Gas Laws part 11

Hinzugefügt: 2026-05-15

[00:00:00]now coming to the kinetic theory of gases here we will be doing that is according to the kinetic theory of gases we are going to prove the ball's law that is charles law and the dalton's law of partial pressure all right that is we are going to explain or we have improved the this particular three gas laws by the help of kinetic theory of gases okay so now first we will come to the boyle's law all right first we will explain the boyle's law or will prove the boyle's law from the kinetic theory of gases now let me tell you boyle's law what it says is that that pressure is inversely proportional to volume when temperature remains constant for a given mass of a dry gas all right p is inversely proportional to v when t remains constant for a given mass of a dragon that is what the boyle's law suggests now we have seen it from the that is we are going to describe the boyle's law so the kinetic gas equation is tv is equal to 1 by 3 mnc square where p is the pressure v is the volume m is the mass of ah one molecule of a gas n stands for the number of molecules ah present in the certain volume of gas v and c is the root mean square velocity we can say that now we can also write this one as 1 by 3 m c square where m stands for the molar mass because m into n mass of one mole of the gas into number of moles will give you the molar mass of the gas m c square now this equation i can write it in this way also that is uh 2 by 3 into half m c square i can write say this 2 to cancel 1 by 3 now why did i write it because half m c square is kinetic energy so pv is equal to two by three k e sorry now next is uh from one of the postulates of kinetic theory of gases we know that k e is directly proportional to t from one of the postulates of the kinetic molecular theory of gases we have studied already now k e is equal to k into that is t we can say ke is equal to kt now we can put it here let us say this is equation number one and this is equation number 2. so we can put the value of 2 in 1 we can put the value of 2 in 1 when we put the value so what we will get pv is equal to 2 by 3 that is 2 by 3 that is instead of k we can write kt now see here it is k is a constant we know is the proportionality constant because k is directly proportional to p where k is a proportionality constant two by three of course it is a number is a constant so pv is directly proportional to t we got it ultimately as a result pv is weekly from here we conclude that pv is really proportional to t that is only the balanced law that is only the boyle's law that pressure is inversely proportional to volume when temperature remains constant all right so here it is nothing but pv is equal to constant we got it we can also say that pv is equal to constant clear so for given when the temperature is also constant so when the temperature is also constant t is constant k is constant 2 is 2 by 3 is constant you can also write pvs directly proportional to t or we can write pv is equal to constant straight away well because in boyle's law t is also constant all right k is constant proportionally constant 2 by 3 is a constant so pv is equal to constant we got it that also we can say that clear in this way what we can say this is this proves the boyle's law okay now next is coming to the charles law next we will come to the charles law volume is directly proportional to its absolute temperature when pressure of a given mass of a dry gas remains constant v is directly proportional to t volume is directly proportional to absolute temperature when pressure of a given mass of a dry gas remains constant okay now just now we have seen it pv is equal to 2 by 3 kt so we got pv is equal to 2 by 3 k t where k is proportional to constant so does it so i can write v by t all right v by t what is that it can be nothing but 2 by 3 that is k what you can say k by p cross multiply p v is equal to you got it 2 by 3 kt will be getting it so v by t is equal to 2 by 3 k p we got it fine now 2 by 3 number constant k is proportional to constant for a what you can say ah for charles law what i said pressure remains constant so hence v by t is equal to constant again just like boyle's law in charleston we got it v by t is equal to constant so it verifies also the charles law all right clear so next after that we will see the dalton's law of partial pressure the dalton's law of partial pressure now what is dalton's law says that dalton's law says that that in a particular container when number of uh gases are present and these gases do not combine with one another then the total pressure exerted by the container is the sum of the individual partial pressure taken together all right let me say again when in a particular container the number of gases are present and the gases do not intermix with one another they do not combine with one another these gases uncombined gases so to say we have studied already then the total pressure exerted by the container is the sum of the individual partial pressure taken together we can say that now we know uh this is your dalton's law we are going to do so we already know dilton's law partial pressure okay so already from the kinetic gas equation we know pv is equal to 1 by 3 m n c square p is equal to 1 by 3 m n c square by v now for different gases for different gases in a particular container number of gases are present so volume remains constant because what i am saying in a particular container wall number of gases are there so volume is constant what is going to differ pressure p1 is equal to 1 by 3 m1 mass will differ number of molecules also will differ and what you can say is that c1 square by v we can say that that is nothing but p 1 is equal to 1 by 3 ah m 1 n 1 c 1 square by v for a particular gas we can see big one for another gas let us say p 2 is equal to what it will be 1 by 3 m2 n2 c2 square by v we can say for the third what you can say gas we can say that what it will be getting it p3 is equal to 1 by 3 m 3 and 3 c 3 square by v we can say that so when i add when i add it that is p total is equal to 1 and added this equation 1 and 2.

