Notes of AKUEB

SLOs	Topic
4.1		Kinetic Molecular Theory:                                                           This Theory describes the behavior of different stats of matter. However it is a best model for an ideal gas. So, it is also called kinetic molecular theory of gases. The main postulates of this theory are as given below:    Postulates: 1)      Gases are composed of a large number of particles that behave like hard, spherical  objects in a state of constant, random motion. 2)      These particles move in a straight line until they collide with another particle or the walls of the container. 3)      These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space. 4)      There is no force of attraction between gas particles or between the particles and the walls of the container. 5)      Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container. 6)      The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else. 7)      Gases exert pressure  which the result of collision of molecule of gas to the walls of container
	4.1.2	GAS LAW:    The gases have volume, pressure, temperature etc. All these quantity are related to one and another according to some statement, called “The gas laws”.. some of the important gas laws are as follow: ü   Boyle’s law. ü   Charle’s law. ü   Avogadro’s law. ü   Graham’s law of diffusion. ü   Dalton’s law of partial pressure. Boyle’s Law:             Robert Boyle, in 1662, showed the relationship between the pressure and the volume of a gas at constant temperature. This is called “BOYLE’S LAW.” Statement 1:             According to the Boyle’s law “At constant temperature, the volume of a given mass of gas is inversely proportional to the pressure applied on it.” Explanation:             It means that the increase in pressure would result in a decrease of volume of a gas, similarly the decrease in pressured result in the increase in the volume. Simply we can say, if the pressure is doubled, the volume becomes half and if the pressure is reduce to half, the volume becomes double.        Mathematic Expression: Mathematically, Boyle’s law can be expressed  as  (at constant temperature)                 ð P x V =K             Where K = proportionality constant. This equation gives another statement Boyle’s law, which is as under: Statement 2: “At constant temperature, the product of pressure and a volume of a given mass of a gas is always constant.” Therefore; if P1 & V1 are initial pressure & volume, & P2 & V2 are changed pressure & volume, Then                            P1V1=P2V2  This is called “Boyle’s law equation Graphical Representation:             When pressure’ P’ of a given mass of a gas is plotted against it’s volume ‘V’, a parabolic curve is obtained, showing the decrease in volume in increasing temperature.  On the contrary, when pressure ‘P’ of a given mass oa a gas is plotted against reciprocal pf volume i.e.  a straight line is obtained. This confirms the direct relationship between ‘P’ and ‘’. Limitations of Boyle’s law: This law is not obeyed by gases under conditions of high pressure & law temperature. CHARLE’S LAW:             In 1787, a French physicist, Charles’s showed the relationship between the volume of a given mass of a gas and it’s temperature at a constant pressure. This law is called Charles’s law STATEMENT # 1:                                                   According to this law: “At constant pressure, the volume of a given mass of a gas is directly proportional to the absolute    temperature.” EXPLAINATION:             It means, if the pressure is kept constant, the increase in temperature would result also in increase the volume of a given mass of a gas. Similarly, the decrease in temperature results also in decrease in the volume of a gas. MATHEMATICAL EXPRESSION:                         Mathematically, Charle’s law can be expressed as: VaT    (At. Constant Pressure) OR      V=KT      OR  This expression gives another statement of Charle’s law, which is as under. STATEMENT#2: “At constant pressure, the ratio of volume to the absolute temperature of given mass of a gas is always constant.” Therefore; if V1&T1 are initial volume & temperature & V2 &T2 are changed volume & temperature. Then This is called “CHARLES’S law equation.” EXPERIMENTAL VERIFICATION:             Consider a gas cylinder fitted with a move able piston. The volume of the gas enclosed in the cylinder is V1 at temp. T1 . When the gas is heated to T2, its volume is increase to V2 by moving the piston upward. It the pressure on the piston is kept constant, then it is observed that the ratio between V1 andT1 is equal to the ratio V2 and T2.i.e.                                                                  This verifies the Charle’s law.                                                                       -300    -200      -100             0                      100         200        300 GRAHAM’S LAW OF DIFFUSION:             Diffusion is the natural process by which gases intermix with one another to form a homogenous mixture. In 1833, Graham established a relation ship between the rate of diffusion of gases and their densities which is terms as “Gaham’s law of diffusion”. STATEMENT:             According to this law, “The rates of diffusion of gases are inversely proportional to the square root of their densities under same condition of temperature and pressure”. MATHEMATICAL Expression:             Mathematically, graham’s law can be expressed as: OR                              Where  r = rate of diffusion of gas,                         d= density of gas,                         K= Proportionality constant.             Suppose two gases with densities d1 & d2, diffuse into each other. If the rate of diffusion of the gases are r1 & r­2 respectively, then according to graham’s law:             For gas 1,        &         For gas 2,        By combining the two equations, we get             Since the density of a gas is proportional to its molecular mass, so Graham’s law may also be expressed as: Experimental Verification:             Take a 100 cm long glass tube. Plug one end of it with a piece of cotton soaked in NH3 solution and the other with a piece of cotton soaked in HCl solution as shown in the diagram.             The vapours of NH3 and HCl escape into the glass tube simultaneously. A white ring of NH4Cl appears at the meeting point of the two gases. Measure out the distance of te white ring from two ends. Suppose, the distance covered by NH3 = 60 cm & the distance covered by HCl = 40 cm Since the time ‘t’ is the same, therefore The rate of diffusion of NH3 gas = & the rate of diffusion of HCl gas = \ Molecular Mass of NH3 = = 17 & Molecular Mass of HCl = = 36.5 \ According to Graham’s law of diffusion, 1.5       =          1.5 Since L.H.S. = R.H.S., therefore Graham’s law of diffusion of gases is verified. Dalton’s Law of Partial Pressure:             The behavior observed, when two or more gases are placed in same container is summarize in Dalton’s Law of Partial Pressure. Statement:                  In 1801, Dalton’s found that             “The total pressure of a gaseous mixture is the sum of the              partial pressure, exerted by each of the gases present in                    the mixture”. Mathematical Expression:             Mathematically this law can be expressed as, P = P1 + P2 + P3 + ……………… Where P          = Total pressure of gaseous mixture                         P1         = Partial Pressure of gas 1.                         P2         = Partial Pressure of gas 2.                         P3         = Partial Pressure of gas 3. Explanation:             When two or more gases which do not react chemically, are mixed in the same container, then each gas will exert the same pressure as it would exert if it alone occupied the volume containing the mixed gases, under the same condition. This portion of the total pressure of a mixture is known as PARTIAL PRESSURE. Dalton observed that the total pressure of a mixture of different gases is always equal to the sum of individual or partial pressure of each gas present in a mixture. Experimental Verification:             Let us suppose that two different gases A & B are confined in two separate compartments as shown, in the figure. Both the compartments are of same size with a pressure measuring device. Now suppose that the pressure of a gas is ‘A’ is 800 torr and that of gas ‘B’ is 900 torr in their separate compartments. If gas ‘A’ was transferred into the compartment ‘B’ with the help of a movable piston through the total pressure in this compartment would be the sum of the original pressure in the two compartments when the gases were occupying same volume separately. i.e.       Ptotal     =          PA        +          PB             1700    =          800      +          900             1700    =          1700 Hence, law is verified.
	4.1.3	KMT EXPLAINATION FOR BOYLE’S LAW   Boyle’s law can easily be explained on the basis of the kinetic theory of gases, when the volume of a given amount of a gas is decrease, there is more crowding of the molecules in that space. This result in more frequent collision between the molecules and the walls of the container and thus the pressure of the gas is increased and vise-versa. Limitations of Boyle’s law: This law is not obeyed by gases under conditions of high pressure & law temperature. KMT EXPLAINATION FOR CHARLES’ LAW             This law can be easily explained with the help of Kinetic molecular theory as: An increase in temperature increases the K.E. of gas molecules which results in their more collision per second against the walls of the container. But if the pressure is kept constant the extra force of the colliding molecules is utilized for the expansion of gas, i.e. increase in volume. KMT EXPLAINATION FOR AVOGADRO ‘S LAW             It means that, if we take different sample of different gases at same temperature and pressure, then if the volume of each gas sample is equal, the no. of molecules of each sample will be also equal evidently, if we increase the volume of gas sample, the no, of molecules will be also increase.             Avogadro’s also found that at the some condition of temperature and pressure, the one mole  of any gas occupies always 22.4dm3 volume, this volume is called molar gas volume. Also, this volume contain always constant no. of particles of gas, and its value is 6.02 x 1023. This value is called Avagadro’s number.
