ICE Chart

Hey guys in this new video, we're gonna do something incredibly important calculating equilibrium concentrations. Now, up to this point, I've been giving you questions in which our reaction is at equilibrium and the numbers I'm giving you are equilibrium amounts. Now, we're gonna be tasked with figuring out what those equilibrium amounts when I give you just initial concentrations. Now remember initial concentrations and equilibrium concentrations are totally different. And we're gonna say sometimes we'll be asked to calculate concentration of equilibrium. After being given initial concentrations, we're gonna say in order to do this, we're gonna have to use our favorite friend the ice chart and remember what does I stand for? I stands for initial change equilibrium. And we're gonna learn how to use an ice chart. And when do we use an ice chart? And what we should realize here is that ice charts are only allowed to have two types of units. We're gonna say they're used to having atmospheres or molar as the units. And remember why those two units because atmospheres are connected to K P and molar is connected to K C. We're still gonna be dealing with our equilibrium constants because they go hand in hand with our ice charts. Now, when do we use an ice chart? You only ask yourself one question or really you say one thing you're gonna say any time we have more than one compound in our balanced equation without an equilibrium concentration, then we have to use an ice chart. So before we start this next question, what do I mean by this? In the next question, we have three compounds within our balanced equation. Let's say I gave you the equilibrium amounts for two of them, we'd only be missing one person at equilibrium. In that case, we wouldn't need to do an ice chart. But let's say I gave you only one person at equilibrium. Technically, we'd have to do an ice chart in order to organize our work to see what the correct answer would be. So again, if you're missing more than one compound at equilibrium, you should use an ice chart. And if you don't have anyone at equilibrium, then you should definitely use an ice chart.

So let's take a look at the first two examples and see how we approach these types of questions. We say here when we have a solution where A G C N two minus gas, C N minus gas and A G positive gas and they have an equilibrium constant K equal to 1.8 times 10 to the negative 19. If the equilibrium concentrations of AGCN 2 - and CN are these numbers respectively. What is the equilibrium concentration of A G positive? So we ask ourselves, do we use a nice chart or not here? I give you the equilibrium amounts of this compound which is 0.30 and this compound which is 0.10, you're missing only one equilibrium amount. If you're missing only one equilibrium amount, then you don't have to do an ice chart. So we're simply gonna say in this case that K equals products over reactants. Yeah, we say that products here would be C N minus squared times A G positive. And since we're gonna need some room guys, I'm gonna remove myself from the image. So we have more room to work with divided by AGCN 2 negative. So what we're gonna do now is we're gonna plug in the numbers that we know. We know what K is. It's 1.8 times 10 to the negative 19 C N negative we said was .10 and it's gonna be squared A G positive is what we're looking for. So we're gonna have it as a variable divided by A G C N two minus which is 20.30. OK. So this question becomes fairly easy. All we have to do now is isolate our A G positive. So what we're gonna do first is multiply both sides by 0.30, these two multiply together to give us a new answer of 5.4 times 10 to the -21. And that equals .10 squared times A G positive. We just want a G positive. So we're gonna divide it out the 0.10 squared. So our final answer at the end for silver ion will be 5.4 times 10 to the negative 19 molar. So again, why didn't we have to use an ice chart? We didn't have to use an ice chart because we're missing only one person at equilibrium when you're missing no one at equilibrium or you're missing only one variable at equilibrium. Then you don't need to do an ice chart. We only do an ice chart when more than when, more than one concentration is missing at equilibrium.