[00:07:44]equation 1 and 2 the equation 1 and 2 when i will add it what will i get i will be getting p 1 plus p 2 equation 1 and 2 what is equation 1 this 1 by 3 m 1 say n 1 c 1 square by v plus 1 by 3 m2 n2 c2 square by v so what is this this is equal to p1 and what is this this is p2 so p total is equal to 1 plus 2 p1 plus v2 that is nothing but p1 plus p2 that is only deltan's law of partial pressure which says that that the total pressure exerted by the gases in the container is equal to the sum of the individual partial pressure taken together finished so in this way this is your dalton's law of partial pressure we have explained it on the basis of the kinetic molecular theory of gases so to say we have explained it on the basis of kinetic molecular theory of gases now we are finished up with this now we will come to the behavior of the ideal gas and the real gas behavior of idle and the real gas now next is you know ideal gas what is that ideal gas is a gas which obeys gas loss under all conditions of temperature and pressure under every conditions of temperature pressure i said you earlier also that this particular ideal gas whatever we say it is completely theoretical it is not possible there is no such gases which will obey gas laws under all conditions of temperature and pressure then what are those gases all those gases are the real gases what are real gases real gases are those gases which obeys gas laws under certain conditions of temperature and pressure not under all conditions of temperature pressure so basically all the gases which we are studying hydrogen oxygen nitrogen and everything alright so they are all real gases they are not an ideal gas they are the real gases we can say that all right so under uh what you can say low pressure and high temperature only a particular gas behaves as an ideal gas remember the conditions under low pressure and high temperature a particular gas can behave as a what you can say an ideal gases all right but there are certain gases which shows a deviation from this particular thing there are certain gases which shows the deviation there are certain gases which shows a deviation now in certain gases the deviation is quite large in certain gas division is quite small because of that like suppose the gases which are highly soluble in water listen carefully children the gases which are highly soluble in water all right or easily liquefable the one which can easily liquefied all right again i repeat the gases which are highly soluble in water the gases which are easily liquefable ah like i can give it to you carbon dioxide sulfur dioxide ammonia this gases all right you already in the lower classes they have got low what you can say that is liquefable point the liquid fat very easily under low pressure only they get liquefied and low pressure and low temperature only get they get liquefied all right so the gases which are easily liquefable like this particular gases which i gave you like carbon dioxide sulphate oxide ammonia they show a large deviation from the ideal behavior all right they show a large deviations got it so larger deviation uh then the gases like what you can say the non-polar gases like hydrogen oxygen nitrogen methane these are the non polar gases you know that they show they also show the deviations these are gases also for the deviation because all these are real gases i said earlier only but the gases which are easily liquidable which are easily soluble in water which are more soluble in water they show a larger deviation than this non-polar gases like hydrogen nitrogen oxygen methane etcetera we can say that all right so hence i said you that ideal gas equation is pv is equal to nrt so ah this particular equation is will ah will be true this particular equation will be two when the pressure is low and the temperature is high so basically the real gases behaves as an ideal gas under these conditions when the condition is reversed then there is a deviation then there is a deviation the deviation which i was talking to you then there is a deviations all right when the condition is reversed now we will come to the study of the division i think you understood what is ideal gas and what is that real gas and what should be the condition again i repeat low pressure and high temperature under these conditions only a particular gas behaves as an ideal gas it shows an ideal behavior otherwise under high temperature sorry under high pressure and low temperature they behave all as real gases got it clear now we are very silly about it that how they they show these particular deviations i said you that certain gashes so larger deviation some gas is so deviation but it is less okay fine to study this deviation from the ideal behavior or to study this deviation from the ideal behavior we will take a particular gas law and explain it so you know that we have taken the we know the boyle's law pv against p so this is a boyle's law graph now in case of boyle's law graph you know this straight line graph i will be getting it all right let me draw a little bit below a straight line graph i will be getting it this is a balanced graph if you remember it pv remains constant all right pv remains constant pv is equal to k just so it told you also according to the kinetic molecular theory of gases so in this way what i find is that one particular law i have to take it and i have to explain the deviation