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Add heterogenous initials

perfect okay I don't have my tripod with these days these ice tables that setting up the ice tables just is one of the most important things right when you're looking at a nice table question you should be thinking to yourself okay when I read the question let's read this question all together at the same time the initial bla bla bla bla bla bla bla bla bla and equilibrium bla bla bla bla bla bla bla bla bla okay so it says something initial something equilibrium something immediately you know you know for sure you're gonna have to use a nice table why do you know for sure you're gonna have to use a nice table given this question it's got initial and it's got equilibrium ah I'm gonna have to use nice table but that's okay cuz you're all you're all amazing an ice table right now so when we look at an ice table the most important part is getting our balanced chemical reaction often on the Diploma exam they'll give you about chemical reaction most of the time but every once in a while you might have to balance it yourself rarely do you have to make an equation now yesterday I asked you to make the equations just because it's good to get you to think about how do I make a chemical reaction right how do I write one how do I do this I kind of think um so in our Google classroom under Chapter 15 assignments I did last night good thing it doesn't say the time because it was very late ice table practice and the practice key and so the key is on there do you want me to go through any of these three examples not using the key do you want me to just go through it from the start and just make sure we're all on the same page are we happy with ice tables who wants me to go through one from the start yeah let's do the last sure let's do the last one together it's gonna be pretty quick it's fast it actually gonna be really quick so there's no harder than doing this okay it says three moles of carbon monoxide are reacted with four moles of oxygen and to Lila and that two liter cylinder if 2.5 moles of carbon dioxide is created that are created the equilibrium man whoever wrote this isn't very good at intercept point carbon dioxide he's created at equilibrium what is the equilibrium concentration so I know read the first sentence does it say the word initial no but is it is it implying at the beginning yes okay you have to note that that means initial right so you got carbon monoxide is reacting with oxygen gas we know it's in equilibrium so I use our equilibrium arrows and it's gonna make carbon dioxide gas now the first thing we have to do is we have to balance this chemical reaction one carbon one carbon three oxygens two oxygens a little trick that sometimes yummy I don't know if you remember this from your science 10 or chem 20 days if you're a scientist and a chem 20 teacher told you this this this is almost like a combustion reaction would you agree there's something with oxygen is making co2 okay so if you're if your oxygens are off right we have three we only want to if your oxygens are off then as long as you balance everything other than the oxygens double everything else just double it so did we successfully balance the first and the last thing are they kind of equal to each other one carbon in one carbon yeah sure so I'm gonna double them two carbons and two carbons and then let's reassess and let's see how many oxygens we need two and four and four oh all right we're done is that okay that's a little trick whenever you're is there's a combustion reaction and it's the oxygens that don't work so we've got a balanced chemical reaction now and it says it wants us to do something something something initial something something something equilibrium so we will put ice three moles of carbon monoxide four moles of oxygen and 2.5 moles of carbon dioxide now straight out of the gate I don't like that I don't like what I just wrote does anybody know why I don't like that just gonna give you ten seconds don't say it out loud do we kind of know you kind of know the problem associated with this what do these numbers mean what are the units attached to these numbers moles and whenever possible what do we want to turn it into moles per liter we sure do so instead of writing three moles of carbon monoxide what should I have written so I'll take my moles right three moles and I'll divide up on my volume so I get moles per liter so this really should be man hopefully this doesn't erase more than I want it to whatever that looks terrible okay 1.5 moles to moles and then this is going to be one nope and this is going to be 1.2 robotics good so now now everything is in moles per liter and now I can do this really really easily or what I consider to be really really easily are there any assumptions that we have to make in our ice table the sky we should but if saying we're starting with this much and it neglects to say anything about any of the products right so they just assume you don't have any well we know that our our change must have been the positive 1.25 and up here I would always like us to put what the change is in general should be so I'll take this value and in order to get my X what should I to divide that by I'll take this value and I'll divide it by two in order to get my X so my X is 0.625 you take that and you divide it by 2 you get 165 so if I'm losing 1 X how much am I losing here 0.625 right 0.625 so two minus zero point six two five is one point three seven five and then if I'm losing two x's well we know two x's 1.25 0.25 are we okay with that at the end yes right yeah so we're gonna find out today and not some more on Monday we're gonna find out today and Monday that it's much better to have the equilibrium values in concentrations already because we're gonna do something today slash from Monday where if they're in moles it won't work but if they're moles per liter it will okay so