now an example to we say we placed 2.5 moles of CEO and 2.5 moles of C 03 in a 10 liter flask and let the system come to equilibrium. What will be the final concentration of co two? Okay, now what? I'm what you need to realize here is I'm saying I'm letting these come to equilibrium. That means that these initial amounts are not equilibrium amounts. I'm giving them time to react so that they can get to equilibrium. So these are initial amounts of our reactions. So I have Onley initial concentrations. I don't have anyone in equilibrium, so I should definitely use a nice chart. So we're gonna say ice initial change, equilibrium. And remember, in a nice chart, just like with K, we ignore solids and liquids. So if we had any solids or liquids in this equation, we would just put a big accident spot. Since everything here is a gas, we don't do it. Now remember, what are the two units in a nice chart, we can either have mole arat, e or atmospheres. Remember molar iti is moles over leaders here. I give us 2.5 moles and 2.5 moles, and they're being placed in a 10 liter flask. So it's 2.5 moles divided by 10 liters. So our concentration is 0.25 Moeller, 0.25 Mueller, I don't tell you anything initially for co two, So it zero initially And remember we use this phrase earlier in the last few videos we lose reactant to make products so are reacting. Should be disappearing over time. So this is gonna be minus X and this is gonna be minus X. We're making products, so it's gonna be plus the coefficient in front of CO two is a two. So plus two x the equilibrium line, we bring down everything, so it's gonna we're gonna bring down the point 25 bring down the minus x so 0.25 minus x 0.25 minus x plus two x So we filled out our first ice chart. So this is how we put everything into it. Now what we're gonna say here is we need to solve for X. So next we're gonna say is K equals products. Overreacting. So equals CO two squared. Divided by CEO Times Co three now just realize that both CEO and CO. Three have the same exact equations at equilibrium. And remember, it's the things from the equilibrium line that we place in here. So at the Equilibrium Line Co. Two is two x, which is going to be squared. And since both of these equations are the same when they multiply together, it's gonna be 0.25 minus X squared. And this is all gonna still equal Now, one of the bad things about the ice chart is that sometimes we need to use the quadratic equation in order to solve for X variable. But don't worry. There are times when we can ignore it. This happens to be one of those times were going to say that this is called the perfect Square method, the perfect square method. We can use it to avoid the quadratic anytime the top is squared and the bottom is squared. Since they're both squared, we can just take the square root. Taking the square root of both sides will help us avoid the quadratic. So now it becomes the square root of 0.47 is 0.686 equals when I take the square root of the right side. The squares just disappear, so it's gonna equal to X over 0.25 minus X. What we're gonna do next is we're gonna multiply both sides by 0.25 minus X. Remember, we're trying to isolate X, so we're going to distribute distribute. So this is gonna become 0.1715 minus 0.686 x, and that's still equals my two X. Let's group X variables together. So add 0.686 x to both sides. So we're gonna say point 1715 equals 2.686 x and then all we have to do now is divide both sides by 2. toe Isolate our x variable. So here actually equal 0.6385 So we just isolated our X variable. But what did I ask us to find? I asked us to find CO two at equilibrium when I say final concentration. I mean equilibrium concentration on the equilibrium line co two equals two. X equals this right here. We just found out what X is. So all you gotta do is take this number and plug it in for X, and we'll know what CO two is at equilibrium. So equals 0.1 to 8 Moeller. So 0.1 to 8. Mueller I know I didn't give us a lot of space to do this one, guys, but what you should realize is holy crap. The ice chart has a lot of detail involved, right? So it's incredibly important that you first realized we had to use a nice chart because we're missing more than one compound of equilibrium. Then we have to realize we needed to use mole arat E because polarity is tied to Casey. And from there we pay very close attention to how we fill out the ice chart. Don't worry, this is the first ice chart we've done. But we'll get to do a lot more through the rest of the videos. And from there you guys are gonna learn the techniques and the approaches that you should take in orderto best do this in the quickest and most efficient way. But this one honestly is a typical type of ice chart. So if you got lost, go back and take a look at all the things that we're doing step by step, because if you mess up in one place in the whole answer will come out is wrong. Now that you guys have seen these first two examples, I want you guys to attempt a practice question left on the bottom. Read it and ask yourself, Does this need a nice chart? If it does, then do one. If it doesn't, then just say K equals products, overreact INTs and solve for the missing variable. Good luck, guys.

