a balanced equation so the well you have a complicated equivalent to solve the equipment concentration it can be very difficult even you are very good in math so in our class we only learn to deal with some simple equilibrium and how to get the equipment concentration from the initial concentration and also from the from the change instead of a change of X and so that is the situation we learn in our class it is to serve ice table and this size table it's actually much simpler than we did a practice or the earlier lectures just because mathematically is too much complicated to deal with those higher coefficient equilibrium so we see a fairly simple equilibrium and the set of ice table set of the assumed the changes x or negative x and just solve it and so the the e4 manners the equipment concentrations the e as we learned it is I plus C initial plus change this change it will be the positive x or two legs or negative x 2x and so forth so once you study e1 is gonna eat since we are having the formula for the equilibrium concentrations we can set up the equation the K should be equal the product raised to the power you might have a lot of a product and likewise you might have multiple reactant so the K is given and the boast P and R have X has a variable X you just solve X so there be lots of a mathematical manipulation involved but those are the easier easier manipulations I actually manipulate in the end rearrange you should have been able get get a quadratic equation based on the change X each one have a changes X you have a quadratic equation based on the change X and then you just need to solve the solve the complete equation but solving this quadratic equation you should have two solutions you have x1 and x2 only one of them is about it the other ones not realistic the other one should give you the native equilibrium concentration and that's the impossible in chemistry maybe math in physics is possible but in chemistry the mass and volume concentration that has me positive value so it's matter we're solving the quadratic equation and then we have equation to solve the solve a quadratic equation and so when you get to this equation along the way you might need to do some manipulation like this so let's do a quick review let's say whether X plus 1 times X plus x times X plus a times X plus B when you do the calculation that should give you the a plus B times X and the last part the know the item that has no X that's a times B so you will need this kind of manipulation in the in your solving quadratic equations this kind of question will be in our quiz on the final so just kind of keep in mind you need to practice couple of times really become very good hunters and comfortable solving quadratic equations and and so finally once you solve okay the valid you have 2x come from solving this quadratic equation okay only one is valid the valid is one that made all the equivalent concentrations positive larger than zero that is only one that's bad you cannot have a both are invalid or both about it if you solve an equation and after all the work you find out the the air makes the equilibrium concentration or positive both X those exits make your concentration positive there is something wrong in your solving equations so you need to go back redo your solving equation okay this chapter is not hard there there's not so much so many equations for you to manipulate and solve problem is only to solve using the quadratic equation to solve the equation concentration okay so let's see a example here I have a tweeze examples I will demonstrate the first one the second one I might love you guys to practice I think the same in PowerPoint and so we have you can see the equilibrium where you are to try to solve the increment concentration and the equilibrium is actually much easier much simpler than the the other equilibrium that we practice practice i stable ways but just because limitation in solving the more advanced polynominal equations we try to avoid those alright so we have this equilibrium nitrogen dinitrogen tetroxide it becomes a two nitrogen dioxide and the K is given it is K schema and calculate the concentration of those when point zero mold and no tool is allowed to react and the Machine equipment so you can see the ended be beginning only the nitrogen dioxide exists the other species by nitrogen tetroxide is not even it's not a mentioned so you assume the nitrogen the dinitrogen tetroxide zero in the beginning and you can see the question star was a mole and volume so you get to the molarity first okay so to solve this I set up an equation and I stable and this equilibrium both our guest so they both should show up in the calculation of the tape all right eyes and let's see the dine nineteen tetroxide at zero it's not mentioned they put a zero and the end no - I know - the molarity is not given but we have a 3.0 more of this volume simple cheerleaders so the each other and OH - it is 3.0 d by the 10.0 so that is the initial concentration and no - you will leave that here and then you work on the change the change we don't know how much change because we were not given the equivalent concentration so assume is negative x and then product coefficient - so it's a positive 2x as it works so with this what we have is and the equivalent concentration we don't have a numerical value but we have the variable what we use this so we'll have Oh interesting zero cross