The reaction A2 + B ∆ A + AB has an equilibrium con-stant Kc = 2. The following pictures represent reaction mix- tures that contain A atoms (red), B atoms (blue), and A2 and AB molecules.

(a) Which reaction mixture is at equilibrium?

Video transcript

hi everyone for this problem. It reads the equilibrium constant of the following reaction is for which of the following diagrams depicts a reaction mixture of P two, R. Q. P R and P Q at equilibrium. Okay. And were given the key for the images or the diagram. So the question that we want to answer is which one represents it at equilibrium. And in order for us to solve this problem, we're going to need to compare K two Q. Where K is our equilibrium constant and Q is our reaction quotient. Let's recall that when Q is equal to K. That means the reaction is at equilibrium. If Q is greater than K then the reaction shifts in the reverse direction to reach equilibrium. And if Q is less than K then the reaction is going to shift right or in the forward direction to reach equilibrium. So we already know what the value of K. Is. That value is given in the problem. The value of K is equal to four. And let's just recall what the equilibrium constant represents. So K. Our equilibrium constant is equal to the concentration of products over the concentration of reactant since. And in the problem we were given the reaction and so if we write it in terms of what was given in the reaction, our products are P R times P Q. So our concentration of P R times the concentration of P Q. That's our products over the concentration of reactant since. Okay, so that's the concentration of P two times the concentration of our cue. So let's just write out what these represent. Alright, so P two is going to represent Pink Pink and we're writing this based off of what was given in the problem. RQ represents green, gray, P p R represents pink green and P Q represents pink. Great. Alright. So what we're going to do then now since the equilibrium expression or the expression for K and Q are the same but the values are going to be different. So we need to calculate the queue for the equilibrium, we need to calculate Q for each diagram and the one that's at equilibrium is going to be the one where Q is equal to K. So we know what K is. It's four. So we want to calculate Q and see which one is going to equal. Four. Alright so four let's go ahead and start off with a diagram. A. Okay so we know that the expression is the same. So our expression for Q. Let's just write that here. Our expression for Q is going to equal the concentration of products over the concentration of reactant and that's going to be the concentration of P. R times P Q over the concentration of P. Two times R. Q. So let's go ahead and calculate Q. For each diagram. Okay, four diagram A. Q is going to equal. So we have for times three over eight times 5. We're looking at the Diagram and counting how many we see for each one. Alright, so then that gives us a. Q equal to 0.3 for diagram A and this shows that Q is less than K. Okay, For diagram B, our cue is going to equal six times four over two times three, Which is equal to four. So here we see that Q is equal to K. And for diagram see our cue is going to equal eight times over two times two, which gives us 12. And for this one, Q is greater than K. So let's remember that equilibrium Q is equal to K and the one that represents that is diagram B. Okay, so that means our answer then for this is beach, this is the diagram that's going to depict a reaction mixture at equilibrium. That is it for this problem. I hope this was helpful.