 Here in this one. We are looking at we're doing some degrees of freedom analysis here for this problem The problem basically states that there is an experiment that is conducted for bacterial growth organisms and that require an environment which is Enriched with moisture so Humid air basically so the process there are some input Streams that will be coming into this reactor, which we will draw in a minute the This reactor it's a bioreactor where it is being sent in and oxygen is we need up enriched oxygen So the stream basically has inputs We are trying to evaporate water into it to get the enriched water enriched With oxygen as well as moisture So there are three streams that are coming in one is the liquid water, which is coming in and Let me write here liquid water is coming in and normal air is coming in into the process And we are also sending in a little more oxygen here So this oxygen this the stream that is coming out from this reactor would have air with oxygen enrichment and also Moisture enrichment humid air that is required for the process. So We're trying to do the mass balance around this around this humidifier so to speak So what is given to us is that liquid water is fed at 20? centimeter cube per minute Okay, so this is coming in so it is given and we are also given that air is coming in and air obviously consists of 79 percent nitrogen and 21% oxygen all right now and It is also said that pure oxygen which is this stream is fed at a rate of One-fifth of this air. So let's let's start labeling this Let's say if we have N1 moles of air coming in and N2 moles of oxygen are coming in But we don't need to specify N2 specifically because we know what N2 is N2 is actually one-fifth of one-fifth of N1 so we can always put this as 0.2 of N1 Oxygen is coming in right so we know that and let's say N2 moles of Water is coming in and N3 moles of product enriched or air enriched with oxygen and and moisture are coming out So we can we can calculate these things actually and it is also stated that The product gases that are coming out contain 1.5% moisture Moisture alright, so that's what is given to us. So rest of the components here constitute The nitrogen and oxygen so there are two other constituents that are not given here So we need to figure that out. So if we write this one, this is N3 moles and What we know is 1.5% 1.5 in a hundred. So if we look at the fraction, it'll be 0.015 of this N3 would would be the moles of H2O coming out per Mall of gas per mall of total gas that is coming out. This is a percentage percent, you know, so That's what we know and so the rest of it together would be point 985 right one minus point zero one five would be point nine eight five and if we have y of y moles of Oxygen coming in coming out rather and Nitrogen coming out would be actually One minus this minus this which is basically point nine eight five one minus point Zero one five minus y would be our end to right, so this is again per mole per mole of total Air in rich air that is flowing out and here also we know that if this is end to But we know because the molecular weight is known Which is 18 we can calculate the number of moles that are going in also here Okay, so let's take a look at and figure out what how to calculate or how to get these things here the n1 and 2 and 3 and in material balances we need to see the species here, you know how many there are no reactions here, so The number of unknowns and the number of knowns we have to match and number of unknowns are one two three here and so unknowns are three and knowns here are By species balances and total number of moles balances we can get actually There is nitrogen that is oxygen and that is That is water or Steam or water vapor, so we have three here, so there are three unknowns and three Nones we can we can solve this or degrees of freedom is zero, so we can solve this Problem, let's let's start how to solve So the first thing that we can do is first step that we can do is balance Or at least figure out this one because we know the flow rate and we know the molecular weight And we know the density of water assuming that it is Basically one gram per centimeter cube We can calculate this, so let's do that So we know the flow rate our n2 is equal to we can calculate that n2 is equal to 20 centimeter cube of H2o per minute is the flow rate right per minute is the flow rate and We know that this is one gram Per centimeter cube the density all right one gram per centimeter cube one gram of H2o per centimeter cube This is the density and once we multiply this volume by density we would get We would get centimeter cube, so if we want to convert centimeter cube into Into moles we need molecular weight So if we were to divide this one by molecular weight or one gram mole Would have 18 grams of H2o right so we can we can Calculate now the Grammoles so So 20 times one divided by 18 that would come out to be 1.11 moles or gram moles of H2o Per minute right so we figured out n2 Now we need to get n1 and n3, so let me erase this and we can Calculate and also now we know would you like this to be a separate video? Same quick you continue. It's the same so Now the second step to calculate would be Use and we can calculate using Hide water vapor balance, so this is another species that we can balance so second step would be H2o balance Total water vapor going in will be here and water vapor is coming out here So if we balance the stream, whatever is going in has to come out so and two is the Flow rate in which is moles of H2o Per minute Of course, we know this number. We already calculated But this must be equal to there is no other H2o going here or here So this must be equal to the moisture that is coming out here, which is Which is actually and three times 0.015 right this is 0.0135 moles Per mole moles of H2o per mole of total gas right so now If we have we know this value, which is one point one one we calculated one point one one moles Per minute. This is the flow rate, right? This is the flow rate This is equal to and three times 0.015 So we can calculate and three and three is equal to Basically one point one one divided by point zero one five that gives us seventy four point one moles Per minute. This is the flow rate So this is the total flow rate Which we calculated to be seventy four point one moles per minute All right, and this we calculated to be one point one seven one point one one moles Per minute right so now we need to calculate and one which is What we can do that by either nitrogen balance or oxygen balance one of the two nitrogen balance Let's do it with one of those and figure out So the third step would be using nitrogen balance one species So doing nitrogen balance here use the screen again nitrogen balance So nitrogen balance if we look at nitrogen is not going in this stream nitrogen is not there in this stream nitrogen Is going only in this stream so and one? moles per minute if it is total gas going in times Every mole will have point seven nine of nitrogen moles of nitrogen per mole So moles and moles can get cancelled here So we have moles of nitrogen flowing in per mole So this must be on the left side must be equal to The nitrogen that is going out here nitrogen that is going out here is actually if we calculate and three moles of Flow rate total flow rate per minute All right times Zero point nine eight five minus y Would be your nitrogen here right nitrogen moles of and to per mole of total gas going out So here also if we were to cancel this moles of moles so moles of nitrogen going in must be equal to moles of nitrogen coming out in this case We know this already. We know this already. We calculated here and And and one is We we have Figured that out. So basically this will be here We we need to we can figure this out actually and one actually we know into an n3 So let's let's use one more equation here to figure this out and one so if we were to look at the total mole balance and one moles are going in and Here there is n2 moles going in and then n3 moles coming out So if we do the total mole balance this stream this stream this stream this stream so n1 plus and one is this stream plus 0.2 and one which is oxygen here plus and two which is Moles of water must be equal to n3 right total mole balance So this is total mole balance So now we know this number. We know this and we can calculate n1. So and so here it is one point Two and one is equal to that was sorry plus one point one one Must be equal to and three which is seventy four point one So and one we can calculate and one Will come out to be seventy one seventy four point one minus this divided by one point two That will come out to be sixty point eight Right sixty point eight this would be moles per minute so now that we know and and This n1 what we can do is we can stick that and one here and Point seven times point seven nine must be equal to n3, which is seventy four point one Times this and we can calculate why? We can calculate why? All right, and if we did that just mathematical, you know juggler here Why would come out to be? zero point three three seven moles of O2 per mole so this one would be zero point three three seven That will be moles per mole and We and N3 we have already calculated and two we have already calculated and One now we have that is equal to sixty point eight moles per minute So this is material balance around this and this is since there are no reactions taking place By just doing species balance we can get the flow rates