Hey, guys, In this brand new video, we're gonna continue with our conversation on calculating equilibrium Concentrations. So let's take a look at this particular question we're gonna say when 0. atmospheres of n 02 was allowed to come to equilibrium, the total pressure was 20.875 atmospheres calculate the KP of the reaction. Now all I'm giving you is 0.600 atmospheres of Eno to I'm saying I'm allowed me to come to equilibrium. What that tells me is this amount is not my equilibrium amount. It's rather my initial amount. So this is my initial pressure. So all we say to ourselves is Do we have to use a nice chart? And the answer here is Yes, because we're gonna have this missing equilibrium amount. This is missing equilibrium amount, and this is missing an equilibrium amount. Any time. More than one of my compounds in my balanced equation is missing an equilibrium amount. I have to do a nice chart. This number here I'm giving it time to get to equilibrium, which means it's my initial pressure. So we're gonna say I is initial. See, it's change. E is equilibrium. So we're gonna say Initially, we're starting out with 0.600 atmospheres. Remember Atmospheres Goals with KP. I don't tell us anything about N. O or 02 so they're initially at zero. Remember the important phrase we've been saying? We're losing reactant to make products. So this is going to be minus two X because of the two and it's minus because it's reacted. Plus two x the two there. That's why it's plus two x plus x Bring down everything. 0.600 minus two X plus two X plus X. Now what we should realize here is they're telling me what the total pressure is now this goes back to Henry's law or actually not Henry's Law. But more importantly, Dalton's law Dalton's Law says that the total pressure that we experience is equal to the pressure of all of the gas is added up. So my total pressure is equal to the pressure of n 02 plus the pressure of Eno plus the pressure of +02 and at equilibrium. That's my equilibrium. Total pressure. So what we're gonna do here is say, at equilibrium. Each of these gasses is equal Thio Each of these equations. So at equilibrium are total pressures. 0.875 atmospheres at equilibrium N 02 is 20.600 minus two x at equilibrium. Eno is two x at equilibrium. 02 was just X. We're going to say that this negative to in this positive to basically cancel each other out. So our equation becomes 0. atmospheres equals 0.600 plus X. We need to isolate X here, so we're gonna subtract 0.600 0.600. So x here equals 0.275 atmospheres. Remember, this is Dalton's law. The total pressure we experience is the pressure from all of the gas is added up together. And this is this an equilibrium, total pressure. We use the equilibrium equations for each of the compounds we just isolated. What? Exes. So all we need to do is take this X answer, plug it in here, plug it in here, plug it in here and we'll know each of them at equilibrium. And if we know each of them at equilibrium, then it's those equilibrium amounts that we plug into KP. Remember, KP is just products overreacting. So it's Enel squared times out to divided by N 02 squared because the two on the two here. So when we plug in the X in for N we get 0.50 atmospheres when we plug it in for N o at equilibrium and ah equals two x plug in the X. And so we just found. So that's a no. And then 02 is just equal to exit equilibrium. So with that same exact number now take all those numbers and plug it in. Okay? And when you do all that, you'll get your KP equal to 33. Now, to do this question, you had to have a knowledge off Dalton's law. Remember that deals with gasses and then apply that concept to this new idea of a nice chart. So it's kind of taking a little bit of old information, combining with some new information in order to obtain R K P value

So the next question says an important reaction in the formation of acid rain is to eso to gas is combined with 102 gas to give us to eso three gas Here we're saying initially, we have 0.23 Moeller s 02 and 0.15 Mueller 02 They're mixed together and allowed to react in an evacuated flask at 340 degrees Celsius. When an equilibrium is established, the equilibrium amount of one of them s 03 was found to be 30.199 Moeller, calculate the equilibrium constant K C for the reaction at 340 degrees Celsius. So we say to ourselves, Do we need to do a nice chart? Well, we know initially this is how much we have of our react INTs equilibrium is reached, but we only know the equilibrium of one compound. So we're still missing the equilibrium from eso to and for Anytime we're missing more than one compound and equilibrium, we have to do