 Hi everyone, today's topic is density. As we can see there are two kinds of densities. One is our absolute density, another is our relative density. We have to basically see what the formulas of densities, how to calculate density for solids, liquids and gases. Now generally I have separated this into two cases. One is case one. We will calculate the density for solids and liquids. Both the densities we will calculate, the absolute as well as the relative one. Now for solids and liquids, the absolute density A D which is also denoted as small d, that is nothing but the basic formula that we have studied in our lower classes that is density is equal to mass by volume. This is our absolute density formula in case of solids and liquids. What about relative density? Relative density is nothing but absolute density upon density of water at 4 degree centigrade. Now this density of water at 4 degree centigrade is a standard density. So the value of it is 1 gram per cc which we also call as 1 gram per ml. Cc and ml is same thing. So 1 gram per cc. So what actually this particular relative density signifies? It signifies that how much more dense or less dense a particular solid or liquid is as compared to the density of water at 4 degree centigrade. So as comparison to this one standard 1 gram per cc, how much more dense or less dense a particular solid or liquid is that is given by relative density. Now relative density is also known as specific gravity. These two are same terms, don't get confused. If they are specific gravity it is same as relative density which is absolute density upon density of water at 4 degree centigrade. And relative density will have no unit. You can see here absolute density also the unit will come in gram per cc. By default it comes as gram per cc. So relative density will have no unit. Why? Because it's a ratio of two densities. So it will have no unit. Please take note of this. Now questions from here are very simple and small. So let's see the type of question that can come. Find density of 10 grams of HNO3 nitric acid in 50 ml of its solution. Now try it on your own by pausing the video once. So here density means we are asked to calculate absolute density. So d will be equal to simple formula m upon v that is mass upon volume. Mass is given how much? 10 and how much is our volume given? 50. So the answer will be 1 upon 5 gram per ml. Next question. Find the specific gravity. So what is specific gravity? Nothing but they are asking relative density. Specific gravity of 40 grams of urea in 100 ml solution. What will we do? Here again we first we will find out absolute density. d is equal to m upon v. It will be 40 upon 100. So 0.4 gram per ml. Now relative density or specific gravity is equal to absolute density upon density of water at 4 degrees centigrade. So 1 gram per cc. How much is the d that we have got? 0.4 gram per ml by 1 gram per ml. So definitely these two units will get cancelled giving the value as only 0.4. So keep this in mind that numerically relative density and absolute density the numeral value will be same just that absolute density will contain a unit that is by default gram per cc or gram per ml but relative density as it is a ratio of two densities it will have no unit. So this was our case one which was for solids and liquids. Now coming to case two that is for our gases. Case two for gases. Now in case of gases the absolute density formula is given by Pm by RT. Pm by RT where P is our pressure in atmosphere. The unit will be atmosphere. M is what? Molecular weight of the gas. R is our universal gas constant. Universal gas constant. And if the pressure is in atmosphere the value of R is 0.0821. So while we are calculating we are solving numerical we can take this value as 1 upon 12 it's the same thing. So it's for easier calculation we can use this value as 1 upon 12 and T is our temperature. Temperature in Kelvin. Now how is this basic formula coming up? We will be studying in later chapters regarding ideal gas equation. What is ideal gas equation? Pv is equal to n RT. We will be studying certain gas laws. In lower classes also Charles law, Boyle's law we have studied and combining all those laws we get one ideal gas law which states that Pv is equal to n RT where P is our pressure, V is volume that is equal to constant at a constant temperature. That should stay that product of pressure and volume should stay constant. That is n RT where n is our number of moles. Here n is number of moles. R is again universal gas constant and T is our temperature in Kelvin. Now P is equal to I am bringing this V in the right side denominator n upon V dot RT. Now please recall what was the formula of for calculating moles. If we relate moles to the weight given what was the specific formula? Try to remember without seeing your notes n was equal to W upon Mw. So if I particularly put this value substitute it here. What will I get? P is equal to W upon Mw. This is volume and Mw dot RT. And what is this? W by V. What is W by V? W by V is nothing but D density. Just now we have studied and game. See here this is our W. This is our V. So that is equal to our absolute density. So we can replace here as D. P is equal to D by Mw I am denoting as M. M is nothing but the molecular weight of the gas I have mentioned here as well. So dot RT. So from here what are we getting? If we make D as the subject what we will get? D is equal to P M RT. So this is how we have got the formula. This particular thing will be more clear when we study states of matter. Although it has been removed from mains but still it is there in advance. So anyways we have to study it. It is very important. So this is the first formula for