straight out of the gates it's nice to put everything in moles per liter that way you don't have to remember it kind of after the fact okay perfect what I want to know this should have been do you agree this should have been two point zero zero to start with like if I if I take into account significant digit okay what is two point zero zero minus zero point six two five is it one point three seven five no it's not okay and this goes back this goes back to our talks about significant digits this goes back to our talks about significant digits now would you all would you all agree that when I take the number like in order to get to point zero zero I had to take four point zero zero and I I divided it by two point zero zero right so my concentration in moles per liter was four point zero zero moles over two point zero zero liters so 4 divided by 2 is 2 and I should have three significant digits moles per liter is that like you've been prot you've probably been using that rule every day in chemistry for the last and these semester with right when if when you took chem 20 that's called the certainty rule there's a certain amount of certainty in both of these numbers and we ask that we have to round to the lowest amount of certainty we have to round to the least certain number of digits but three digits divided by three digits as three digits okay sure no problem but think of this I'm gonna take my two point zero zero and I'm gonna take away 0.625 so let's do this by hand um what's who knows minus five do you know what that number is no you have no idea what that number is would you agree you've got absolutely no idea it doesn't give you a value here I mean what do we kind of assume it to be zero we assume it to zero because there's there's no other option we can't assume it to be nine that would be ludicrous all right so we just used two must be zero zero minus five is five but it's still a question mark we don't actually know that it's five you've you've got no idea but whatever okay Wow so that much that so left nine nine minus two is seven nine nine nine three zero six is three 2 minus 0 is 2 so no holy no that doesn't work good thing that's going up okay so our answer should be one point three seven five this is what we call the precision rule you left around to the least precise measurement which one of these measurements was less precise the top one or the bottom one which one has less decimal places the top one so this five you don't actually know that it's a five but we're gonna assume it's kind of a vibe and use it to round to the least number of the decimal places so there's two decimal places here three years so we gotta round to two decimal places right should this seven seven to this seven stay as a seven no no it should round up to an eight and that's like an often not used like when was the last time you use that that principle when you were doing rounding and things like that yeah so anyways that so that's why if you look on the key if you look on the key for this thing the first answer is not zero point four three five because it's the exact same thing right you don't know what that digit is minus five it's a five but the fives got around the three up to a four so that's that's why the answer for the first one is zero point four four moles the second one's fine no it's not sorry it's not fine it's the same thing it's a twenty one point eight and then one point tribute but anyways the keys up on on Google bathroom and we're gonna move on to bigger and better things here in a second let me know if you want more ice table practice I can probably whip up some more ice table practice but for the meantime we're gonna talk about equilibrium expressions and this idea of Kacie so I don't know if you remember me kind of harping on the idea that percent reactions don't hold up across all of the concentrations right if I vary the concentrations a little bit of my reactance I can actually get a totally different percent reaction so instead of using percent reactions we're going to use an idea called an equilibrium constant or a KC or sometimes it's even called keq a stands for equilibrium constant or equilibrium constant whatever it doesn't matter the constant is calculated using the equilibrium expression below so let's write an equation I don't know pick four letters hey fine whatever pick four single-digit numbers nine three five six so nine of these reacts with three of these to make five of these and six of those okay so here's our chemical reaction and I want to be very clear the concentrations of all of these chemicals at equilibrium not initially but once equilibrium is established the equilibrium concentrations are all related based on the following principle KC in general you can think about it as products over reactants but more specifically that's a terrible cake more specifically the KC is equal to each individual product raised to the power of their coefficient KC just stands for equilibrium constant that's all it means this is a constant this is a number that will always hold for this particular chemical reaction at this specific temperature okay so see the what's the coefficient on c5 so it's raised to the power five what's the coefficients on these six so it's raised to the power six and we've got a raised to the power 9 and B raised to the power 3 now if that confuses you you're probably not alone I'm gonna write I'm gonna write this chemical reaction in a different way okay and I'm I'm ruing the time that I asked you for for random single-digit numbers but whatever it doesn't really matter I'm gonna write this reaction in a different way how many A's are reacting together a plus a plus a plus a two four six seven plus a plus and how many B's are reacting together three plus B plus B plus B gives us is in equilibrium with how many C's is it making hmm C plus C plus C plus C plus C and how many DS are we making six would you agree that this