Gas laws part 8

Ajouté : 2026-05-15

[00:00:00]now coming to the next law that is avogadro's law so avogadro's law we have studied earlier also in the previous chapter once again let me tell you regarding this context regarding the context of the gaseous state equal volumes of all gases under similar conditions of temperature and pressure contain the same number of molecules equal volumes of all gases under same conditions under similar conditions of temperature and pressure contain the same number of molecules so here as one mole of a gas you know that contains avogadro's number of molecules that is six point zero two three or zero two two into ten to the power twenty three molecules we can select this this means or that means that one mole of any gas at the same temperature and pressure should have the same volume again repeat one mole of any gas under the same conditions of temperature and pressure should have the same volume and what i said one mole of any gas isn't it one mole of any gas contains how many molecules avogadro's number so under similar conditions temperature and pressure one mole of any gas will contain the same number of what i said that is molecules so if it is containing the same number of molecules it will also have the same volume because again i repeat equal volume of all gases any gas intake equal volume for example if you take five liter of oxygen five liter of carbon dioxide five liter of nitrogen under the same conditions of temperature and pressure they will contain how many equal number of molecules all right five liter of oxygen contain the same molecule as 5 liter of oxygen as same molecules are 5 liter of nitrogen same number of molecules is 5 liter of carbon dioxide so here the volume is 5 liter you can see the same number of molecules is also same under the same conditions of temperature and pressure that you remember it so what i said this means that one mole of each gas or any gas under the same conditions of temperature and pressure should contain the same num should contain the same volume we can say that clear so based upon this if you take the volume under stp then what is that known as that is molar value stp means when temperature is 273 kelvin pressure is 180 m then the molar volume of the gas is 22.4 liter you know that all right if i take under same conditions of temperature and pressure and if the temperature and pressure condition is under stp or ntp what does it mean st pure ntp stp means standard temperature pressure ntp means normal temperature and pressure where the temperature is 273 kelvin and pressure is one area all right so what is the volume of the gas the volume of the gas is 22.4 liter or 22 ah what you can say 2 2 4 0 0 ml we can say that clear now let me come to the law that is volume is directly proportional to number of moles just now we discussed not a v is rightly proportional to n because equal volume of all gases under similar conditions of temperature and pressure contain the same number of molecules all right here one mole contains avogadro's number of molecules under the same conditions we can say that so n stands for the number of molecules we know n is equal to weight by molecular weight weight of the substance my molecular weight of the substance again so i can ah what you can do is that to remove the proportional sign i can take a constant that is k this is your proportionality constant to remove the proportional sign i can i can take a constant that is k where k is a proportionality constant understood so k n so instead of this n i can write w 1 by m 1 because that isn't it w 1 by m 1 i can write it out so now i can also write it this way m 1 is equal to k into w 1 by v now what is w 1 by v made by volume is nothing but density so m 1 is equal to k into t where d is equal to w1 by v we can say that so hence what we come to know that molecular weight of any gas under similar conditions of temperature pressure is directly proportional to density all right molecular weight of any gas under similar conditions of temperature and pressure is directly proportional to density if you remove this k again so then n m one is directly proportional to d look at it so molecular weight of any gas is under similar conditions of temperature and pressure is directly proportional to its density so fine we got this particular ah relationship also from the avogadro's law but the main relationship of the avogadro's law is this v is directly proportional to n that is v is equal to k n we can say that clear and and you can simplify further and we can get this particular one fine now there are two more conditions where you need to understand it one condition already has tell you you also know it stp or ntp where temperature is 273 and pressure of the gas is 180 so the volume is 22.4 liter now instead of uh pressure which is one atm because one atm pressure we measured we do not measure the atmospheric pressure in atm we measure the atmospheric pressure in bar so when temperature is 273 kelvin pressure is equal to one bar instead of one atm because bar is the unit to measure the atmospheric pressure not atm rather we consider that so generally we use bar so at that time the volume is not 2.4 liter remember it