networks I should have get a negative x it's okay the the X so far we don't know the positive negative but based on the the concentration of the chemicals cannot be negative so the X the worst scenario might be eight maybe zero but the most likely to be addictive because final concentration has a positive or maybe zero by the way in the chemical equilibrium in the real world of chemical equilibrium no concentration can be zero because we have a zero your reaction quotient or K will be either zero or on the infinitely large so the concentration cannot be zero in the real world of reactions just because he reversible reaction this is Tuesday when they ring the cost and I mentioned about Orange County Riverside that commute even one a city poverty than zero then that city will have no people leaving a lot of people coming they've been at a gain in the population so in the end another city have zero population the same was a camp equipment neither reactant or product can be zero concentration at equilibrium it can be very small or can be very large yeah so anyway we have this and they end the point three zero change professor shouldn't the changes be switch signs because we're starting with the nitrogen dioxide and we can't really get any more on the other side we have we have mentioned dioxide on one side of the equilibrium that's the way you have changes it would make it seem like we're going to get more nice dioxide which we can't access will be less but anyway this part you can just treat as a mathematical you can pretend you have no idea that the extra be positive I think it's better just solve this equation you'll find out the better just solve an equation find out yeah the this reaction n 2 O 4 0 so in the end n 2 O 4 so gain and all personal gain so that I mean I know truth will decrease to lose the I know to change should be it should be negative change what you needed lose and not you well anyway that's what you solve the equator you'll find out so far mathematically this part again is treated pure math you can just pretend you don't know what their X is positive it's a solid you find out yeah this is kind of strange when you look at the n2o4 next it looks like a very strange it is actually work out you will work out good so what I really care is the e Clement concentration for these two and at equilibrium that means I carried the quotient that should equals K and to calculate the quotient I use a product release of power of the collision and so I have set up equation any point K equals point to zero and that's really caused the increment concentration point zero plus 2x and this one coefficient is 2 so just make it a square and that divided by divided by minus X so we have a we have an equation to solve ok so the rest is just to reap rockets what we learn in algebra ok so the next I can times negative x on both there are many ways by the way you can do whatever we you like deepens our how we practiced my times negative x on both side of the equation and so I can focus on the square of this the square of this that should be should be square of this and square of the two works and then there's in between and there should be the square of this first and then the tool times this and that so that's kind of a we have rehash me practically to learn algebra so that's kind of quick and go over there algebra how you learned okay anyone of you tell me what's the answer for this I write down on the top just kind of practice X plus B's or the square of ax plus B what should be the answer square of ax plus B anyone and remember high school where we're looking the equation on top right and under the title of this PowerPoint ax plus P anyone remember the equation yes what's that a takes okay let's deal with this first vtune plus ax B 2 ax p yeah that's fine yeah that's and I can put X in n because X is variable and the other a and B is supposed to come supposed to given what about ax the first one is Square right you guys and finally B Square so remember this it is what he should have learned in high school intermediate school it's not an advanced calculus don't need a calculus for this kind of question but if the matter with the algebra okay so now I continue in this I square of this right and a square of I leave that square later but I have a 2 times point 3 0 times 2 2 times 2 times 1 3 that shouldn't give me 1 point 2 X and find it 4x squared can you guys verify should I give the number it's correct yeah so will you solve the equations in this server it's about this basically some basic manipulations all right so finally I can we combine together become give me the quadratic equation so I like to pull the X first so that I always start with I basically add the coin to 0 X on both sides equation you can add 1/2 to 0 X at appointment to they're on to their legs I will get my final equation and I would like the x squared on my xi side so I start with a 4 X square and plus 1 point for X and then we have plus point zero 9 equals 0 so that's a quadratic equation I can start solving and stop quadratic equation the equation itself yeah I think it's like where I ran out of space I'm how to arrange some of the work here and then go back anyway the equation we're supposed to have the X I should have two answers X so y equals native okay let me write down the quadratic equation and then the X should be this part is completely algebra okay what are we learned before right