a nice shirt. So in this case, we're gonna do a nice chart. Now I'm gonna remove myself from the image guy so that we can work this problem out with more space. So let's take a look. We know we have to do a nice chart, so it's gonna be to s 02 plus o two. Gas gives me to s 03 gas initial change equilibrium. So now what we're gonna do here is we're gonna We're gonna plug in what we know initially. So initially, we know the amount for s 02 is 20.23 Moeller and we know what the initial amount of 02 is. It's gonna be point 015 Moeller. I don't tell you anything about s 03 So initially it's going to be equal to zero. Then we're gonna say, Remember the important phrase we lose react INTs to make products. This helps us figure out how we exactly we put in the change. So it's gonna be minus two x because of the two minus X plus two acts because of the two bring down everything to 3 minus two x 0.15 minus x plus two x Hopefully you guys were able to fill out your ice chart in the same way, as I did next, we're gonna say the important thing here is we know what s 03 is at equilibrium at equilibrium. Eso three equals two X. But the important thing here that we should realizes that I tell us another piece of information I actually tell us what s 03 is at equilibrium. At equilibrium, it equals 30.19 So that means two X also equals 20. Because we know this, we can isolate our x variable. So we're gonna divide. Both sides were gonna divide this by two and this by to toe isolate our x variable. So we're gonna stay here. X equals point 0009 Mueller. And now, because we know what X is, we can take that X answer, and we can plug it in for the other compounds. So we plug it in for this x and in this X So we're gonna say eso to equilibrium equals 0.23 minus two x. We just solve what? The exes. So when we work that out, we'll find out what our answer is for. Okay. Here. No equal 0.2101 Now we're gonna do the same thing for 02 At equilibrium 02 equals 20.15 minus X plug in what we know for X. So it equals 0. Okay, now we know everyone in equilibrium. So now we're able to find Casey. K C equals products, overreact INTs. So all we do now is we plug in their equilibrium amount that we just calculated. So we know SL three equilibrium is 30.199 squared S 02 is 20.2101 squared. And so too is just point 4005 Plug all that in and we'll get our answer. Okay. When we do that, our Casey is 0.641 as our answer. Hopefully, you guys were able to see the connections that we needed here. We're only given one person at equilibrium. So technically, we should have done a nice chart. The great thing is because we knew one person that equilibrium, we could isolate our X. Once we isolated Rx, we take that answer and plug it into each one of the compounds. Add the equilibrium line and doing that helped us find out what Casey is

Hey, guys, In this new video, we're gonna continue with our discussion on calculating mawr equilibrium concentrations. So if we take a look at this first one, it says if Casey is 32.7 at 300 degrees Celsius for the following reaction, the reaction is to one mole of H two gas plus one mole of BR to gas gives us two moles of H P R gas. What is the concentration off H two at equilibrium? If a 20 liter flask contains five moles of h br initially. Now what we should say to ourselves is Do I have to do a nice chart or not? What we should realize here is all I'm giving you is initially Onley this amount of product so we don't have anyone in equilibrium. And therefore we have to do a nice chart. Remember, if you're missing mawr than one compound at equilibrium, you must do a nice chart. But something's weird about this particular question. We're used to seeing initial amounts for our react. It's and we're used to seeing zero amounts for our products. This one's actually written backwards. So what we're gonna do here is we're actually going to flip this reaction so that it makes more sense. We should initially have some reactant and then our products are normally at zero initially and it's gonna be ice chart, because again, we only have the initial amount of now are reacting HPR. And remember, we're doing this because again we're used to seeing initial amounts for our react. It's not our products and realized if we reverse the reaction, then this is gonna change. What are K value is Just remember here, reversing the reaction will give us the reciprocal of K. So now Casey becomes 1/32 0. and that answer is going to be 3.6 times 10 to the negative, too. Now, what we're gonna do here is we're going to say initially, how much reacting do we have? We have five moles and we're gonna divide it by 20 leaders. And