absolute density for gases. Coming to the next part that is our relative density. Relative density. What is relative density? It is the density of one gas with respect to another gas. So we are comparing two gases. Okay. Density relative density of one gas with respect to another gas. At same temperature and pressure. Pressure and temperature is constant. So from here relative density will be equal to D1 upon D2. When D1 is the density of gas one and D2 is the density of gas two. Now just now we have seen the absolute density formula. D is equal to PF upon RT. So can I write from here D1 is equal to P M1 by RT when pressure and temperature is constant. And R is the constant from our childhood. R is always constant. Okay. So it just depends on the unit in which you are taking the pressure. So if pressure is in ATM R will be 1 upon 12. So what is changing basically? So the change will be we can take different gases. So at that time the molecular weight of the gas can change. So that will justify the density. Based on different molecular weights the density will also change. So for gas one density is equal to P M1 by RT. And similarly D2 will be equal to P M2 by RT. Now I am replacing these two particular values in this equation P M1 by RT divided by P M2 by RT. Now all the constants will get cancelled. Pressure, pressure gets cancelled, RT, RT gets cancelled giving us M1 upon M2. Okay. So what did we get ultimately? We got relative density is equal to D1 upon D2 that is equal to the ratio of the molecular weights. Here also we will have no unit at it is the ratio of two similar things. Now what actually does it signify? It is signifying that gas one how much when we are talking about relative density of gas one that means the gas one is how much more dense or less dense as with respect to or as compared to the gas two that we have taken. Okay. So it is a comparison like in compared to the density of the gas two how much more or less dense our gas one is that is relative density of gas one. Now there is another type of density especially in case of gases what is that vapor density vapor density what is vapor density we denoted as VD. So vapor density it is the density it is kind of similar to relative density but just that here in this vapor density we are specifying what gas we have taken as gas two. What does it mean? So density of gas with respect to hydrogen gas. So here gas two we have specified that it is hydrogen gas only. So again VD will be equal to D1 upon D2 that is equal to M1 upon M2. Now specifically we know that this gas two is what? H2 gas. So what will be the molecular weight of this H2 gas? Definitely two grams. So vapor density is equal to vapor density of any particular gas one is equal to molecular weight of that gas upon two. So from this particular concept it is coming that molecular weight is equal to two into vapor density. So our second so in in case of gases we have got three total formulas one is this one D is equal to PM upon RT second for relative density this is the one we have got. This is our second one and this is our third one. So if we try to see or analyze vapor density what what will it signify? It will signify how much more dense or less dense a specific gas is in comparison to here we know the gas that is hydrogen gas. Now we will see certain applications of this. Let's say find density of SO2 at two atmosphere pressure and 480 Kelvin. This is the first question. I am writing the question first then I will solve it. Relative density of SO2 with respect to CH4 at same temperature and pressure. So you can pause the video and try it on your own right. The first one we need to find out the absolute density that is D. D is equal to PM upon RT. So it will be pressure is given as two atmosphere into what is the molecular weight of SO2. SO2 molecular weight sulfur molecular weight is 32 plus oxygen one atom atomic weight is 16. So 16 into 2 that is 64. So now 2 into 64 upon R value when the pressure is in atmosphere what will be the R value 1 upon 12 into temperature given as 480 to the calculation 40. So the answer will be 3.2 gram per if you write ML it will be wrong. Here it is gram per litre. So by default in case of gases the density will come in gram per litre. But in case of solids or liquids it will be in gram per CC or gram per ML. Now next question. Relative density formula was now I have to find the relative density of SO2. So I have to keep this SO2 mass in the numerator M SO2 upon M CH4. So M SO2 molecular weight of SO2 just now we have calculated that is 64 upon what is the molecular weight of CH4 it will be 16. So it gets cancelled with 4. So this means that this particular density of SO2 is 4 times as compared to the density of CH4. So this is the physical significance of this Rd is equal to 4 that the density of SO2 is 4 times than that of CH4. One more question related to vapor density. Find vapor density of O2 and CO2. Okay. So what is the molecular weight of O2? Molecular weight of O2 is 32. So vapor density will be equal to 32 upon 2 that is 16. Here also we will have no unit because it is the ratio of the equal what it is the ratio of the two quantities which are same. So the units will get cancelled. Then mass of CO2 is how much? 12 plus 32 that is 44. So here the vapor density will be 44 upon 2 that is our 22. So here what does it mean? What does it signify? That the density of CO2 is 22 times than that of density of hydrogen. So here the second gas will not be given. By default we know that vapor density it is telling means the second gas the comparison gas is our hydrogen itself. I hope you have understood all the types of densities. Thank you so much. See you in the next class.