this is the equation since the equation will be given in the midterm you just need to know how music how you set up the quadratic equation solved that's the format or how to solve X be the solution for quadratic equation anyway we should have two answers because there is plus minus and only one of them is about it okay so let's just let's solve x one next one next one I do the plus and negative B beanie is at one point four so it is negative one point four B is one point four and I do the prospers and inside the it is B Square 1.4 squared minus four times a a is 4 4 times 4 fix a is 4 and C is point zero nine all right so that's a numerator and then divide by 2 a 2 times 4 T that's upset all right you guys will you solve quadratic equation yes there should be a lets me be it should be C all right so and then you can just get answer for this I just leave here so good answer and we have a second X second solutions X 2 thanks to is very the same equation except you have a negative this negative one point four minus square root by the way the so far we've solved X don't assume the your X is negative is invalid no it's not exit is not the negative X may be the solution in mind it is a final concentration they eat in those boxes these boxes have to be positive so and looks like I still have two negative answers both X and negative but only one is also correct all right so let's just continue on this one point four minus one point four square minus and divided by eight two point four and then I stopped the other X okay can you uh you guys take some moments just let's solve these two x DX number of sig figs if you look at our ice table our ice table in this ice table has only two decimal place so you solve the eggs should keep two decimal place in your final X but let's keep one more digit okay let's keep three decimal places and let's around in the very end how about everyone take a moment calculate those in the room one okay those are the room one you can do the X 1 and those in the room too let's try to solve the X 2 and let's get two numbers to work with and I need to erase my whiteboard to make some room for following discussions you use your calculator to work on the x1 x2 so room 1 which I mean breakout room 1 work on x1 a breakout room to work on the world on x2 yeah let me know if you have answers if you are not so not so sure about your ex there's a way to check out you plug in this k equals point to zero and goes that you plan your ex into this equation if your calculate the this piece give you close to point to zero then you get a right answer okay that's how you verify it that's how you verify your answer is correct or not by plugging the this formula to calculate K and then you will know both X should be neck here but then we need to plug in which one's more correct both seems like will satisfy this equation but only one is about it one of the next I solve is ninety one point zero six ones ninety one point zero six and the other one is yeah I'm supposed to keep it one more digit but that's that it is too small wouldn't matter okay so I have both acts did you get it against these two numbers oh wait a minute wait wait wait wait I took the T vitamin wrong number that's why haha no not these are wrong these are two divided by divided by eight I need not be age it should be bows our but smaller more than this okay anyone have answers with this zero eight five and the other one is two divided by eight nineteen point two six five so that's X and we need to check which one's invalid the first boses are native it looks good because that oughta make them my n2o4 being a positive but we have to check the other one if bows are bows are shows promising those are promising based on one of the end one of the equipment concentration we need to look the other way so by looking at this one I can see the second the X the X 2 would make me the equivalent concentrate region for and O 2 negative ok the X 2 will make the and no.2 concentration thank you so at this point we need a more room if you to solve the question and show the answer the works you need to plug both the X into the equilibrium concentration formula and whichever concentration give you negative Darleen valid for this car we discard the answer and keep the one that would make both compensation positive only aches and one can do so thank you so at this point we can just set up a more work takes one and let's do this let's do the and 204 and no.2 concentration since I have 2x i plug in both X and calculate the n2o4 concentration is simply just negative x so the n2o4 with this X my final concentration should be the positive point zero eight five looks good and then you plug in the end o - I know - it should be points three zero plus 2x so points three zero plus 2 times negative point zero eight 5.30 and that will give me a women naked nice one make sure you don't forget that this kind of question is not hard but be very careful at every step you can see sometimes I keep talking and I'm do not paint it and what I write what I do I can make mistakes so make sure of negative x here and data way you get financers positive point one three I can see that that's B final find the equivalent concentration for and no - so these are final concentration with x1 the first first is solution found that a quadratic equation so that looks good that's the tail of the other okay we need to do all of them we need to check out