remember, we're doing this because the units we can use in a nice chart on polarity or atmospheres. Since we have moles and leaders in this question, that's gonna help us find mole Arat E. So that's gonna be point 25 Moeller. So that's our initial amount. I don't tell you anything. Initially about are reacting. So there's zero. Remember, we're losing react INTs to make product plus X plus x. This is gonna be 0.25 minus two acts plus X plus X. Now what we're gonna do is we're going to solve for X variable. So now we're gonna say that K C equals products overreacting. So it equals h two times br to over HBR squared and it's squared because remember the two here. Now we're just gonna plug in the numbers. We know we know what Casey is. It's 3.6 times 10 to the negative, too. That's gonna equal at equilibrium H two and B R two are both x so x Times X is gonna give me X squared divided by yeah, 0.25 minus two x squared. Now remember, we have toe isolate our X variable, but the problem is, sometimes we'll have to use the quadratic. There are two times when we can ignore the we can get around this limitation. Okay, so there's two times we will be able to manipulate the equations so that we can avoid the quadratic formula. This happens to be one of those times. Remember, we've talked about this before. We have the perfect square method here. Remember, The perfect square method means we have the top is squared in the bottom of squared. And since both top and bottom r squared, I can take the square root to avoid the quadratic So square with this square. With this, that's going to mean my answer now is 0.175 equals taking the square root of those squares just gets rid of the squares. So it's gonna be X over 0.25 minus x minus two x multiply both sides by 0.25 minus two x 0. minus two X. Now you're going to distribute distribute, since we're gonna need some more room to work this out, guys, I'm going to remove myself from the image so we have more room to work with. Okay, so now we're gonna have 0.4375 And remember, how do we get that? The 0.175 multiplied times the 0.25 when we distribute it minus 0. x equals. It's still equal to x Group. The X variables together. Okay, this X is actually one X we're gonna add 0.350 x to it. So I'm gonna say 0.4375 equals 1.350 x divide by 1.350 on both sides. So we're gonna say here that are X equals 0.3 to 4 Moeller. Now, remember, we shouldn't just circle this, so we're gonna take away that circle. We shouldn't say that this is our answer. We have to look and see. What did they ask me to find an equilibrium? They're asking me to find hte to equilibrium. If we go to the equilibrium line, we see that indeed H two equals X. So this answer we just found is acceptable. But remember, if I had asked for the equilibrium amount of HB are at equilibrium, we would take this X and plug it in here and then find the correct answer for HBR. So always be careful. Just because you find X, that doesn't mean that's your answer. Check to see what you're asked to find and then check to see what it's equation is on the equilibrium line. That's the best approach you want to take. Now that you guys have seen that one, I want to see if you guys can try to tackle this particular question. We're gonna say at a given temperature, the gas phase reaction H two gas plus O two gas gives us to. And actually we're gonna change this H two to a nitrogen two and two plus Gas gives me too, eh? No gas has an equilibrium constant off 4. times 10 to the negative. 15. What will be the concentration of Eno equilibrium if two moles of nitrogen and six moles of oxygen are allowed to come to equilibrium in a two liter flask? So what we need to realize here is do we need to do a nice charter or not? Once you guys figure that out, I want you guys to at least attempt to do this. Don't worry. If you don't know where to go with it, just click on the explanation button and I'll appear and I'll be ableto answer it. Look at the strategies that I use in order to solve this particular one. Good luck guys attempted on your own First. If you get stuck, go and click on the explanation button

