Class 141 GASEOUS STATE PHYSICAL CHEMISTRY B.Sc. FIRST YEAR FIRST SEMESTER

Thermo & Stat Mech - Spring 2006 Class 142 Maxwell Velocity Distribution Maxwell’s in 1886 suggested that : Maxwell’s in 1886 suggested that : “At a particular temperature,the fraction of molecules possessing particular velocities remain almost constant.” “At a particular temperature,the fraction of molecules possessing particular velocities remain almost constant.”

Thermo & Stat Mech - Spring 2006 Class 143 On the basis of laws of probability, fraction of molecules having velocities between c and c+dc Where dnc is the no of molecules having velocities between c and c+dc,out of a total of n molecules of the gas and T are the molecular mass and absolute temperature of the gas. The above equation may be rewritten as

Thermo & Stat Mech - Spring 2006 Class 144 C p=1/n.dnc /d c α FIGURE:-1 MAXWELL’S DISTRIBUTION OF VELOCITIES

Thermo & Stat Mech - Spring 2006 Class 145 MAXWELL’S DISTRIBUTION OF VELOCITIES TTTThe Fraction of the molecules having very low velocities or very High velocities are very small. TTTThe fraction of molecules possessing higher speeds keeps on increasing till it reaches a peak and thereafter it starts decreasing. TTTThe maximum fraction of molecules possess a velocity corresponding to the peak in the curve.This velocity is referred as Most probable velocity.

Thermo & Stat Mech - Spring 2006 Class 146 EFFECT OF TEMPERATURE ON MAXWELL’S DISTRIBUTION OF VELOCITIES With increase of temperature, the curve shifts as shown in fig. Two changes may be noticed: i)The peak of the curve shifts forward. he peak of the curve shifts downward and is flattened. FIGURE:-2 DISTRIBUTION OF VELOCITIES AT TWO DIFFERENT TEMPERATURE T1T1 T2T2

Thermo & Stat Mech - Spring 2006 Class 147 Collision diameter The closest distance of approach between the centres of the molecules taking part in a collision is called collision diameter. it is usually represented by σ. σ FIGURE:3 MOLECULAR DIAMETER

Thermo & Stat Mech - Spring 2006 Class 148 Collision Number The no of collision which a single molecules makes with other molecules in one second is called collision number. On the basis of kinetic theory of gases, it can be shown that: NC =√2πνσ2n Where v=average velocity of the gas molecules in cm per sec σ=molecular diameter in cm n=no of molecules/cm

Thermo & Stat Mech - Spring 2006 Class 149 Derivation of collision no & collision frequency Consider a particular molecule A moving in a particular direction. Average speed of the molecule = v cm/sec Distance travel in one second = v cm Radius(equal to molecular diameter) = σ FIGURE:-4 MOVEMENT OF MOLECULE A ASSUMING OTHER MOLECULES TO BE STATIONARY 2σ2σ σ v cm A

Thermo & Stat Mech - Spring 2006 Class 1410 TYPES OF MOLECULAR COLLISION (a) (b) (c ) (a) (b) (c ) Relative velocity=0 Relative velocity=2v Relative velocity= √2 ν FIGURE:-5 TYPES OF MOLECULAR COLLISION

Thermo & Stat Mech - Spring 2006 Class 1411 COLLISION FREQUENCY The number of collision which takes place in one second among the molecules present in one centimeter cube of the gas is called collision frequency.(Z) Z=1/ √2π ν σ 2 n 2 Thus Z is directly proportional to 1)average velocity of the gas molecules(v) 2)Square of the molecular diameter (σ 2 ) 3)Square of the molecules per cm cube (n 2 )

Thermo & Stat Mech - Spring 2006 Class 1412 THE FREE PATH OF A MOLECULE The distance travelled by a molecule before colliding with another molecule is called the free path. FIGURE:-6 DIFFERENT FREE PATHS OF A MOLECULE

Thermo & Stat Mech - Spring 2006 Class 1413 THE MEAN FREE PATH The mean distance travelled by a molecule between any two successive collision is called the mean free path. The mean distance travelled by a molecule between any two successive collision is called the mean free path. l=v /N c l=v /N c but Nc= √ 2πνσ 2 n but Nc= √ 2πνσ 2 n therefore l=v/ √ 2πνσ 2 n therefore l=v/ √ 2πνσ 2 n l=1/ √ 2πσ 2 n l=1/ √ 2πσ 2 n