all of them because if you are both X tv+ concentrations there's something wrong with your work you go back to we solve the equation so let's continue work on that and the the second X 2 is X 2 is such and same way we let's find the equivalent concentrated by n2o4 that should be pause eight point two six five so this is again give it holiday it looks good let's listen continue come on all right so next one the endo tool should be point three zero same way point 3 0 Plus this this is a give you more than the it'll be an etic and smaller than point 90 + 3 0 so this actually give me an icky number because these two multiply will give me point negative point five three zero and I add the points v-0 final answers negative point two Street so that means the X 2 is not valid because that'll give me the native final concentration it's not valid you can pretty much cross this out because these probably the answer you solve is not good all right so we have the problem solved ok so we have a these two are the financer but at this point when you solve the quadratic equation and bag enforce do you feel confident that you get the right answer I don't feel confident so I need to do the final checkup so do the checkup you plug in you need final equiptment concentrations back to the way as a for manner to calculate ok the base that you use those concentrations the K should be the endo - molarity square square of the concentration and the tool square divided by the n2o4 so the final confirmation or verification it is you calculate all these aren't any criminal concentrations seeing even good cops 2.20 it is normal it is normal that your childhood use this equation your answers may not be exactly one to zero the reason because in the calculation we limited to only two dozen place here actually I came to one more decimal place we're supposed to keep only two decimal and if you do the tool there's no by rounding your final answer can be way off certain singing them off but anyway let's find out let's find out you see I wouldn't have a and no tool in the N is point three zero so this is plugging point one three square divided by the nth row four point zero eight five and let's calculate what do we have seeing a good a pretty lucky pretty pretty close pointed one three square divided by point zero eight five I got a point one nine nine basically it could keep only tool two seconds pigs that are the exactly point two zero this is the final verification what it get is that point it is point two zero okay Eve you around the final answer to two decimal place and will you do the verification your answer might be off okay these are all normal as long as cost your final verification close to the the given K you should have the confidence so let's pretend that we around it and let's pretend I'm around and remember we get the point zero if i if i round it then my answer might be off even more since we recorded I'm just an erase whatever we did is that really do pretend we do those present we do those let's pretend I round it around here - yeah - a different number and same here - a different number if I round him the answer might be off I mean I need to erase more of those this kind of calculations keep one more digit now you should then you should have just like any solving problem is multiple steps and each step has a significant issues you should have keep the one more than you should have rounding invariance so let's kind of pretend to solve this one we see I round early and let's see you let's see if it wrong early what will happen and I will change the different color all right that's wrong so let's say this part I'm supposed to keep only two different ways decimal so I get around to a point here mine and the same way with same way with this I keep only two decimal and a good ninety point two seven all right so data will change my number a little bit yeah the end to all a and and 2:04 that'll be still that and there's one to seven but regardless actually I don't need to I don't need to redo the exo okay pigs x2 is already shown not valid I don't even do that so that's good thing I don't need next door I just need to redo x1 and let's see the final verification what it will give what will give me to continue and anoche and plus 2x 2x each ones that is a two tongues name alright and then I can calculate down sir - be positive point one two all right this will be the if I rounded the final equal concentration which is also key by the way it becomes this if I round it so regardless we need to do the verification so these two the Green answers the green ones let's plug in plug in this equation see what you have and - and no - the equipment concentrated now it is pointed point one point one to the right by point eight zero nine square okay if you do this right you see I'm sorry to confuse very confused too much work I got confused there's not square square should be the no.2 so this is a supposed to give me the equivalent constant and then I compared for you the point two zero it's 0.12 square there's something not right square / point zero nine so by doing this they if I round early my answer become point one six did you guys get it a number did you guys get the number the new number after if I wrong early I also got that six seven I think maybe you do not run or you should get a point one six the point is okay we're supposed to get a point two zero and now we try the youth around the