consider the following reaction. So a reaction mixture initially contains 15 Moeller of c O B R. Two, determine the equilibrium concentration of carbon monoxide. If Casey for the reaction at this temperature is 2.15 times 10 to the minus three. All right, so in this question, they're only giving us the initial amount of this compound we're missing. Equilibrium amounts for all compounds within the equation, so we're gonna have to do a nice chart. So we're gonna set up the ice chart. And remember, in our ice chart, we ignore solids and liquids. Everything here is a gas. So it's fine. Remember, our ice chart stands for initial change and equilibrium. Since we're dealing with Casey, we know the units need to be in polarity, which they are. They're gonna plug that in. These initially are zero. Remember, we lose react INTs in order to make products, bring down everything. So we feel that our ice chart now we're gonna do our equilibrium expression K C equals products overreacted. So seo times br to over c o B r two, we're gonna plug in the values we have for each. So Casey is 2.15 times 10 to the minus three equals at equilibrium. Both of our products are equal to X, so that's X squared, divided by 15 minus X. At this point, we have to check to see Can I ignore this minus X here, the top in the bottom or not both squared so I can't take the square root. So we're gonna do next. We're gonna take the initial concentration, and you're gonna divide it by your K value. If you get a number greater than 500 you'll be able to ignore that minus X and avoid the quadratic formula. So if we plug these concentration, this concentration in 15 and divided by R. K, we get an answer of 69. So that number definitely isn't greater than 500. So we cannot ignore that minus X on. We have to keep it and do the quadratic formula. We're gonna multiply both sides now by 15 minus X, we're going to distribute, distribute. So when we distribute, we're gonna get here 3.23 times 10 to the negative four minus 2.15 times 10 to the minus three x equals X squared. This X variable has the largest power source our lead term, which means everything has to go toe it's side. So we're gonna add this to both sides here. We're gonna subtract this from both sides. Minus So now our new expression becomes X squared plus 2.15 times 10 to the minus three X minus 3 to 3 times 10 to the minus four. This represents my A might be and my seat. So the quadratic formula is negative. B plus or minus B squared minus four A. C over two A. So we're gonna start plugging these numbers in. So negative 2.15 times 10 to the minus three plus or minus B squared till 215 times 10 to the minus. Three squared minus four. Here A has a one in front of it. So that's one for C. Do not forget the negative sign. So negative. 3.23 times 10 to the minus four divided by two times one. Realize here at this point, this is plus or minus plus or minus. So I mean, we're gonna get to possibilities. All right, so I'm going to do all the math in here. Then take the square root of that number. So we're gonna get negative 2.15 times 10 to the minus three plus or minus 0. divided by two. Again, it's plus or minus. So there's two possibilities for my ex one where I am adding these two numbers together, then dividing by two or one where I'm subtracting them from each other, then dividing by two. So when I do that, I get to answers. One is 10.169 and the other one is negative. 10.19 Both of these X variables cannot be my answer. Only one of them is the correct answer. How do we check which one is the right one? Well, what you're gonna do here is you're gonna take those two X variables, and it doesn't matter where you plug it in at equilibrium. You should always get a positive number. Negative concentration. Negative amounts of equilibrium do not exist. Okay, So that would mean that the negative one I cannot use because it's not always gonna give me a positive answer back. Depending on where I put it, so this would be the total for X. Now we go back and look at what they asked me to find. Well, in the question, we're asked to figure out the equilibrium concentration of CEO at equilibrium. CEO equals X. So that is our answer. We're done. And the units are more clarity because my initial units were polarity. If my initial units were atmospheres, then my answer at the end will be atmospheres. Also, if we wanted the equilibrium concentration of, say, the reactant, you would take that X and plug it into here. So it be 15 minus that X variable to find our equilibrium concentration of our reactant. So just remember, when you find X, it doesn't necessarily mean that is the final answer. You have to go back to the ice chart, look at the equilibrium line here and see what is the equation for that particular compound. Here We were looking for carbon monoxide at equilibrium. It is just equal to X. So the X that we found is the right answer right from the beginning. But again, if I had asked for let's say, the equilibrium amount of our our reactant then I'd have to plug it into this formula to figure out my final equilibrium amount would be. So always be careful and look exactly what you need to find.