The following picture represents the equilibrium state for the reaction 2 AB ∆ A2 + B2. Which rate constant is larger, kf or kr? Explain.

Video transcript

hi everyone This problem reads the equilibrium state for the reaction shown is depicted in the following image, which rate constant the rate constant of the reverse or the rate constant of the forward is bigger, explain. So we want to know which one is bigger and we have an image that we're going to reference here. Okay, so let's go ahead and assume that the green spheres is why? So we'll say the green spheres is why and the orange spheres is X. Alright. So if we define it this way, what we're going to get is Y two is going to equal three, X two equals 1 and X Y equals three. Alright, so our rate constant K. C. So K. C. This is equal to the concentration of products over the concentration of reactant since Alright, so if we rewrite this, it's going to be our product is X. Y. So we have our concentration of X. Y. And look we have two moles of this. So this becomes the exponent. Alright. And this is going to be over the concentration of reactant. We have to react ints we have X two. So the concentration of X two times the concentration of Y. Two. Alright, so let's go ahead and plug in the numbers. So for X Y we said there are three. So this becomes three and this three is squared and for X two there's one. Alright. And we're looking at these here, how we define them and for Y two there is three. Alright. So when we saw for this the value that we're going to get for KC. Is three. Alright. So recall that we have some things we're going to define here and that is if K is less than one then the reverse reaction is favored. And that means that the equilibrium constant of the reverse is bigger than the equilibrium constant of the forward. If K is greater than one, that means the forward reaction is favored. And this means that the rate constant of the forward is greater than the rate constant of the reverse and when K is equal to one this means the reaction is at equilibrium And that means the rate constant of the forward is equal to the rate constant of the reverse. Alright, so to answer this question, the answer it asks which rate constant is bigger. The rate constant of the forward is bigger than the rate constant of the reverse because the equilibrium constant of the reaction is greater than one. So the equilibrium constant we calculated is three and this is greater than one. So that means our final answer is the rate constant of the forward is bigger and we'll write because K Is greater than one. So this is our answer and the explanation and that is it for this problem. I hope this was helpful