is the exact same thing as that it's just that we've almost like combined our like terms it's a mapping right good yeah so 9s are reacting with three B's to make five season six these well the idea is that we want to take the concentrations of all the products and multiply them together right on top is the concentrations of all the products and you multiply them all together and you divide by the concentrations of all the reactants and you multiply them all together well how many days should I have on the bottom because it's a reactant how many eighths so I'm going to have the concentration of a times the concentration of a time's the concentration of a time's the concentration of a time's the concentration of a how many days are here nice oh that's a to the power 9 does that make sense that's where this come from a to the power and nine times B to the power three it's just all the A's and all the B's being multiplied by themselves are we okay with that and then all the C's and all the DS on top that's where the that's why the coefficients come into play like that so note what do square brackets mean concentration in moles per liter that's why when we look at our ice tables it's super important it's really really important to have these in moles per liter because if a question ever asks you to calculate the equilibrium constants of a reaction you just take these values and you plug them into your equation but if you calculate it if you did your ice table in moles then you have to remember to divide by your volume and then do it so there is a big difference between those okay so let's let's just do an example so we've got the reaction to ammonia's are turning into nitrogen gas and three hydrogen gases now I will always try my best to give you a temperature because when I change the temperature I change KC the equilibrium constant is only good for a specific temperature if I heat up a reaction we'll learn this later but if I heat up a reaction I change the number of products and the number of reactants and that alters our equilibrium okay but that's fine that's just for later the equilibrium concentrations at 673 Kelvin are this-this-this for those things so what I want to do is write an equilibrium law expression I want to be very clear the expression is just the formula products over reactants that's the equation okay so I want to see the equation in the second step I want to actually physically calculate the number KC the number so let's write the equilibrium law expression for this reaction in general hey C is what always what on top products all the products being multiplied together probably procs to me up here to write so I'm going to go the concentration of n2 gas times the concentration of h2 gas and I'm going to divide it by my reactants which is nh3 gaps what's the problem with this no.not units because we haven't put a number in yet right a unit is always associated with a number yeah I gotta have those coefficients in there right I need to have this coefficient what's what's the coefficient on n - one so I'm just gonna leave it right something raised to power one doesn't matter H 2 raised to the power of three and NH 3 raised to the power of two that's the expression so if I ever ask you for an expression that's what it means it's like the equation what is just what does this look like now I'm asking for the actual value of the equilibrium constant this should be pretty easy we're just gonna take our values plug them into the equation and see what we get so the concentration for n 2 is 1 mole per liter so that's 1 mole per liter raised to the power 1 concentration of hydrogen is 0.5 moles per liter raised to the power 3 and the concentration of ammonia right on the bottom was two so I want you to try this out take out your calculator does anybody need a calculator yeah Katelyn can you catch John can you catch anybody else can you catch so you should get you should get a pretty tiny number like a relatively small number right what if what did we get zero point zero three one three five three one two five yes zero point zero three one two five now I want to make it very clear kc values are like ph's we define them we define them to have no units okay a kc value will never have units I know I know you could make you could make a set of units out of this but it's a constant that has no units okay now I want to be very clear our answers wrong right yeah why is it wrong should only have three significant digits right what so this should be three point one three three point one three times ten to the power negative two right three point one three times ten to the power of negative two perfect now I don't want you to write anything down I'm just gonna I'm just gonna go back up here and we're just gonna take a very general perspective at what this is if I set a reaction was greater than 50% would that mean reactants are favored or would that mean products are favored if I set a reaction that would mean products are favored right because would you agree if greater than 50% of this stuff turned into that then that means we've got more products than we do reactants right now we can do the exact same thing with kc values i'm gonna write down i'm gonna write down the concentrations up here and you tell me if this reaction is products favored or reactants favourite nh3 was two moles per liter n2 was one mole per liter and h2 0.5 moles per year so does it look like based on these concentrations does it look like it was reactants favored or products favored would you agree in general it seems like there are more reactants than products just in general okay so reactants are favored and what did we get for a kc value did we get a really large kc value or did we get a really small kc value oh that's interesting curious okay let's move on without talking about it again for a little bit let's talk about homogenious equilibria and heterogenous men you've probably heard