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Consider the following reaction at a certain temperature$$\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}$$The mixing of 1 mole of $\mathrm{A}_{2}$ with 3 moles of $\mathrm{B}_{2}$ gives rise to $x$ mole of $\mathrm{AB}$ at equilibrium. The addition of 2 more moles of $\mathrm{A}_{2}$ produces another $x$ mole of $\mathrm{AB}$. What is the equilibrium constant for the reaction?

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$$K=4.0$$

Chemistry 102

Chapter 14

Chemical Equilibrium

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10:03

In thermodynamics, a state of thermodynamic equilibrium is a state in which a system is in thermal equilibrium with its surroundings. A system in thermodynamic equilibrium is in thermal equilibrium, mechanical equilibrium, electrical equilibrium, and chemical equilibrium. A system is in equilibrium when it is in thermal equilibrium with its surroundings.

00:54

In chemistry, chemical equilibrium (also known as dynamic equilibrium) is a state of chemical stability in which the concentrations of the chemical substances do not change in the course of time due to their reaction with each other in a closed system. Chemical equilibrium is an example of dynamic equilibrium, a thermodynamic concept.

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For the reaction a + 3b is…

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Given: $\mathrm{A}(\mathrm…

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Consider the following rea…

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Consider the reaction and …

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Consider the following equ…

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05:19

So for this problem we're looking at, what happens if we add a certain amount of moles of our reactant him? What? We haven't equilibrium it. But then we're going to add more moles to that equilibrium value, and that will give us a new equilibrium. But our main goal is to find the equilibrium constant or K four, this balanced chemical equation. So, first and foremost, we want to use the information that we've been given. We're gonna make it ice table. So for this, we know we have one mole of our first reacted a in three moles or second reacted b. We're also told that equilibrium we have X here for our problem for our product. And we know you start with zero product. So since we know that we end with X here, we know this is gonna be a positive X for a change. But based on squeaking on a tree, we would expect this toe on Lee B E minus X. But because of this story geometry, and since this is an X instead of a two x 22 divide by two, we're going to do the same thing here that gives us at equilibrium one minus. So for two three minus X over to within the X that we knew already. But this isn't the equilibrium value before we ADM or so we're going to do a another ice table. But this one is after the addition of two moles of our first reactant. So we're gonna use the's values as our initial values. But we are going to take into account that we have added two moles to the initial here, but everything else will stay the same for our change. We're going to do the same change that we saw in our first ice table. If they were looking at equilibrium. We know that this is just equivalent to three minus x. Same here because when you add the three minus X over two with a negative X over to it just gives you negative one X and then we have a positive two x here. So now what we want to dio is look at the equilibrium constants for each of these go up a little bit again. So the equilibrium constant here for the 1st 1 we're going to dio more products race to how many moles but then we're gonna do one minus. So for two and three minus thanks or two, there's no story Gallantry coefficient here. So we only are raising raising thes toe one, because only thing here isn't understood one. So then we can write another equilibrium, constant expression for our second nice table. And we have scroll down a little bit so that you can easily see we're working with two x three minus x three minus x. So since thes are both equilibrium constants for the same balanced equation at the same pressure and temperature, we can sit them equal to one another. Let's go ahead and do that. We have our first. They're gonna copy them down here. So it's easiest for us to see them clearly X and we're gonna set it equal to the ST one. And that's going to be a to eggs squared. But then a three minus x in the three minus X. I put parentheses here, but they should also be brackets. You write that one. Here we go. So now we want to simplify what we can so we can dio x squared its focus on the other side. First it was on the great size or just gonna leave the left side The same for right now we're gonna do this equals four x squared, and then we can see this is equivalent to three minus x squared. So let's go ahead and simplify this down again. If we were to calculate this out, we would be able to his output pull forth out X squared minus eight X plus 12. And that is equivalent to what we see on this other side. We must point out the bottom and then cancelled out what we could. They would get the falling. So then, if we simplify this further again, we can see that we're dealing with NATO. Six X plus nine equals a native eight X plus 12. Just gonna do this next part out so that we were sure we can get the right answer together. So nine equals negative two X plus 12. Subtract 12 from both sides. What we're going to see here Negative three won't do negative two X, which means X is equivalent to 2/3 or 1.5. And since we know that this whole thing is in one leader that here do you remember anything divided by itself. Is there anything divided by one is just itself. Which means since we only have one leader for the concentrations, we can just use the mole values. Because if you take the mole value divided by the leaders to find the concentration here, we would take the moles and divide by one. So it just be itself. So let's go ahead and plug it in. Two r K equation. How right it here again just so that we have it, since it's up a little higher on this screen for our final equilibrium. And if we go ahead e and substitute and we could do two times 1.5 raised to the power to but then three minus 1.5 square says we have to those if we go ahead and calculate this out. BC you get a value floor point. Oh,

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