volume is 22.7 liter volume is 22.7 liter and you know that one bar is equal to 0.9878 we have discussed already all these things 1 bar is equal to 0.987 180 or 1 atm is equal to 1.01325 that is bar all right there is one point nothing but 0 1 three to five bar i should say that one uh that is atm we can say that clear so this way uh we can say that the volume is at the one bar pressure is slightly more that is nothing but 22.7 liter i should say that clear 22.7 liter clear so we need to understand this that what is how much is 1 bar 1 bar is also nothing but it is 10 to the power 5 pascals you must understand this that one bar is 10 to the power 5 pascals one pascal is nothing but 1 newton per meter square we can say that clear so in this way in this way you have to remember this particular value that pascal is nothing but one newton per meter square and one bar is ten to the power five pascal one bar is zero point nine eight seven eighty m one eighty m is zero point one point zero one three two five but we can say that clear fine now so when the temperature is this much pressure is this meant the volume is not 20.4 remember the volume is 22.7 liter now similarly we have got another condition now scientists are of the opinion that that when we are uh doing the what you can say the laboratory experiment when we are doing the experiment in the lab then the pressure is neither what you can say ah one atm and temperature is neither 273 kelvin that is rhodius integral is it no we are doing at room temperature and under atmospheric pressure is one bar isn't it this is the practical conditions which prevails which prevails when we are doing the experiment in the lab it is not 273 zero decent liquid so generally that condition is called as satp conditions what is satp standard ambient temperature pressure standard ambient temperature pressure where temperature is not 273 kelvin it is 298 kelvin the or 25 degrees celsius you know 25 plus 273 will add 298 kelvin which is known as the room temperature and pressure is not 180 which is one bar then you how much then you know how much is the volume of that gas it is not 22.7 or 22.4 liters it is 24.8 liters you need to remember this value this is very important in the numericals which is going to come you will see that will be used so under sctp condition which is actually the practicable conditions all right the temperature is to 95 298 kelvin which is 25 resources and pressure is one bar and the volume of the gas the molar volume of the gas is 24.8 liters it is not 22.4 neither 22.7 liters so to say now next is using all these things that is we have studied ball's law charles law amundance law avogadro's law perfect gas equation which is p 1 v 1 by t 1 is equal to p 2 v 2 by t 2 we can sub i we will find it out another equation which is known as ideal gas equation i have told you what is an ideal gas ideal gas is a gas which obeys gas loss under all conditions of temperature and pressure again i repeat ideal gas is a gas which obeys gas laws gas loss means boyle's law charles law amendment's law dalton's law audit avocados law all these laws which obeys gas laws got it under all conditions of temperature and pressure under every conditions of temperature pressure if you do this gas laws then that particular gas is called as an ideal gas otherwise it is known as what real gas if it does not obey ah the gas flows under all conditions of temperature pressure it is called as a real gas real gas so generally in the nature of the gases which you are getting it all are the real gases because ideal gas is theoretical it is hypothetical hypothetical because it is not possible that all the gases will obey gas laws under all conditions of temperature pressure is it no for example suppose you are heating a particular gas let us say charles law volume is directly proportional to temperature so temperature increases volume increases how will you show it you have done the balloon experiment we have done the balloon experiment you have seen in my last heavies that we will take a balloon we will put it at the mouth of the vessel and we will heat the gas which is present inside the vessel what you find is that the volume is going to increase do you think that as we increase the temperature infinitely the volume of the balloon will also increase infinitely now beyond a certain temperature value is going to burst so it's not that you'll say that okay so we'll take still a bigger value okay but what you find is that you know when you are heating a particular gas when the gas gets heated or heated up heated up when the temperature goes on rising rising rising what happens the gas itself becomes combustible itself it starts burning we can say that itself all right so hence in that particular case can we apply the charles law no we can't isn't it similarly in case of balls loss pressure is inversely proportional to volume suppose in a vessel some gas is there you are increasing the pressure you are going on increasing volume is going on decreasing is that suppose a vessel is there some gas is present in it you are increasing the pressure on increasing the pressure volume decreases again increasing again decreases again into the end decreases