early keeps the proper thing face through the verification Kimmy point one six the difference between these two seems like a big like twenty percent difference twenty percent even actually it is a reasonable because the when you have a one sig figs you round early that can make a big difference if you are two sig figs two decimals rounding action will not make that about difference so just because one second things hanging around anyway the point is there's a lot of work in the solving this equation as you can see from your homework or the online quiz first you will have two answers x1 x2 and there's only one that is about it there should be only one it's about it which you which should give me positive concentration in the end that's a key okay and the after you solve the the eggs and then you find the increment concentrations you need to do the verification okay you do the very end that there last part because all the hard work anybody answers off then your you look big big chunk in the credit in the points to the very verification and so this is a kind of ice table one step further than the Tuesday cost okay any questions any counts so small things going to involve in solving the quadratic equations and when you show the work on the solving quadratic equations I would ask you first you need to show the ice table because this is the words equation come from shows ice table and the ice table the equivalent concentration in with the variables that's where the hardness of the equation and saw solve the equation is mathematical I think some of you pretty good in math now remember you are applying to a solving the real world a chemistry problem the concentration has be positive so these two concentration has a positive even though we have two solutions there should be only one is about it and yeah you'll see this kind of question in the quiz I give a lot of points about five point four out of eight twenty thirty point quiz that's just because a lot of work and involved make sure show all your work and with all the work in the end needed verify verify answer make sure you answer give you the K that is supposed to be close very close to the initial K and when you solve this ice table your concentration I'm just solving should be the same decimal place as where to start from if you start from 2 decimal place then your X should be 2 decimal but in the middle of calculation keep one more digits and that is a city common practice when you learn we learned about safety rules and when you have calculations and multiple steps you should keep in one more than you keep it one more dealer than you should keep based on the rule and then round in the very end okay rounding the end any questions comments so small work in this part this is nature the chapter equivalent chapter is the one of the easier chapters actually the song becomes one equation it is essentially only in this chapter in this chapter we must you use a software that equation but it's actually much easier way and we oftentimes use approximation to solve the problems in the next chapter but here we need to know mathematically how to solve a quadratic equation in the real in reality the K will be either very large or very small in those cases we only had use approximation no need of solving the exact X so that's the solving quadratic equation to answer the equilibrium problems and ok let's move to the next one next are learning gates to the practice ok so you kind of see how we set up the ice table like this and next question is similar but ice table looks very different and but still the solving the the rest of the song is very similar you need to apply the algebra to do the distribution and a combination and so forth factor eating whatever learn before now it shows shows up you're gonna use what you learned in your algebra to solve problems in the aquarium okay so I'm gonna stop pause my recording alright to solve this equation we have our ice table and you can see this equation autumn again so Takeda should have all the concentration equipment concentrations and ice table concentrations we have a 5.0 mole in a 10 liter so you have only the Co co2 that's at 0.5 0 0 and both carbon monoxide and chlorine are not mentioned when you have concentrated star with zero the mass slightly easier okay because the e the end it should be only there be only X there we know the number costs of X it's actually easier but you can see these are all doing kind of practice again this problem record actually easier because you are having those anyway and your K is point a 3 so point a strings equals these two concentration bows are coefficients of 1 so simply just x times X X square divided by 0.5 there's your -6 now and then let's go ahead solve this quadratic equation you get the keep your answer keep your answer sweet decimals and you have 2x1 of the X only 1x give you all positive concentrations and that is should be the valid X and the final do the verification this is actually easier than the last one we saw but let's suppose I can make the problem harder I just created show you the what a harder problem what looks like and then involve more math okay because you might see those in the quiz or test or homework all right let's say we have a different aquarium and these are all gas all of them aghast I suppose all of them the gas and the initial let's say I just made up of numbers 0.01 0.2 0.3 0.4 0 and this is initial