those terms at least three times before would you agree homogeneous and heterogeneous probably more yeah but I I mean in three separate contexts what does the prefix write a prefix is a word that you glue on to the beginning of another word what does the prefix homo means it means same homo sapiens is the correct genus and species term for human beings Homo sapiens means same as us are we all the same species let's move on without commenting on that okay so a homogeneous equilibria is where all the reactants and products are the same state of matter if a reaction is homogeneous if they're all the same state of matter then we will use every substance to calculate the equilibrium constant if it's not if it's heterogeneous and what I mean by heterogeneous is when you look at all these states of matter what are all of them they're all gases if one of them is different then that means it's a heterogeneous reaction there's a separate set of rules and we'll talk about why that is when we come to it so for example right the equilibrium expression for this reaction well you've already done right we just did that what was the equilibrium expression for this reaction hey see is what the concentration of hydrogen gas raised for the power of what 3 times the concentration of nitrogen gas raised to the power of what 1 so we just won't write it all divided by the concentration of ammonia gas grace the power what okay in general in general the equilibrium constant expression is always what over what products over reactants always always always okay here let's take a look at this I know that this is a crazy chemical reaction I understand that okay but let's take a look at it and let's ask ourselves is this homogeneous or is it heterogeneous this is homogeneous would you agree all of the states of matter are the same as each other then it doesn't matter what they are you have to use every single one of these terms in the equilibrium constant KC specifically for this reaction KC is what it's ch3coo ch3 liquid being raised to the power what one so we don't write times water liquid being raised to the power one so we don't write it it's all divided by the concentration of methanol liquid raised to the power once we don't write it multiplied by the concentration of acetic acid ah praise the power once of it all right was that very difficult yeah okay hey heterogeneous reactions but a reaction is heterogeneous we only use aqueous and gaseous States in our equilibrium constant is that okay we are not allowed to use liquids and what else are we not allowed to use and the reason why that is is if we look at a reaction if we look at a reaction so there's a beaker right the bottle and the stop or something like that and we've got a liquid in here I want to be very careful of the way I express this let's say there's some gaseous particles right and they're they're condensing into a liquid so something's going from a liquid to a gas and vice versa okay so we've got condensation and we've got evaporation happening in this bottle it doesn't really matter it just really honestly matter how much liquid is in here because there's the liquid at the bottom of the flask is it is it doing anything it's the liquid at the bottom of the flask evaporator no it's not doing anything and also if I added more water with the concentration of the water change no if I added more water the volume would get bigger so the concentration doesn't change okay you can't change the concentration of liquid water if it's only liquid present okay can I change the concentration of this gas if I added more gas molecules could I change the concentration of the gas yes because gases can be compressed okay so you can change the concentration of a gas you can't really change the concentration of a liquid unless it's a reaction like this one when they're all liquids if you pour two liquids together they mix together and their concentrations change based on how much of one liquid there is if that's complicated and if you didn't understand that that's totally fine the moral of the story is if you have a heterogeneous reaction you only use aqueous and gaseous entities in your equilibrium constant so let's take a look at this is this homogeneous or is it heterogeneous this is heterogeneous immediately you know etc genus because I see aqueous and gas boom two different things we have to use our heterogeneous laws in order to do this so we're still calculating pazi are we allowed to use the concentration of hydrogen in my kc yes because it's a gas and gases their concentrations can change right h2 gas raised to the power what 1 so we don't write it am i allowed to use the concentration of zinc chloride yeah because it's aqueous can you change the concentration of an aqueous substance yes an aqueous substance you can by just adding more zinc chloride it dissolves in the water if I add more zinc chloride to water does the water's volume change dramatically no it dissolves into the water and the volume doesn't necessarily change so the concentration of zinc chloride is not fixed it can change so we're allowed to use it zinc chloride race the power one on the bottom are we allowed to use zinc no because if I if I add a chunk of zinc does it dissolve into the water no it doesn't remember elements don't dissolve right or they don't dissolve to any appreciable extent so if I add more zinc I'm just adding more chunks of metal and that's increasing the volume of everything but the concentration of zinc isn't changed does that kind of makes sense so we're not allowed to use zinc what we will do you don't have to do this but we can put the number one as a placeholder we can just we can just say that its concentration is 1 and it'll never change we're just using that as a placeholder this equilibrium constant is just a number it just represents the extent of the reaction it's okay if you didn't put one cuz what happens when you divide by one