so beyond a particular pressure what will happen the gas is going to get liquefied the gas will liquefy can you apply the gas laws there bird's flow there no we can't so hence practically speaking gas loss is not applicable under all conditions of temperature pressure it is applicable under certain conditions of temperature and pressure only so ideal gas is basically a theoretical conditions hypothetical conditions all right whatever it is we need to study this particular one so just say clarifying what is an ideal gas and what is the real gas ideal gas is a gas which obeys gas laws under all conditions of temperature and pressure but real gas is a gas which obese gas and the certain conditions of temperature and pressure began so that clear and i said you also the ideal gas is hypothetical condition because there is no such gases which will obey gas loss under all conditions of temperature pressure so hence all the gases are real gases i gave you the example i gave you what you can say examples also i explained you also that what you can say the limitations of the boyle's law and the child so i've explained you now my main question was by using this law i will find the ideal gas equation now what is that according to boyle square you know v is inversely proportional to p according to paul's law we have studied when temperature remains constant now according to charles law we know v is directly proportional to t when pressure remains constant here temperature remains constant air pressure remains constant you have sorry now according to avogadro's law you know v is really proportional to n n stands for number of moles by combining this all these three v is greatly proportional to n t by p we can say that now to remove this proportional sign we'll use a constant that is k v is equal to k n t by p we can say that k n t by p clear or pv is equal to k n t here this proportionality constant we are using a particular value a constant value a calculated value we are using it which is nothing but known as pv is equal to r and d here k is equal to r we can say that the proportionality constant we have used where r stands for what universal gas constant universal gas constant where r stands for universal gas constant so we got it pv is equal to nrt we can say that where p is the pressure of the gas v is the volume of the gas which is measured in beta pressure may be measured in atm r is universal gas constant we will find out the value now n is the number of moles and t is the temperature in kelvin mind it temperature should be in kelvin only but if it is not in kelvin you need to convert into kelvin you know that so in this way by combining the three laws boyle's law chancellor and avogadro's law we got this ideal gas equation that is pv is equal to nrt we can still simplify it further if you want you can still simplify further let me simplify it pv is equal to nrt n is equal to what is that w1 by m1 weight of the ah substance by molecular weight of the substance that is weight of the gas by molecular weight of the gas any gas all right here n is equal to w1 by m1 click w one by m one here n is equal to i do not have space here i am writing it here you can see that so this p v is equal to w one by m one into r t because that still we can uh simplify this one we can say p is equal to w1 by m1 into v rt now what is w1 by v made by volume just now i discussed with you which is nothing but density so p is equal to drt by m1 this is another formula we got it in terms of density p is equal to d r t by m one where weight by volume is your density here d is equal to w one by v made by volume okay so this way according to the question we'll be using the formula suppose if weight and molecular weight is given then definitely you'll be simplifying n and you'll be putting this value if density is given then we'll be using this formula p is equal to d r t by m one m one is the molecular weight of the gas minus molecular weight of the gas and w1 is the weight of the gas which is taken in the questions the weight of the gas will be given all right weight of the certain gas will be given and from the name itself you can calculate the molecular weight you know that suppose if i say sulfur dioxide six gram of sulphur dioxide so w one is six gram and m one is a molecular weight of sulphur actually i will find it sulfur atomic weight is thirty thirty two oxygen is sixteen sixteen two thirty thirty two plus 30 64. so molecular weight is 64.

[00:16:23]so 6 by 64. just an example i gave you just again this way you can find it out similarly if density is given then you can use this particular formula and we can find it out all right so this is your ideal gas equation basically pv is equal to nrt where r is universal gas constant now coming to the question that what should be the value of r by what we will take the value of r all right now the value of r depends upon the what you can say units of pressure and volume of the different units of pressure and volume the value of r changes all right it also depends whether the r is uh written in s i unit or cgs in it all right or any other older unit we can say that so we will see it what is the value of r will derive it and we'll find out thank you