change and let's say the K it is 1/10 that make it a little easier for myself and I'll have the change in name X negative x positive x positive and so the end equilibriums initial plus the change I think this will be perhaps the hardest when you solve the manipulate and try to get to the quadratic equation just to get to the quadratic equation it might be more work and so with the end like this and K equals 10 so I can still have equating like that 10 equals products over reactants so we have that point of three zero plus X divided by the reactant all right and I tell there's a big tip a shortcut yeah should I keep those zeros like to the that second this one point zero it is actually not necessary just keep in mind when you saw in the end each one the concentration eclair mine concentration and X must have two decimal place okay you don't need Kindle zeros that I will really simplify your work just keep your acts at two decimal place you don't you keep those accessories you just not work and then make your get distracted so when you have this and then you just use the equation that I mentioned earlier okay so I would have that should become 10 times 10 times both denominators okay and in times of these two on both side of the equation anyway I know this well this is minus X minus I don't like that X has a negative coefficient I like the flip post let both when I flip both is making Nick and composite and I want to change my numbers like I said I keep only as simple as possible I don't need to keep them any zeros all right that equation becomes this any questions you guys you guys okay I'll be quiet you guys are listening you know I'm new to that and so that what we call distribute and so there's X square minus minus point zero one minus point zero two so these tools simply just a feather - one two three so you've got to be familiar with those distribution the process how to distribute when you have a two things multiplied and this the number is come from the negative one zero one times maybe their poncho so good positive or zero - all right and this part you gotta be quick the we have a quadratic relation to solve it should not spend too much time struggling on this process unfortunately you have to this is a very brutal fact you got to be quick on this and so this part is X square X times X X square plus and and then the what are called a first-order component is the point three plus point for those are positive so positive point seven X and the last term is these two multiplying point one two anyway the rest should be easy I will not continue work on this it's kind of give you to get to a little taste what are the complicated a quadratic equation solving process might inhale okay so I think this chopper mass another heart just be quick on the we have this kind of equilibrium how to deal with that I might have this kind of question the homework or the test and you can see the changes actually easy the changes of naked eggs project all the cohesion one but solving can be a little more work on that other than there's no difference you solve it works so to access question yes if we get this on the test like can you have a piece of paper to it uh for the test yeah piece of paper yes piece of paper is allowed but I have not done that well it has been not convenient to do that because if user IVA used Pretoria they cannot allow you to submit the PDF or image upload any upload is not not actually with the port Oriole so you basically type in your work type your work and so basically what I mainly in look for if you type in the Box the text box it is the equation final quadratic equation you know we still like write on a paper and then copy the work over cuz like I need a few points okay yeah I need to see this no matter what kind of answer you solve I need to see the quadratic equation and you saw the two eggs so the two X so the main work and not the entire entire worth it might have more a lot more steps so this chapter is not test how much how well how good are your good in math you're comfortable is not but that's kind of a require you to show them you understand how to set up an equation based on the ice table and the K expression so but still in the quiz I have not set up a quiz like this but you can upload the image of your work they take a picture and the out of the upload as image well you submit your work that's okay now the PDA have actually more hassle I don't like to deal with that PDF except for grading your PDF you can just submit your work as an image the Jaypee JPEG file or MP PNG file not as the PDF PDF have to be open over by software but the image can be open just by by the internet explorer or editors well sure usually how we will know where our mistake when you grade it like you give me a name but I don't know where I lost the toolbar nothing you think you're you're saying you're a PDF file I'm mark on your PDF file you should look back you are submitted I'm mark on your PDF file okay thank you yeah you should take that so this is the practice what could have done but we don't have time to continue all the way but kind of a similar idea so let's go back do guys want the we have this PowerPoint have a one question about Sochi you guys are one of all proxies don't use a PowerPoint example the back to the PowerPoint not necessarily okay and this properties you have to do it by yourself this is the example is actually easy one of the easiest aw