what's gonna happen nothing and that's the beauty of us putting one okay it doesn't actually change the value of the constant I have to use hydrogen chloride because it's aqueous and what's it raised to the power of two so it doesn't matter if you put the one there it doesn't matter if you don't put the one there the math stays the same I just I want to be very clear that this can be used as a placeholder is that okay okay because some of you we're gonna I'm gonna give you another worksheet here in a little bit and some of you are gonna be hella confused by some stuff so so let's try the second one really quickly it's the concentration of carbonic acid aqueous / the concentration of carbon dioxide gas multiplied by the concentration of water liquid no no that's wrong isn't it that's the worst thing I've ever seen in my entire life what should I do erase the water why erase the water it's a liquid in a heterogeneous reaction good you can use the number one as a placeholder if you want right we just define it to be one as because it's not gonna change doesn't really matter what number we put in there you can't not that you can't but solids don't typically react with each other okay because solids do not have enough kinetic energy to collide and to be able to change their potential but solids typically don't have enough kinetic energy to be able to do that so what I would like us to do is work on this homogeneous heterogeneous reaction I apologize they're not [Music] [Music] so what I would suggest that you do the way I would suggest you do this is yeah I know I know it says write the equilibrium expressions that's that's great do that that's kind of the main purpose of this activity the first thing I would I would suggest that you do go through the entire list of whatever however many reactions there are 12 or whatever 11 reaction and label them as homogeneous or heterogeneous why does that go 1-1 okay there actually is well whatever it doesn't matter they both want to be another line this way first first label them as homogeneous or heterogeneous and then make the case the expression [Music] yeah they can be on like JC if I said if I sent this what's what's the reactant of what are the reactants or reactants and what are the products are seized the product it's the same thing to here it's always products on top always the things on the right on top always the thing is on the left on the bottom always always and I'm almost that that that reaction is backwards okay I want JC I want you to take a look at her this is gonna sound stupid I want it I want you to take a look at me the second number one right so that is this reaction and the reaction labeled orally what do you notice about them exactly so I want I want you to write the expression where products are on top reactants are on the bottom no matter [Music] well yes because you asked it's stupid okay but only because that's why some people because water can be gas if you boil it right yes so it's just it's gas that was made or its water that was made in eventually the key is at the front if you're done or if you are you're halfway through and you want to take a peek or whatever the P is at the crunch I just I asked let me know at the end a I'll give you two or three more minutes yeah there's an answer but I just I just want you to be aware that that is a possibility so on the whole exam if there's there's a value missing and then you can assume it not that it's one little bleeder but we're just using the number one [Music] no no I know no no I know it's fine but that's we're just trying to make sure that right away it's good trust me Chelsea it's good you would never make that mistake again yes again yeah I'm going to give you another minute or I'm gonna put the key on Google classroom later but yeah take take pictures all you want right regardless regardless of how far you've gone on that worksheet can I make sure everybody attempts the very last question please I would like everybody to attempt with very last question in the next minute no I just I just want to use it as a litmus test I just want to use it to to see if we all [Music] okay 30 seconds try the last one okay so hopefully you had a little bit of time to try out that last question okay so we're gonna go through the first couple reactions and hopefully this makes sense in that in that first reaction is there anything we're not allowed to put in our case new expression yeah h2o so you can either leave it out or put the number one it's perfectly fine if you do either as long as you're aware for the second one is there anything I know it says number one whatever for the second one is there anything we're allowed to leave out no because it's homogeneous anytime you see a homogeneous reaction you have to use every single one of them okay carbon dioxide and hydrogen and carbon monoxide and water I wanna I want to just do the next one but then I'm going to come back to this absolutely you are allowed to use concentrations of ions if you're using the concentration of an eye on you you have to tell me it's the ion so you have to put positive or negative or positive 2 or negative 2 or whatever right but absolutely you're totally allowed to do that we're not allowed to use water why liquid in a heterogeneous reaction awesome hey can I get everybody to focus on this is confusing the second number one look at the second number one and also at the exact same time look at number four what do you notice about those two reactions what do you notice about this reaction and number four they're the exact same reaction it's just that we're expressing it in a reverse way right would you agree carbon monoxide plus water turning into carbon dioxide and hydrogen gas is the exact opposite of carbon dioxide and hydrogen gas making carbon monoxide as water right it's just reverse so if a reaction gets reversed what do you do with the kc expression flip it do you agree