	4.2.1	Charles’s law can also be explained by graphical method, if the volume of the given mass of a gas is plotted against its absolute temperature values at a constant pressure, a straight line is obtained, showing the direct relationship between ‘V’ and ’T’. If the straight line is extra plotted it intercepts the temperature axis at -273.16oC. This temperature is called “ABSOLUTE ZERO”. ABSOLUTE ZERO:             It is a hypothetical temperature, at which the volume of all gases become zero. Its value is -273.16oC.This temperature can never be achieved. The scale on which -273.16oC is taken as zero is called “KELVIN SCALE” and is indicated by K. Centigrade is related to Kelvin scale as; oK = oC + 273
	4.2.2	NUMBERICAL
	4.3.1	AVAGADRO’S LAW:             In 1811, Amadeo Avagadro stated the relation ship between the volume and the no. of molecules of the gas. This is called “AVAGADRO’S LAW”. Statement:             According to Avogadro’s law;“The Volume of a gas is directly proportional to the number of molecules of the gas at constant temperature & pressure”. Explanation:             It means that, if we take different sample of different gases at same temperature and pressure, then if the volume of each gas sample is equal, the no. of molecules of each sample will be also equal evidently, if we increase the volume of gas sample, the no, of molecules will be also increase.             Avogadro’s also found that at the some condition of temperature and pressure, the one mole  of any gas occupies always 22.4dm3 volume, this volume is called molar gas volume. Also, this volume contain always constant no. of particles of gas, and its value is 6.02 x 1023. This value is called Avagadro’s number. Mathematical Expression:             Mathematically, Avogadro’s law can be written as, V µ n OR V = K n Where n= no. of molecules of gas
	4.4.1	General Gas Equation:             Boyle’s law, Charles law and Avogadro’s law may be combined together to give a general relation between the pressure, volume, temperature and no. of moles of a gas. This relationship is called “General Gas Equation”             According to Boyle’s law                   According to Charle’s law      V µ T On combining these three laws. We get  OR      OR      PV= nRT             This expression is called ‘GENERAL GAS EQUATION’. Where ‘R’ is a proportionally constant and is called gas constant. For 1mole of a gas, n=1. \PV=RT
	4.4.2	When the temperature of a gas changes from T1 to T2, then its volume as well as pressure changes from V1 to V2 and P1 to P2.                 \ For initial state:                         & For final state: Combine these two, we have             This relationship is used to solve problems regarding changes of volume of gases, due to the changes in the pressure & temperature. VALUES & UNIT’S OF ‘R’: (a)                           According to Avagadro’s law, at S.T.P the one mole of any gas occupies a volume of 22.4dm3. i.e.       T=0˚C=273oK ,           P=1atm.,          n=1mole  and V=22.4dm3             Then the value and unit of gas constant will be; (b)                           When ‘P’ is expressed in and volume ‘V’ in m3,then at                  S.T.P,                         P=101300 ,V=0.0224m3           , n=1mol.  And             T=273oK.                         Then the value and unit of gas constant will be. \ R = 8.314 N.m / mole x K R = 8.314 J/mole x K
	4.4.3		U
	4.4.4		A
4.5	4.5.1	Deviations from ideal behavior Ideal gas : a gas which obeys the general gas equation and other gas laws under all conditions of temperature and pressure is known as Ideal gas or perfect gas. The molecules of an ideal gas : (i)                 Occupy negligible or no volume (ii)               Have no inter-molecular attractive forces. Real gas : a gas which does not obeys  general gas equation and all other gas laws strictly but tends towards ideality at low pressure and high temperature is knonw as real gas . Ideal gas Real gas 1 It obeys gas laws (PV=nRT)under all conditions of temperature and pressure . It  obeys gas laws at high temperature and low  pressure . 2 It does not exist in actual practice. Gases like N2 ,H2, etc. which cannot liquefied easily are nearly ideal.  All gases are real gases. 3 Volume occupied by a gas molecule is negligible as compared to the total volume of gas . Volume  occupied by molecules of   gas negligible . 4 Attractive forces between gas molecules are negligible  Attractive forces between gas molecules are appreciable due to which pressure exerted is less than that calculated from gas laws.       Cause of deviations from ideal behavior In order  to explain deviations from ideal behavior ,Vander waal pointed out that the following two assumptions in kinetic theory are faulty. (i)                 The volume occupied by the gas molecules themselves is negligible as compared to total volume of the gas The above assumption is nearly valid if the pressure is low .At low pressure ,the gas molecules are widely separated  and the free space between the molecules is very large in comparison to the actual volume of molecules of the gas. Under such condition, the volume of the gas molecules can be neglected in comparison to the total volume. At the high pressure, the molecules of gas are relatively closed together and the total volume is significantly less . However  the actual volume of the gas  molecules remains unchanged because the gas molecules are incompressible. Under these conditions, the volume of  a real gas is larger than that for an ideal gas. (ii)               The molecules of a gas exert no appreciable attraction upon each other . This assumption is nearly valid when the pressure is low and the temperature is high so that  the molecules are far away from each other . if the pressure is high and the temperature is low , the volume of the gas decrease .Gas molecules come closer to each other .The attractive force between  the gas molecules under these conditions are quite appreciable and can not neglected .    Reff. ISC  Chemistry FOR CLASS XI VOLUME I                                           By K.L.CHUGH (Deptt. Of chemistry ,Arya college LUDHIANA) KALYANI PUBLISHERS	U
	4.5.2	Numerical for ideal equation
4.6	4.6.1