from the real gases from the ideal behavior listen carefully repeatedly i am saying you alright so what i find is that ah here this line which i have done it it is for which gas this is for ideal gas i'll prove it also how it is ideal yes so in this way it is for the ideal gas because what i said ideal gas is the gases which obeys gas laws under all conditions of temperature and pressure so which i'm taking this graph depicts which law boys pv against p graph we will be getting a straight line graph under what condition when pv is equal to constant we have done it already in the boltz law you go to go back to the ball's law and you see it we have done this particular graph we have seen this particular graph even if you don't understand i have explained you also just telling the kinetic molecular theory that pv remains constant we can say that so in this way pv remains constant so here this graph you can see is for the ideal cases fine now anything any gases above this below this shows deviations of the ideal gases any gases having the graph above this having the graph below this shows deviation from ideal behavior it shows deviation from ideal behavior so to say now if you draw it you'll find like the non-polar gases like nitrogen hydrogen they show deviation from ideal behavior in this particular manner all right the graph is in this manner now certain gases the one which is easily liquefable the gases like carbon dioxide residue gases like ammonia institute sulphur dioxide acidity they show this sort of graph this sort of deviation now you need to understand this all right you have to understand this particular part that how this shows this sort of deviations got it clear now before going to this particular graph one more thing i want to tell you here we will be studying the compressibility factor now what i said you certain gases are easily liquefable which guesses i've explained you carbon dioxide ammonia sulfur so these are the gases etc also many are more gases are there like excel and all we are also there so they are easily fabricable compared to non polar nitrogen hydrogen what you can say oxygen methane and all those gases which are non polar in nature fine now for liquefying a particular gas what should be the condition the condition should be temperature should be low and the pressure should be high when temperature should be low the pressure should be high is different from the ideal behavior you see what i say a particular gas behaves as an ideal gas under low pressure and high temperature find it and the low pressure high temperature behaves as an ideal gas but what i am saying you here for liquefying a particular gas pressure should be high you have read it in the lower classes also liquefication the process how do you liquefy a particular gas when the pressure is higher and temperature is low when the temperature is being lowered and the pressure is being hired then only the gases gets easily liquefied this is the condition for liquefying a particular gas pressure should be high temperature that means it is a deviation from ideal behavior the condition is different from the ideal behavior now based upon this particular conditions we are going to calculate a factor which is called as compressibility factor denoted by the letter z this is called compressibility factor z stands for compressibility factor how do we calculate that z is equal to pv by nrt z is equal to pv by nrt we can say that okay compressive effect is z now in case of ideal gas pv is equal to nrt compressibility factor z is z is equal to pv energy is the formula for the compressive factor pv by nrt okay compressibility factor now for ideal gas what is the formula the gases which are ideal in nature what is the formula what is ideal gas equation pv is equal to energy now you put the value here in place of z you put it the value what is that you put it in place of nrt you put pv or in place of pv you put energy whatever it is it is going to get cancelled for ideal gas the value is going to get cancelled all right again i repeat this is your compressible factor z this is a formula compressive factor z we have calculated it it has been calculated practically and this is a formula for the ideal gas equation pv is equal to energy you know that now you put this value here you put it here so in place of energy put pv so pv pv gets cancelled z becomes one this is for what gas for ideal gas the value of z is one for ideal gas so here see this is z is equal to one this here z is equal to one i said that i'll be proving it say approved that's z is equal to one this line it's an ideal gas now that means this value is z greater than one and here this area is that less than 1 but if this area is above this better and below this it is less so here it is the value of z is greater than one and below this value of z is less than one see this is the line i am taking now this is the line i'm taking so above this is greater than one and below this that is less than one definitely so in this way here the compressibility factor is greater than one and here the compressibility factor is less than one when i say the compressive factor is greater than one compressibility factor is greater than one that means compressive factor is more it is more so when the compressive factor will be more all right then what is the nature of the gas understand it when the compressibility factor is more what