Thermo & Stat Mech - Spring 2006 Class 1414 IDEAL AND REAL GASES IDEAL GAS:- A gas which obeys the gas equation (PV=nRT) under all condition of temperature and pressure is called an ideal gas. for example: hydrogen, oxygen, nitrogen REAL GAS:- A gas which obeys the gas laws fairly well under low pressure or high temperature. for example: carbon dioxide,sulpur dioxide, ammonia

Thermo & Stat Mech - Spring 2006 Class 1415 DEVIATION FROM THE GAS LAWS AND EXPLAINATION IN TERM OF COMPRESSIBILITY FACTOR AND BOYLE TEMPERATURE The Effect of temperature and pressure on the behaviours of a gas may be studied in terms of a quantity ‘z’ called compressibility factor which is defined as The Effect of temperature and pressure on the behaviours of a gas may be studied in terms of a quantity ‘z’ called compressibility factor which is defined as z=PV/nRT z=PV/nRT

Thermo & Stat Mech - Spring 2006 Class 1416 EFFECT OF PRESSURE:COMPRESSIBILITY FACTOR Compressibility factor,z is mathematically expressed as z=PV/nRT In case of ideal gas,PV=nRT z=1 In case of real gas,PV≠nRT z≠1 Thus in case of real gases,the value of z can be 1. (i)When z<1, it indicates negative deviation. (ii)When z>1,it indicates positive deviation.it means gas is less compressible.

Thermo & Stat Mech - Spring 2006 Class 1417 PLOT OF COMPRESSIBILITY FACTOR (z ) VS PRESSURE FOR SOME GASES FIGURE:-7 PLOT OF Z vs P

Thermo & Stat Mech - Spring 2006 Class 1418 EFFECT OF TEMPERATURE:BOYLE TEMPERATURE The deviation from ideal behaviour become less and less with increase in temperature. The temperature at which a real gas behave like an ideal gas is called boyle’s temperature. The deviation from ideal behaviour become less and less with increase in temperature. The temperature at which a real gas behave like an ideal gas is called boyle’s temperature. The boyle temperature is different for different gases. The boyle temperature is different for different gases.

Thermo & Stat Mech - Spring 2006 Class 1419 z P (Atmosphere) IDEAL GAS 50⁰C 100⁰C -50⁰C 0⁰C PLOT OF COMPRESSIBILITY FACTOR z vs pressure FOR N 2 AT DIFFERENT TEMPERATURE. 50°C -50°C 0°C FIGURE:- 8 PLOT OF z vs P FOR N 2 AT DIFF. TEMP

Thermo & Stat Mech - Spring 2006 Class 1420 CRITICAL CONSTANTS The critical temperature, critical pressure and critical volume of a gas are collectively called as the critical constants.These constants are represented by T C,CC. The critical temperature, critical pressure and critical volume of a gas are collectively called as the critical constants.These constants are represented by T C, P C V C. Critical Temperature of a gas may be defined as that temperature above which the gas can’t be liquefied. Critical pressure of a gas may be defined as the minimum pressure required to liquefy the gas at critical temperature. Critical volume of a gas may be defined as the volume occupied by one mole of the gas at the critical temperature and pressure.

Thermo & Stat Mech - Spring 2006 Class 1421 MEASUREMENT OF CRITICAL CONSTANTS The measurement of critical temperature is based upon the observation that when a liquid is heated in a closed space, the surface of separation between liquid and the vapour disappears at a definite temperature and on cooling,the surface of separation reappears at the same temperature.The temperature at which this occur is called critical temperature. The measurement of critical temperature is based upon the observation that when a liquid is heated in a closed space, the surface of separation between liquid and the vapour disappears at a definite temperature and on cooling,the surface of separation reappears at the same temperature.The temperature at which this occur is called critical temperature.

Thermo & Stat Mech - Spring 2006 Class 1422 MEASUREMENT OF CRITICAL TEMPERTURE AND CRITICAL PRESSURE AIR MANOMETER HEATING JACKET VAPOUR LIQUID OR LIQUIFIED GAS FIGURE:-9

Thermo & Stat Mech - Spring 2006 Class 1423 MEASUREMENT OF VC The measurement of critical volume is based upon a rule given by Cailletet and Mathias in 1886 which states that “the mean of the densities of any substance in the state of liquid and saturated vapour at the same temperature is the linear function of the temperature”.