that our products in one version become the reactants in the reverse version does that make sense so because you flip the reaction you have to flip your x equilibrium expression does that make sense that's gonna come into play here in a little bit okay I'm gonna skip I'm gonna put the key on Google classroom if you want to go slowly fine I'm gonna skip all the way to the very end how many people made the mistake of ignoring everything for this last reaction okay lots of people aren't being honest but that's fine whatever as long as you understand hey this is homogenius I cannot look at the states of matter any more you have to use them and the reason why that is when I mix methanol and and pure acetic acid together their volumes combined and they mix together and so you're changing their concentrations their concentrations because it's too was mixed together their concentrations are allowed to change now so because their concentrations are allowed to change we're not allowed to use the number one as a placeholder hopefully that makes sense okay whoo now there's kind of one last thing that I'd like to talk about and then we will get into using ice tables a book at a zoo okay well if you put it in the binder and you need to stake the stapler okay Casey is a value that communicates the relative position of an equilibrium what that means is is is it quantitative is it reactance favorite is a products favored or is there no reaction okay so um let's use our percent yield descriptions that don't work all the time so greater than 99 percent yield remember that was quantitative greater than fifty percent less than 50 percent and zero percent reaction so the term we use for greater than 99% that was wanted what I say a reaction is quantitative that means all of this turns into the products every single last little bit except for maybe the point zero zero zero zero one percent that's great in the fifty percent is that products favored or is that reactants favored if a reaction if greater than 50 percent of this turns into that what do we have more of products or reactants products right right if we start with ten of this and more than 50 percent let's say six under the tent six turned into this and we're left with four right greater than fifty percent means products paper so that means products favored and because I don't have a lot of room I'm just live putting P favorite hopefully you know what that means greater less than 50% means reactants favored and zero percent meant there was no reaction putting no our accent again cuz I'm a chemist and I'm a lazy what kind of an arrow what kind of an arrow would we use for a quantitative reaction just a straight just one arrow that's all you need to show me that this reaction is 100 percent in one direction products and reactants favored are the equilibrium arrows but we have to put greater than or less than fifty percent above it right less than 50% sorry it's all kind of blurring together I call it maybe I'll try and sure okay and no reaction we just write no arrow I think we just typically don't use an arrow maybe I should put it'll be pretty obvious now what I want to think about let's use this example was this products favorite or resist reactants favored at equilibrium what's there more of products right okay so let's think about this let's assume that this was the concentrations of these two things what would be the KC for this reaction KC is the concentration of B right divided by the concentration of a what would that what would that be in this case it would be what it's not not B to the 6 or anything like it's just six divided by or what's 6 divided by 4 1 point 5 so products favorite if something is products favored are KC is always going to be greater than one can you understand if we had a reaction that was exactly 50% exactly 50% right what would these two numbers be 5 and 5 what's 5 divided by 5 1 if a reaction if a reaction is 50% that means KC equals 1 another way of thinking about this probably a more effective way of thinking about it is in general what is KC always products over reactants if products are favored right that means the top is big and the bottom is small if you've got a big number on top and a small number on the bottom is your case devalue gonna be bigger small big it's gonna be great right right so let's say 2 over 1 that's gonna be greater than 1 would you agree right well what if reactants were favored what if reactants were favorite leader 1 over 2 is that KC gonna be greater than 1 or less than 1 it's gonna be less than 1 so this is what we're saying if the products are favored you can tell using the KC value because the KC value will be greater than 1 if a reaction if reactants favors the the reactants or the reaction favors the reactants your KC will be less than 1 it'll still be positive right you can't get a negative KC that's not possible what if there's a no reaction if you form zero products and everything stays as reactants zero zero divided by something as zero or very very very very small right now what if what if 99.99999% of it turns into products and 0.000001 percent turns into repairs stays as reactants yeah approaching infinity or we just say it's we say it's very large sometimes it's so large you cannot measure that value it's impossible to measure @kc that's a million divided by zero point zero zero zero zero zero zero zero zero one right if you mess up by half on the bottom your number doubles it's impossible to be able to measure that accurately we just say it's very large man this thing this thing reacts so much that you might as well not even think about is that okay are we good with that you know how much things how much stuff do you think we can squeeze into 40 seconds yes I'm gonna put the key to end me this kind of worksheet that you adjusted I'm gonna put it on Google classroom here in a little bit somebody

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