is the compressive factor required temperature should be low pressure should be high now this factor should be more when this factor will be more when the gases are not easily liquefied when the gases are not easily liquefied because when the gases will be easily liquefable then easily you can compress it then the compressive factor will be less means for compressing what are the factors required what is the factor require repeatedly i am saying you temperature should be low pressure should be high so this factor will be less for the gases which are easily liquefied but when i what i am talking to here is that greater than once that greater than one means compressive factor is more it will be more for which gases means temperature should be much much lower and the pressure should be much much higher that means z greater than that means that means the factor which is required for compressing a gas that is more means what is the factor required again i am saying temperature should be lower pressure should be high that should be higher so where it will be when the gases are not easily liquefied then only you will be requiring very low temperature and very high pressure so as to bring the gases closer to each other that means the gases which repel one another listen carefully the gases which repel one another they do not have any intermolecular forces of attractions among themselves the gases which do not have an intermolecular force or which have got very less intermolecular force of attraction on themselves so the gases they will come very close to each other easily then they are easily equivalent but when they are not coming closer rather when you are bringing them closer they are going to repel one another which gases non-polar gases hydrogen nitrogen oxygen methane they are the non-polar they will not come closer you have read it already in the previous chemical bonding chapter the different types of forces divide forces london forces dispersive forces got it ah some forces we have studied so what you find is that here it is between non polar and non polar molecules suppose we have taken hydrogen gas so all our non-polarity nature so hydrogen and another hydrogen molecule they are non polar now you cannot bring closer to each other very easily why because they will they are not having an intermolecular force of attraction among themselves so here the compressibility factor is high that means you have to lower the temperature like anything you have to increase the pressure also like anything so the pressure should be very very high and temperature should be very very low so here the value of z is greater than one so remember it when the value of z will be greater than one you may write it down the value of z will be greater than one when the gases are not easily liquefied that means the gases are non-polar in nature these gases nitrogen hydrogen oxygen methane all these gases which are non-polar in nature so to say alright and they have got very least intermolecular forces of attraction between them then that means they are repelling one another those gases the compressor factor is greater than one you can see transfer factor greater than one see the graph is going upward see that graph is upward for this particular is a nitrogen if i do peroxide also the graph is upward but there are also gases got it which are easily liquefable like carbon dioxide ammonia sulphur dioxide these are easily equivalent gases then the compressor factor is less than one z is less than one it is less than one that means those chances which are easily liquidable those gases which have got high intermolecular force of attraction among themselves there the compressivity factor is less than one because you can easily compress now they are easily uh brought closer to each other because what i am saying they have got strong intermolecular force of attractions if you if you have taken number of sulphur dioxide gases sulfur and dioxide and sulfur side they are pulling one another so hence they are easily equivalent so there the z is less than one got it now the question is why the graph is increasing why it is decreasing okay it is decreasing z value is decreasing the night is increasing white is increasing mean that is the deviation it starts from the ideal behavior that is only the deviations because you cannot compress a gas you cannot uh liquefy a gas to any extent to a certain extent you can liquefy that suppose you are applying a pressure the gas gets liquefied sulphur dioxide gets signified carbon dioxide gets liquefied then after that if you increase the pressure what will happen will it liquefy further already it has got liquefied so in that case it is not going to liquify further so in that case the graph is going to rise up so in case of sulphur dioxide and carbon dioxide ammonia the z value is less than one so hence when you are increasing the pressure and lowering the temperature the gas is going to get liquefied but once it gets liquefied then what happens the gas the graph rises up because it cannot be quite further all right so if you increase the pressure in that case though it is not liquefying rather the graph is going up we can say that so hence it shows deviation so understood now when the value of z is greater than one when it is less than one when it is equal to one okay this is the deviation and real gas source from the ideal behavior got it thank you