Thermo & Stat Mech - Spring 2006 Class 1424 DETERMINATION OF CRITICAL DENSITY B D A MEAN DENSITIES DENSITIES OF LIQUID C DENSITIES OF VAPOUR (d l +d v )/2 DENSITY TEMPERATURE FIGURE:-10

Thermo & Stat Mech - Spring 2006 Class 1425 ISOTHERMS OF CARBON DIOXIDE Andrews,in 1861, was the first to study the effect of temperature and pressure on the volume of carbon dioxide. Each time, keeping the temperature constant at a particular value, he measured the volume of carbon dioxide at different pressure. He then plotted the volumes against pressure,at constant temperature. Such a plot of P vs V at constant T is called as isotherm or isothermal. Andrews,in 1861, was the first to study the effect of temperature and pressure on the volume of carbon dioxide. Each time, keeping the temperature constant at a particular value, he measured the volume of carbon dioxide at different pressure. He then plotted the volumes against pressure,at constant temperature. Such a plot of P vs V at constant T is called as isotherm or isothermal.

Thermo & Stat Mech - Spring 2006 Class 1426 ISOTHERMS OF CARBON DIOXIDE PRESSUREPRESSURE VOLUME CB LIQUID GASEOUS A E a b 48.1°C 35.5°C 32.5°C 31.1°C 21.5°C 13.1°C FIGURE :-11

Thermo & Stat Mech - Spring 2006 Class 1427 LIQUEFACTION OF GASES A gas can be liquefied by cooling or by application of pressure or by the combined effect of both. A gas can be liquefied by cooling or by application of pressure or by the combined effect of both. No of attempts were made earlier,that of Faraday is well known in No of attempts were made earlier,that of Faraday is well known in 1823.

Thermo & Stat Mech - Spring 2006 Class 1428 Reactants Liquefied gas Freezing mixture FARADAY’S METHOD FIGURE:-12

Thermo & Stat Mech - Spring 2006 Class 1429 PERMANENT GASES Gases like hydrogen,helium,oxygen,nitrogen etc however, could not be liquefied by the application of pressure alone, however high it may be. Such gases, therefore, called “permanent gases”. Gases like hydrogen,helium,oxygen,nitrogen etc however, could not be liquefied by the application of pressure alone, however high it may be. Such gases, therefore, called “permanent gases”. Even these gases could be liquefied provided these were first cooled to or below their respective critical temperatures. Even these gases could be liquefied provided these were first cooled to or below their respective critical temperatures.

Thermo & Stat Mech - Spring 2006 Class 1430 EARLIER METHODS  By the rapid evaporation of volatile liquids. liquids.  By the use of freezing mixtures

Thermo & Stat Mech - Spring 2006 Class 1431 MODERN METHODS 1)BY THE ADIABATIC EXPANSION OF COMPRESSED GAS-LINDE’S PROCESS:- This process is based upon Joule-Thomson Effect which states :- This process is based upon Joule-Thomson Effect which states :- When a gas under high pressure is allowed to expand adiabatically through a fine hole into a region of low pressure it is accompanied by cooling. When a gas under high pressure is allowed to expand adiabatically through a fine hole into a region of low pressure it is accompanied by cooling.

Thermo & Stat Mech - Spring 2006 Class 1432 A C H2OH2O D F E G LINDE’S PROCESS FOR LIQUEFACTION OF AIR B FIGURE:-13

Thermo & Stat Mech - Spring 2006 Class )BY THE ADIABATIC EXPANSION OF A COMPRESSED GAS INVOLVING MECHANICAL WORK-CLAUDE’S PROCESS:- This is based upon principle that when a gas expands adiabatically against a piston in an engine, it does some external work; hence its internal energy falls and consequently the temperature of the gas falls.

Thermo & Stat Mech - Spring 2006 Class 1434 CLAUDE’S PROCESS AIR COMPRESSOR X Y J D G LIQUID AIR FIGURE:-14

Thermo & Stat Mech - Spring 2006 Class )BY ADIABATIC DEMAGNETISATION:- This process was given independently by Debye and Giauque.This process is based upon the principle that when a magnetised body is demagnetised adiabatically the temperature of the body must fall.

Thermo & Stat Mech - Spring 2006 Class 1436 THANK YOU